Daily Papers

Cortical circuits exhibit intricate recurrent architectures that are remarkably similar across different brain areas. Such stereotyped structure suggests the existence of common computational principles. However, such principles have remained largely elusive. Inspired by gated-memory networks, namely long short-term memory networks (LSTMs), we introduce a recurrent neural network in which information is gated through inhibitory cells that are subtractive (subLSTM). We propose a natural mapping of subLSTMs onto known canonical excitatory-inhibitory cortical microcircuits. Our empirical evaluation across sequential image classification and language modelling tasks shows that subLSTM units can achieve similar performance to LSTM units. These results suggest that cortical circuits can be optimised to solve complex contextual problems and proposes a novel view on their computational function. Overall our work provides a step towards unifying recurrent networks as used in machine learning with their biological counterparts.

Accurate segmentation of cardiac chambers in echocardiography sequences is crucial for the quantitative analysis of cardiac function, aiding in clinical diagnosis and treatment. The imaging noise, artifacts, and the deformation and motion of the heart pose challenges to segmentation algorithms. While existing methods based on convolutional neural networks, Transformers, and space-time memory networks have improved segmentation accuracy, they often struggle with the trade-off between capturing long-range spatiotemporal dependencies and maintaining computational efficiency with fine-grained feature representation. In this paper, we introduce GDKVM, a novel architecture for echocardiography video segmentation. The model employs Linear Key-Value Association (LKVA) to effectively model inter-frame correlations, and introduces Gated Delta Rule (GDR) to efficiently store intermediate memory states. Key-Pixel Feature Fusion (KPFF) module is designed to integrate local and global features at multiple scales, enhancing robustness against boundary blurring and noise interference. We validated GDKVM on two mainstream echocardiography video datasets (CAMUS and EchoNet-Dynamic) and compared it with various state-of-the-art methods. Experimental results show that GDKVM outperforms existing approaches in terms of segmentation accuracy and robustness, while ensuring real-time performance. Code is available at https://github.com/wangrui2025/GDKVM.

This paper presents a novel multimodal framework to distinguish between different symptom classes of subjects in the schizophrenia spectrum and healthy controls using audio, video, and text modalities. We implemented Convolution Neural Network and Long Short Term Memory based unimodal models and experimented on various multimodal fusion approaches to come up with the proposed framework. We utilized a minimal Gated multimodal unit (mGMU) to obtain a bi-modal intermediate fusion of the features extracted from the input modalities before finally fusing the outputs of the bimodal fusions to perform subject-wise classifications. The use of mGMU units in the multimodal framework improved the performance in both weighted f1-score and weighted AUC-ROC scores.

Video Captioning and Summarization have become very popular in the recent years due to advancements in Sequence Modelling, with the resurgence of Long-Short Term Memory networks (LSTMs) and introduction of Gated Recurrent Units (GRUs). Existing architectures extract spatio-temporal features using CNNs and utilize either GRUs or LSTMs to model dependencies with soft attention layers. These attention layers do help in attending to the most prominent features and improve upon the recurrent units, however, these models suffer from the inherent drawbacks of the recurrent units themselves. The introduction of the Transformer model has driven the Sequence Modelling field into a new direction. In this project, we implement a Transformer-based model for Video captioning, utilizing 3D CNN architectures like C3D and Two-stream I3D for video extraction. We also apply certain dimensionality reduction techniques so as to keep the overall size of the model within limits. We finally present our results on the MSVD and ActivityNet datasets for Single and Dense video captioning tasks respectively.

Fast Weight Programmers (FWPs) encode temporal dependencies through dynamically updated parameters rather than recurrent hidden states. Quantum FWPs (QFWPs) extend this idea with variational quantum circuits (VQCs), but existing implementations rely on multi-qubit architectures that are difficult to scale on noisy intermediate-scale quantum (NISQ) devices and expensive to simulate classically. We propose gated QKAN-FWP, a fast-weight framework that integrates FWP with Quantum-inspired Kolmogorov-Arnold Network (QKAN) using single-qubit data re-uploading circuits as learnable nonlinear activation, known as DatA Re-Uploading ActivatioN (DARUAN). We further introduce a scalar-gated fast-weight update rule that stabilizes parameter evolution, supported by a theoretical analysis of its adaptive memory kernel, geometric boundedness, and parallelizable gradient paths. We evaluate the framework across time-series benchmarks, MiniGrid reinforcement learning, and highlight real-world solar cycle forecasting as our main practical result. In the long-horizon setting with 528-month input window and 132-month forecast horizon, our 12.5k-parameter model achieves lower scaled Mean Square Error (MSE), peak amplitude error, and peak timing error than a suite of classical recurrent baselines with up to 13x more parameters, including Long Short-Term Memory (LSTM) networks (25.9k-89.1k parameters), WaveNet-LSTM (167k), Vanilla recurrent neural network (11.5k), and a Modified Echo State Network (132k). To validate NISQ compatibility, we further deploy the trained fast programmer on IonQ and IBM Quantum processors, recovering forecasting accuracy within 0.1% relative MSE of the noiseless simulator at 1024 shots. These results position gated QKAN-FWP as a scalable, parameter-efficient, and NISQ-compatible approach to quantum-inspired sequence modeling.

This paper presents a comprehensive study on stock price prediction, leveragingadvanced machine learning (ML) and deep learning (DL) techniques to improve financial forecasting accuracy. The research evaluates the performance of various recurrent neural network (RNN) architectures, including Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRU), and attention-based models. These models are assessed for their ability to capture complex temporal dependencies inherent in stock market data. Our findings show that attention-based models outperform other architectures, achieving the highest accuracy by capturing both short and long-term dependencies. This study contributes valuable insights into AI-driven financial forecasting, offering practical guidance for developing more accurate and efficient trading systems.

Linear Transformers have gained attention as efficient alternatives to standard Transformers, but their performance in retrieval and long-context tasks has been limited. To address these limitations, recent work has explored two distinct mechanisms: gating for adaptive memory control and the delta update rule for precise memory modifications. We observe that these mechanisms are complementary: gating enables rapid memory erasure while the delta rule facilitates targeted updates. Building on this insight, we introduce the gated delta rule and develop a parallel training algorithm optimized for modern hardware. Our proposed architecture, Gated DeltaNet, consistently surpasses existing models like Mamba2 and DeltaNet across multiple benchmarks, including language modeling, common-sense reasoning, in-context retrieval, length extrapolation, and long-context understanding. We further enhance performance by developing hybrid architectures that combine Gated DeltaNet layers with sliding window attention or Mamba2 layers, achieving both improved training efficiency and superior task performance.

In this paper we compare different types of recurrent units in recurrent neural networks (RNNs). Especially, we focus on more sophisticated units that implement a gating mechanism, such as a long short-term memory (LSTM) unit and a recently proposed gated recurrent unit (GRU). We evaluate these recurrent units on the tasks of polyphonic music modeling and speech signal modeling. Our experiments revealed that these advanced recurrent units are indeed better than more traditional recurrent units such as tanh units. Also, we found GRU to be comparable to LSTM.

Proper weight initialization prior to training has historically been one of the key factors that helped kick off the deep learning revolution. Initialization is even more crucial in "reservoir computing", where the weights of a readout layer are learned linearly while the reservoir weights are fixed and largely determine the richness, stability and memory of the resulting dynamics. In the infinite-width limit it has been shown that meaningful initializations are those sitting at an effective critical point of the randomly initialized model. The phase transition is controlled by the weight variance g^2 and separates an ordered phase from a chaotic one where information progressively degrades. Here we derive a simple criterion to estimate the critical g_c for a broad class of recurrent architectures and we show that it closely tracks the gain at which a gated-RNN reservoir achieves peak performance on a chaotic forecasting task. Finally, we argue that our criterion can serve as a design principle for future initialization schemes.

We present a Transformer architecture for long-context language modeling that combines global attention with two biologically inspired components: chunked local attention and a gated FIFO memory mechanism. This unified attention block allows the model to efficiently handle both short-range and long-range dependencies without increasing attention cost quadratically. The memory module persistently stores past token representations using a gated update mechanism inspired by recurrent networks. Rotary positional encoding is applied per attention head to enable directionally disentangled, scale-invariant positional signals. The architecture is implemented entirely from scratch in PyTorch, with no reliance on high-level libraries, enabling transparent and modular experimentation. Our model offers a lightweight and extensible design for tasks such as dialogue modeling, code completion, and document understanding.

We propose a novel method called Long Expressive Memory (LEM) for learning long-term sequential dependencies. LEM is gradient-based, it can efficiently process sequential tasks with very long-term dependencies, and it is sufficiently expressive to be able to learn complicated input-output maps. To derive LEM, we consider a system of multiscale ordinary differential equations, as well as a suitable time-discretization of this system. For LEM, we derive rigorous bounds to show the mitigation of the exploding and vanishing gradients problem, a well-known challenge for gradient-based recurrent sequential learning methods. We also prove that LEM can approximate a large class of dynamical systems to high accuracy. Our empirical results, ranging from image and time-series classification through dynamical systems prediction to speech recognition and language modeling, demonstrate that LEM outperforms state-of-the-art recurrent neural networks, gated recurrent units, and long short-term memory models.

Deep learning is a group of exciting new technologies for neural networks. Through a combination of advanced training techniques and neural network architectural components, it is now possible to create neural networks that can handle tabular data, images, text, and audio as both input and output. Deep learning allows a neural network to learn hierarchies of information in a way that is like the function of the human brain. This course will introduce the student to classic neural network structures, Convolution Neural Networks (CNN), Long Short-Term Memory (LSTM), Gated Recurrent Neural Networks (GRU), General Adversarial Networks (GAN), and reinforcement learning. Application of these architectures to computer vision, time series, security, natural language processing (NLP), and data generation will be covered. High-Performance Computing (HPC) aspects will demonstrate how deep learning can be leveraged both on graphical processing units (GPUs), as well as grids. Focus is primarily upon the application of deep learning to problems, with some introduction to mathematical foundations. Readers will use the Python programming language to implement deep learning using Google TensorFlow and Keras. It is not necessary to know Python prior to this book; however, familiarity with at least one programming language is assumed.

Deep learning, and in particular Recurrent Neural Networks (RNN) have shown superior accuracy in a large variety of tasks including machine translation, language understanding, and movie frame generation. However, these deep learning approaches are very expensive in terms of computation. In most cases, Graphic Processing Units (GPUs) are in used for large scale implementations. Meanwhile, energy efficient RNN approaches are proposed for deploying solutions on special purpose hardware including Field Programming Gate Arrays (FPGAs) and mobile platforms. In this paper, we propose an effective quantization approach for Recurrent Neural Networks (RNN) techniques including Long Short Term Memory (LSTM), Gated Recurrent Units (GRU), and Convolutional Long Short Term Memory (ConvLSTM). We have implemented different quantization methods including Binary Connect {-1, 1}, Ternary Connect {-1, 0, 1}, and Quaternary Connect {-1, -0.5, 0.5, 1}. These proposed approaches are evaluated on different datasets for sentiment analysis on IMDB and video frame predictions on the moving MNIST dataset. The experimental results are compared against the full precision versions of the LSTM, GRU, and ConvLSTM. They show promising results for both sentiment analysis and video frame prediction.

This paper investigates the problem of forecasting multivariate aggregated human mobility while preserving the privacy of the individuals concerned. Differential privacy, a state-of-the-art formal notion, has been used as the privacy guarantee in two different and independent steps when training deep learning models. On one hand, we considered gradient perturbation, which uses the differentially private stochastic gradient descent algorithm to guarantee the privacy of each time series sample in the learning stage. On the other hand, we considered input perturbation, which adds differential privacy guarantees in each sample of the series before applying any learning. We compared four state-of-the-art recurrent neural networks: Long Short-Term Memory, Gated Recurrent Unit, and their Bidirectional architectures, i.e., Bidirectional-LSTM and Bidirectional-GRU. Extensive experiments were conducted with a real-world multivariate mobility dataset, which we published openly along with this paper. As shown in the results, differentially private deep learning models trained under gradient or input perturbation achieve nearly the same performance as non-private deep learning models, with loss in performance varying between 0.57% to 2.8%. The contribution of this paper is significant for those involved in urban planning and decision-making, providing a solution to the human mobility multivariate forecast problem through differentially private deep learning models.

The pervasive use of the Internet and social media introduces significant challenges to automated sentiment analysis, particularly for sarcastic expressions in user-generated content. Sarcasm conveys negative emotions through ostensibly positive or exaggerated language, complicating its detection within natural language processing tasks. To address this, we propose an innovative sarcasm detection model integrating Convolutional Neural Networks (CNN), Gated Recurrent Units (GRU), Long Short-Term Memory (LSTM), and Multi-Head Attention mechanisms. The CNN component captures local n-gram features, while GRU and LSTM layers model sequential dependencies and contextual information. Multi-Head Attention enhances the model's focus on relevant parts of the input, improving interpretability. Experiments on two sarcasm detection datasets, Headlines and Riloff, demonstrate that the model achieves an accuracy of 81.20% and an F1 score of 80.77% on Headlines, and an accuracy of 79.72% with an F1 score of 61.39% on Riloff, outperforming traditional models. These results validate the effectiveness of our hybrid approach for sarcasm detection in social media texts.

As the use of Lithium-ion batteries continues to grow, it becomes increasingly important to be able to predict their remaining useful life. This work aims to compare the relative performance of different machine learning algorithms, both traditional machine learning and deep learning, in order to determine the best-performing algorithms for battery cycle life prediction based on minimal data. We investigated 14 different machine learning models that were fed handcrafted features based on statistical data and split into 3 feature groups for testing. For deep learning models, we tested a variety of neural network models including different configurations of standard Recurrent Neural Networks, Gated Recurrent Units, and Long Short Term Memory with and without attention mechanism. Deep learning models were fed multivariate time series signals based on the raw data for each battery across the first 100 cycles. Our experiments revealed that the machine learning algorithms on handcrafted features performed particularly well, resulting in 10-20% average mean absolute percentage error. The best-performing algorithm was the Random Forest Regressor, which gave a minimum 9.8% mean absolute percentage error. Traditional machine learning models excelled due to their capability to comprehend general data set trends. In comparison, deep learning models were observed to perform particularly poorly on raw, limited data. Algorithms like GRU and RNNs that focused on capturing medium-range data dependencies were less adept at recognizing the gradual, slow trends critical for this task. Our investigation reveals that implementing machine learning models with hand-crafted features proves to be more effective than advanced deep learning models for predicting the remaining useful Lithium-ion battery life with limited data availability.

The objective of continual learning (CL) is to learn tasks sequentially without retraining on earlier tasks. However, when subjected to CL, traditional neural networks exhibit catastrophic forgetting and limited generalization. To overcome these problems, we introduce a novel method called 'Gate and Obstruct Network' (GateON). GateON combines learnable gating of activity and online estimation of parameter relevance to safeguard crucial knowledge from being overwritten. Our method generates partially overlapping pathways between tasks which permits forward and backward transfer during sequential learning. GateON addresses the issue of network saturation after parameter fixation by a re-activation mechanism of fixed neurons, enabling large-scale continual learning. GateON is implemented on a wide range of networks (fully-connected, CNN, Transformers), has low computational complexity, effectively learns up to 100 MNIST learning tasks, and achieves top-tier results for pre-trained BERT in CL-based NLP tasks.

Mobile and embedded machine learning developers frequently have to compromise between two inferior on-device deployment strategies: sacrifice accuracy and aggressively shrink their models to run on dedicated low-power cores; or sacrifice battery by running larger models on more powerful compute cores such as neural processing units or the main application processor. In this paper, we propose a novel Gated Compression layer that can be applied to transform existing neural network architectures into Gated Neural Networks. Gated Neural Networks have multiple properties that excel for on-device use cases that help significantly reduce power, boost accuracy, and take advantage of heterogeneous compute cores. We provide results across five public image and audio datasets that demonstrate the proposed Gated Compression layer effectively stops up to 96% of negative samples, compresses 97% of positive samples, while maintaining or improving model accuracy.

The Transformer architecture, underpinned by the self-attention mechanism, has become the de facto standard for sequence modeling tasks. However, its core computational primitive scales quadratically with sequence length (O(N^2)), creating a significant bottleneck for processing long contexts. In this paper, we propose the Gated Associative Memory (GAM) network, a novel, fully parallel architecture for sequence modeling that exhibits linear complexity (O(N)) with respect to sequence length. The GAM block replaces the self-attention layer with two parallel pathways: a causal convolution to efficiently capture local, position-dependent context, and a parallel associative memory retrieval mechanism to model global, content-based patterns. These pathways are dynamically fused using a gating mechanism, allowing the model to flexibly combine local and global information for each token. We implement GAM from scratch and conduct a rigorous comparative analysis against a standard Transformer model and a modern linear-time baseline (Mamba) on the WikiText-2 benchmark, as well as against the Transformer on the TinyStories dataset. Our experiments demonstrate that GAM is consistently faster, outperforming both baselines on training speed, and achieves a superior or competitive final validation perplexity across all datasets, establishing it as a promising and efficient alternative for sequence modeling.

Linear attention replaces the unbounded cache of softmax attention with a fixed-size recurrent state, reducing sequence mixing to linear time and decoding to constant memory. The hard part is not just what to forget, but how to edit this compressed memory without scrambling existing associations. Delta-rule models subtract the current read before writing a new value, and Kimi Delta Attention (KDA) sharpens forgetting with channel-wise decay. But the active edit still uses a single scalar gate to control two different things: how much old content to erase on the key side and how much new content to commit on the value side. We introduce Gated DeltaNet-2, which generalizes both Gated DeltaNet and KDA by inheriting adaptive forgetting and channel-wise decay while addressing their shared limitation, the scalar tie between erasing and writing. Gated Delta Rule-2 separates these roles with a channel-wise erase gate b_t and a channel-wise write gate w_t, reducing to KDA when both gates collapse to the same scalar and to Gated DeltaNet when the decay also collapses. We derive a fast-weight update view, a chunkwise WY algorithm with channel-wise decay absorbed into asymmetric erase factors, and a gate-aware backward pass that preserves efficient parallel training. At 1.3B parameters trained on 100B FineWeb-Edu tokens, Gated DeltaNet-2 achieves the strongest overall results among Mamba-2, Gated DeltaNet, KDA, and Mamba-3 variants across language modeling, commonsense reasoning, and retrieval. Its advantage is most pronounced on long-context RULER needle-in-a-haystack benchmarks, where it improves the evaluated multi-key retrieval setting and remains strong in both recurrent and hybrid settings. Code is available at https://github.com/NVlabs/GatedDeltaNet-2.

Linear attention Transformers and their gated variants, celebrated for enabling parallel training and efficient recurrent inference, still fall short in recall-intensive tasks compared to traditional Transformers and demand significant resources for training from scratch. This paper introduces Gated Slot Attention (GSA), which enhances Attention with Bounded-memory-Control (ABC) by incorporating a gating mechanism inspired by Gated Linear Attention (GLA). Essentially, GSA comprises a two-layer GLA linked via softmax, utilizing context-aware memory reading and adaptive forgetting to improve memory capacity while maintaining compact recurrent state size. This design greatly enhances both training and inference efficiency through GLA's hardware-efficient training algorithm and reduced state size. Additionally, retaining the softmax operation is particularly beneficial in "finetuning pretrained Transformers to RNNs" (T2R) settings, reducing the need for extensive training from scratch. Extensive experiments confirm GSA's superior performance in scenarios requiring in-context recall and in T2R settings.

Neural Memory Networks (NMNs) have received increased attention in recent years compared to deep architectures that use a constrained memory. Despite their new appeal, the success of NMNs hinges on the ability of the gradient-based optimiser to perform incremental training of the NMN controllers, determining how to leverage their high capacity for knowledge retrieval. This means that while excellent performance can be achieved when the training data is consistent and well distributed, rare data samples are hard to learn from as the controllers fail to incorporate them effectively during model training. Drawing inspiration from the human cognition process, in particular the utilisation of neuromodulators in the human brain, we propose to decouple the learning process of the NMN controllers to allow them to achieve flexible, rapid adaptation in the presence of new information. This trait is highly beneficial for meta-learning tasks where the memory controllers must quickly grasp abstract concepts in the target domain, and adapt stored knowledge. This allows the NMN controllers to quickly determine which memories are to be retained and which are to be erased, and swiftly adapt their strategy to the new task at hand. Through both quantitative and qualitative evaluations on multiple public benchmarks, including classification and regression tasks, we demonstrate the utility of the proposed approach. Our evaluations not only highlight the ability of the proposed NMN architecture to outperform the current state-of-the-art methods, but also provide insights on how the proposed augmentations help achieve such superior results. In addition, we demonstrate the practical implications of the proposed learning strategy, where the feedback path can be shared among multiple neural memory networks as a mechanism for knowledge sharing.

In this paper, we introduce the gated perceptron, an enhancement of the conventional perceptron, which incorporates an additional input computed as the product of the existing inputs. This allows the perceptron to capture non-linear interactions between features, significantly improving its ability to classify and regress on complex datasets. We explore its application in both linear and non-linear regression tasks using the Iris dataset, as well as binary and multi-class classification problems, including the PIMA Indian dataset and Breast Cancer Wisconsin dataset. Our results demonstrate that the gated perceptron can generate more distinct decision regions compared to traditional perceptrons, enhancing its classification capabilities, particularly in handling non-linear data. Performance comparisons show that the gated perceptron competes with state-of-the-art classifiers while maintaining a simple architecture.

We describe a new class of learning models called memory networks. Memory networks reason with inference components combined with a long-term memory component; they learn how to use these jointly. The long-term memory can be read and written to, with the goal of using it for prediction. We investigate these models in the context of question answering (QA) where the long-term memory effectively acts as a (dynamic) knowledge base, and the output is a textual response. We evaluate them on a large-scale QA task, and a smaller, but more complex, toy task generated from a simulated world. In the latter, we show the reasoning power of such models by chaining multiple supporting sentences to answer questions that require understanding the intension of verbs.

Modern autoregressive models rely on attention, yet the Softmax full attention in Transformers scales quadratically with sequence length. Sliding Window Attention (SWA) achieves linear-time encoding/decoding by constraining the attention pattern, but under an Associative Memory interpretation, its difference-style update renders the training objective effectively unbounded. In contrast, Softmax attention normalizes updates, leading to memory shrinkage and gradient vanishing. We propose GatedFWA: a Memory-Gated (Flash) Windowed Attention mechanism that preserves SWAs efficiency while stabilizing memory updates and making gradient flow controllable. In essence, GatedFWA accumulate a per-token/head gate into a decay bias added to the attention logits, acting as a learnable contraction in the memory recurrence. We implement a fused one-pass gate preprocessing and a FlashAttention-compatible kernel that injects the gate under a sliding mask, ensuring I/O efficiency and numerical stability. On language modelling benchmarks, GatedFWA delivers competitive throughput with negligible overhead and better use of global context, and it integrates cleanly with token compression/selection methods such as NSA and generalizes to various autoregressive domains.

Transformers have surpassed RNNs in popularity due to their superior abilities in parallel training and long-term dependency modeling. Recently, there has been a renewed interest in using linear RNNs for efficient sequence modeling. These linear RNNs often employ gating mechanisms in the output of the linear recurrence layer while ignoring the significance of using forget gates within the recurrence. In this paper, we propose a gated linear RNN model dubbed Hierarchically Gated Recurrent Neural Network (HGRN), which includes forget gates that are lower bounded by a learnable value. The lower bound increases monotonically when moving up layers. This allows the upper layers to model long-term dependencies and the lower layers to model more local, short-term dependencies. Experiments on language modeling, image classification, and long-range arena benchmarks showcase the efficiency and effectiveness of our proposed model. The source code is available at https://github.com/OpenNLPLab/HGRN.

Designing architectures for deep neural networks requires expert knowledge and substantial computation time. We propose a technique to accelerate architecture selection by learning an auxiliary HyperNet that generates the weights of a main model conditioned on that model's architecture. By comparing the relative validation performance of networks with HyperNet-generated weights, we can effectively search over a wide range of architectures at the cost of a single training run. To facilitate this search, we develop a flexible mechanism based on memory read-writes that allows us to define a wide range of network connectivity patterns, with ResNet, DenseNet, and FractalNet blocks as special cases. We validate our method (SMASH) on CIFAR-10 and CIFAR-100, STL-10, ModelNet10, and Imagenet32x32, achieving competitive performance with similarly-sized hand-designed networks. Our code is available at https://github.com/ajbrock/SMASH

Kolmogorov-Arnold Networks (KANs) face a fundamental memory wall: their learned basis functions create parameter counts that impose extreme bandwidth demands, hindering deployment in memory-constrained environments. We show that Vision KANs exhibit a holographic topology, where information is distributed across the interference of splines rather than localized to specific edges. Consequently, traditional pruning fails (10% sparsity degrades mAP from 85.23% to 45%, a sim40-point drop). To address this, we present SHARe-KAN, a framework utilizing Gain-Shape-Bias Vector Quantization to exploit functional redundancy while preserving the dense topology. Coupled with LUTHAM, a hardware-aware compiler with static memory planning, we achieve 88times runtime memory reduction (1.13 GB to 12.91 MB) and match uncompressed baseline accuracy on PASCAL VOC. Profiling on NVIDIA Ampere architecture confirms >90% L2 cache residency, demonstrating that the workload is decoupled from DRAM bandwidth constraints inherent to spline-based architectures.

Recent advances in language modeling have demonstrated the effectiveness of State Space Models (SSMs) for efficient sequence modeling. While hybrid architectures such as Samba and the decoder-decoder architecture, YOCO, have shown promising performance gains over Transformers, prior works have not investigated the efficiency potential of representation sharing between SSM layers. In this paper, we introduce the Gated Memory Unit (GMU), a simple yet effective mechanism for efficient memory sharing across layers. We apply it to create SambaY, a decoder-hybrid-decoder architecture that incorporates GMUs in the cross-decoder to share memory readout states from a Samba-based self-decoder. SambaY significantly enhances decoding efficiency, preserves linear pre-filling time complexity, and boosts long-context performance, all while eliminating the need for explicit positional encoding. Through extensive scaling experiments, we demonstrate that our model exhibits a significantly lower irreducible loss compared to a strong YOCO baseline, indicating superior performance scalability under large-scale compute regimes. Our largest model enhanced with Differential Attention, Phi4-mini-Flash-Reasoning, achieves significantly better performance than Phi4-mini-Reasoning on reasoning tasks such as Math500, AIME24/25, and GPQA Diamond without any reinforcement learning, while delivering up to 10x higher decoding throughput on 2K-length prompts with 32K generation length under the vLLM inference framework. We release our training codebase on open-source data at https://github.com/microsoft/ArchScale.

Large language models (LLMs) have demonstrated remarkable success across diverse artificial intelligence tasks, driven by scaling laws that correlate model size and training data with performance improvements. However, this scaling paradigm incurs substantial memory overhead, creating significant challenges for both training and inference. While existing research has primarily addressed parameter and optimizer state memory reduction, activation memory-particularly from feed-forward networks (FFNs)-has become the critical bottleneck, especially when FlashAttention is implemented. In this work, we conduct a detailed memory profiling of LLMs and identify FFN activations as the predominant source to activation memory overhead. Motivated by this, we introduce Mixture-of-Channels (MoC), a novel FFN architecture that selectively activates only the Top-K most relevant channels per token determined by SwiGLU's native gating mechanism. MoC substantially reduces activation memory during pre-training and improves inference efficiency by reducing memory access through partial weight loading into GPU SRAM. Extensive experiments validate that MoC delivers significant memory savings and throughput gains while maintaining competitive model performance.

Modern neural networks demonstrate state-of-the-art performance on numerous existing benchmarks; however, their high computational requirements and energy consumption prompt researchers to seek more efficient solutions for real-world deployment. Logic gate networks (LGNs) learns a large network of logic gates for efficient image classification. However, learning a network that can solve a simple problem like CIFAR-10 can take days to weeks to train. Even then, almost half of the network remains unused, causing a discretization gap. This discretization gap hinders real-world deployment of LGNs, as the performance drop between training and inference negatively impacts accuracy. We inject Gumbel noise with a straight-through estimator during training to significantly speed up training, improve neuron utilization, and decrease the discretization gap. We theoretically show that this results from implicit Hessian regularization, which improves the convergence properties of LGNs. We train networks 4.5 times faster in wall-clock time, reduce the discretization gap by 98%, and reduce the number of unused gates by 100%.

A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used in deep learning. On the associative memory side of this duality, a family of models that smoothly interpolates between two limiting cases can be constructed. One limit is referred to as the feature-matching mode of pattern recognition, and the other one as the prototype regime. On the deep learning side of the duality, this family corresponds to feedforward neural networks with one hidden layer and various activation functions, which transmit the activities of the visible neurons to the hidden layer. This family of activation functions includes logistics, rectified linear units, and rectified polynomials of higher degrees. The proposed duality makes it possible to apply energy-based intuition from associative memory to analyze computational properties of neural networks with unusual activation functions - the higher rectified polynomials which until now have not been used in deep learning. The utility of the dense memories is illustrated for two test cases: the logical gate XOR and the recognition of handwritten digits from the MNIST data set.

Large Language Models (LLMs) currently struggle to sequentially add new memories and integrate new knowledge. These limitations contrast with the human ability to continuously learn from new experiences and acquire knowledge throughout life. Most existing approaches add memories either through large context windows or external memory buffers (e.g., Retrieval-Augmented Generation), and studies on knowledge injection rarely test scenarios resembling everyday life events. In this work, we introduce a continual learning framework, Memory Embedded in Gated LLMs (MEGa), which injects event memories directly into the weights of LLMs. Each memory is stored in a dedicated set of gated low-rank weights. During inference, a gating mechanism activates relevant memory weights by matching query embeddings to stored memory embeddings. This enables the model to both recall entire memories and answer related questions. On two datasets - fictional characters and Wikipedia events - MEGa outperforms baseline approaches in mitigating catastrophic forgetting. Our model draws inspiration from the complementary memory system of the human brain.

Algorithm learning is a core problem in artificial intelligence with significant implications on automation level that can be achieved by machines. Recently deep learning methods are emerging for synthesizing an algorithm from its input-output examples, the most successful being the Neural GPU, capable of learning multiplication. We present several improvements to the Neural GPU that substantially reduces training time and improves generalization. We introduce a new technique - hard nonlinearities with saturation costs- that has general applicability. We also introduce a technique of diagonal gates that can be applied to active-memory models. The proposed architecture is the first capable of learning decimal multiplication end-to-end.

The brain is a noisy system subject to energy constraints. These facts are rarely taken into account when modelling artificial neural networks. In this paper, we are interested in demonstrating that those factors can actually lead to the appearance of robust associative memories. We first propose a simplified model of noise in the brain, taking into account synaptic noise and interference from neurons external to the network. When coarsely quantized, we show that this noise can be reduced to insertions and erasures. We take a neural network with recurrent modifiable connections, and subject it to noisy external inputs. We introduce an energy usage limitation principle in the network as well as consolidated Hebbian learning, resulting in an incremental processing of inputs. We show that the connections naturally formed correspond to state-of-the-art binary sparse associative memories.

Differentiable logic gate networks (DLGNs) exhibit extraordinary efficiency at inference while sustaining competitive accuracy. But vanishing gradients, discretization errors, and high training cost impede scaling these networks. Even with dedicated parameter initialization schemes from subsequent works, increasing depth still harms accuracy. We show that the root cause of these issues lies in the underlying parametrization of logic gate neurons themselves. To overcome this issue, we propose a reparametrization that also shrinks the parameter size logarithmically in the number of inputs per gate. For binary inputs, this already reduces the model size by 4x, speeds up the backward pass by up to 1.86x, and converges in 8.5x fewer training steps. On top of that, we show that the accuracy on CIFAR-100 remains stable and sometimes superior to the original parametrization.

We introduce Gated-SwinRMT, a family of hybrid vision transformers that combine the shifted-window attention of the Swin Transformer with the Manhattan-distance spatial decay of Retentive Networks (RMT), augmented by input-dependent gating. Self-attention is decomposed into consecutive width-wise and height-wise retention passes within each shifted window, where per-head exponential decay masks provide a two-dimensional locality prior without learned positional biases. Two variants are proposed. Gated-SwinRMT-SWAT substitutes softmax with sigmoid activation, implements balanced ALiBi slopes with multiplicative post-activation spatial decay, and gates the value projection via SwiGLU; the Normalized output implicitly suppresses uninformative attention scores. Gated-SwinRMT-Retention retains softmax-normalized retention with an additive log-space decay bias and incorporates an explicit G1 sigmoid gate -- projected from the block input and applied after local context enhancement (LCE) but prior to the output projection~W_O -- to alleviate the low-rank W_V !cdot! W_O bottleneck and enable input-dependent suppression of attended outputs. We assess both variants on Mini-ImageNet (224{times}224, 100 classes) and CIFAR-10 (32{times}32, 10 classes) under identical training protocols, utilizing a single GPU due to resource limitations. At {approx}77--79\,M parameters, Gated-SwinRMT-SWAT achieves 80.22% and Gated-SwinRMT-Retention 78.20% top-1 test accuracy on Mini-ImageNet, compared with 73.74% for the RMT baseline. On CIFAR-10 -- where small feature maps cause the adaptive windowing mechanism to collapse attention to global scope -- the accuracy advantage compresses from +6.48\,pp to +0.56\,pp.

Recent studies introduce conditional memory modules that decouple knowledge storage from neural computation, enabling more direct knowledge access. Compared to MoE, which relies on dynamic computation paths, explicit lookup provides a more efficient knowledge retrieval mechanism. However, these approaches still depend on learned memory embeddings, requiring additional training and limiting flexibility. To address this, we propose N-gram Memory (NGM), a training-free, plug-and-play module composed of a Causal N-Gram Encoder and a Cosine-Gated Memory Injector. The Causal N-Gram Encoder directly averages the pretrained token embeddings of the backbone model to construct N-gram representations, thereby eliminating the need to train separate N-gram embeddings from scratch. This design requires neither an additional memory table nor a retrieval pipeline. The Cosine-Gated Memory Injector then uses a non-parametric cosine gate with ReLU to modulate the retrieved embeddings into the contextual representations. We evaluate NGM on the Qwen3 series from 0.6B to 14B across eight benchmarks. NGM improves average performance by 0.5 to 1.2 points, with particularly clear gains on code generation and knowledge-intensive tasks (e.g., +3.0 on LiveCodeBench and +3.03 on GPQA for Qwen3-14B). Moreover, NGM also improves performance in multimodal benchmarks (e.g., MMStar +1.53 on Qwen3-VL-2B).

Neural algorithmic reasoning is an emerging research direction that endows neural networks with the ability to mimic algorithmic executions step-by-step. A common paradigm in existing designs involves the use of historical embeddings in predicting the results of future execution steps. Our observation in this work is that such historical dependence intrinsically contradicts the Markov nature of algorithmic reasoning tasks. Based on this motivation, we present our ForgetNet, which does not use historical embeddings and thus is consistent with the Markov nature of the tasks. To address challenges in training ForgetNet at early stages, we further introduce G-ForgetNet, which uses a gating mechanism to allow for the selective integration of historical embeddings. Such an enhanced capability provides valuable computational pathways during the model's early training phase. Our extensive experiments, based on the CLRS-30 algorithmic reasoning benchmark, demonstrate that both ForgetNet and G-ForgetNet achieve better generalization capability than existing methods. Furthermore, we investigate the behavior of the gating mechanism, highlighting its degree of alignment with our intuitions and its effectiveness for robust performance.

Long-sequence modeling faces a fundamental trade-off between the efficiency of compressive fixed-size memory in RNN-like models and the fidelity of lossless growing memory in attention-based Transformers. Inspired by the Multi-Store Model in cognitive science, we introduce a memory framework of artificial neural networks. Our method maintains a sliding window of the Transformer's KV cache as lossless short-term memory, while a learnable module termed Artificial Hippocampus Network (AHN) recurrently compresses out-of-window information into a fixed-size compact long-term memory. To validate this framework, we instantiate AHNs using modern RNN-like architectures, including Mamba2, DeltaNet, and Gated DeltaNet. Extensive experiments on long-context benchmarks LV-Eval and InfiniteBench demonstrate that AHN-augmented models consistently outperform sliding window baselines and achieve performance comparable or even superior to full-attention models, while substantially reducing computational and memory requirements. For instance, augmenting the Qwen2.5-3B-Instruct with AHNs reduces inference FLOPs by 40.5% and memory cache by 74.0%, while improving its average score on LV-Eval (128k sequence length) from 4.41 to 5.88. Code is available at: https://github.com/ByteDance-Seed/AHN.

This work introduces a new computational theory of mind grounded in set theory and hyperdimensional computing. Whereas traditional neural networks rely on continuous weights and matrix multiplication, this framework works with sparse binary data. It represents information as discrete sets, directly modeling biological neural population codes. I demonstrate that associative memory emerges naturally from network topologies featuring a combinatorially expanded hidden layer. Learning is driven by topological plasticity rather than scalar weight adjustments. This architecture unifies auto-associative and hetero-associative learning under a single core algorithm: information retrieval via subset pattern matching and exact nearest-neighbor search. Operating with constant-time complexity, these mechanisms bridge perceptual data (sparse distributed representations) and symbols (sparse holographic representations) without continuous bottlenecks. Mapping this framework to neuroanatomy, I propose that both the cerebellum and the neocortex implement variants of this algorithm, making subset pattern matching the fundamental engine of cognition. Because it relies on discrete logic rather than matrix arithmetic, this algorithm translates directly into in-memory hardware. This opens a new route toward synthetic intelligence with human-level energy efficiency.

State space models have shown to be effective at modeling long range dependencies, specially on sequence classification tasks. In this work we focus on autoregressive sequence modeling over English books, Github source code and ArXiv mathematics articles. Based on recent developments around the effectiveness of gated activation functions, we propose a new layer named Gated State Space (GSS) and show that it trains significantly faster than the diagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several well-tuned Transformer-based baselines and exhibits zero-shot generalization to longer inputs while being straightforward to implement. Finally, we show that leveraging self-attention to model local dependencies improves the performance of GSS even further.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

Differentiable Logic Gate Networks (DLGNs) are a very fast and energy-efficient alternative to conventional feed-forward networks. With learnable combinations of logical gates, DLGNs enable fast inference by hardware-friendly execution. Since the concept of DLGNs has only recently gained attention, these networks are still in their developmental infancy, including the design and scalability of their output layer. To date, this architecture has primarily been tested on datasets with up to ten classes. This work examines the behavior of DLGNs on large multi-class datasets. We investigate its general expressiveness, its scalability, and evaluate alternative output strategies. Using both synthetic and real-world datasets, we provide key insights into the importance of temperature tuning and its impact on output layer performance. We evaluate conditions under which the Group-Sum layer performs well and how it can be applied to large-scale classification of up to 2000 classes.

Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is previous work on Graph Neural Networks (Scarselli et al., 2009), which we modify to use gated recurrent units and modern optimization techniques and then extend to output sequences. The result is a flexible and broadly useful class of neural network models that has favorable inductive biases relative to purely sequence-based models (e.g., LSTMs) when the problem is graph-structured. We demonstrate the capabilities on some simple AI (bAbI) and graph algorithm learning tasks. We then show it achieves state-of-the-art performance on a problem from program verification, in which subgraphs need to be matched to abstract data structures.

Due to the recurrent structure of RNN, the long information propagation path poses limitations in capturing long-term dependencies, gradient explosion/vanishing issues, and inefficient sequential execution. Based on this, we propose a novel paradigm called Parallel Gated Network (PGN) as the new successor to RNN. PGN directly captures information from previous time steps through the designed Historical Information Extraction (HIE) layer and leverages gated mechanisms to select and fuse it with the current time step information. This reduces the information propagation path to O(1), effectively addressing the limitations of RNN. To enhance PGN's performance in long-range time series forecasting tasks, we propose a novel temporal modeling framework called Temporal PGN (TPGN). TPGN incorporates two branches to comprehensively capture the semantic information of time series. One branch utilizes PGN to capture long-term periodic patterns while preserving their local characteristics. The other branch employs patches to capture short-term information and aggregate the global representation of the series. TPGN achieves a theoretical complexity of O(L), ensuring efficiency in its operations. Experimental results on five benchmark datasets demonstrate the state-of-the-art (SOTA) performance and high efficiency of TPGN, further confirming the effectiveness of PGN as the new successor to RNN in long-range time series forecasting. The code is available in this repository: https://github.com/Water2sea/TPGN.

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

Memory-based neural networks model temporal data by leveraging an ability to remember information for long periods. It is unclear, however, whether they also have an ability to perform complex relational reasoning with the information they remember. Here, we first confirm our intuitions that standard memory architectures may struggle at tasks that heavily involve an understanding of the ways in which entities are connected -- i.e., tasks involving relational reasoning. We then improve upon these deficits by using a new memory module -- a Relational Memory Core (RMC) -- which employs multi-head dot product attention to allow memories to interact. Finally, we test the RMC on a suite of tasks that may profit from more capable relational reasoning across sequential information, and show large gains in RL domains (e.g. Mini PacMan), program evaluation, and language modeling, achieving state-of-the-art results on the WikiText-103, Project Gutenberg, and GigaWord datasets.

Attention-free language models that combine gating and convolutions are growing in popularity due to their efficiency and increasingly competitive performance. To better understand these architectures, we pretrain a suite of 17 attention and "gated-convolution" language models, finding that SoTA gated-convolution architectures still underperform attention by up to 2.1 perplexity points on the Pile. In fine-grained analysis, we find 82% of the gap is explained by each model's ability to recall information that is previously mentioned in-context, e.g. "Hakuna Matata means no worries Hakuna Matata it means no" rightarrow "??". On this task, termed "associative recall", we find that attention outperforms gated-convolutions by a large margin: a 70M parameter attention model outperforms a 1.4 billion parameter gated-convolution model on associative recall. This is surprising because prior work shows gated convolutions can perfectly solve synthetic tests for AR capability. To close the gap between synthetics and real language, we develop a new formalization of the task called multi-query associative recall (MQAR) that better reflects actual language. We perform an empirical and theoretical study of MQAR that elucidates differences in the parameter-efficiency of attention and gated-convolution recall. Informed by our analysis, we evaluate simple convolution-attention hybrids and show that hybrids with input-dependent sparse attention patterns can close 97.4% of the gap to attention, while maintaining sub-quadratic scaling. Our code is accessible at: https://github.com/HazyResearch/zoology.

We describe the architecture and ablations of Qwen3.8-Flash-Next, a sparse mixture-of-experts model with 125B parameters, 6B activated per token, and additional 51B parameters of n-gram embedding tables held off the accelerator. On fourteen pre-training benchmarks the model leads the 397B-A17B predecessor on eight and trails it on the rest by at most 2.6 points, at 1/3 the activated parameters, 1/3 the training tokens, and roughly 1/9 the training FLOPs. Token mixing uses a layer-wise hybrid of Gated DeltaNet (GDN) and global attention, with one full-attention layer in every four; at continued-pretraining time those full-attention layers are replaced by Qwen Sparse Attention (QSA), which scores context at micro-block granularity with a compressed lightweight indexer. The residual stream is widened to four branches and read through an elementwise gate, a design we call the Gated Residual (GR). Capacity is added outside the backbone by a single n-gram embedding layer whose tables are prefetched from host memory. We evaluate every candidate change along three axes: loss together with downstream benchmarks; the cost of the change in training, prefill and decode; and its effect on the optimal hyperparameters and training stability. Loss and downstream accuracy do not always move together: enlarging the n-gram vocabulary lowers loss monotonically while downstream accuracy saturates. The architecture and the Muon optimizer together shift the optimal learning rate and batch size upwards, render batch-size warmup unnecessary, and substantially improve stability under stress tests. Loss, benchmarks, efficiency and stability form one design problem. Solved jointly, they yield a recipe that is simultaneously more efficient, more capable and more stable.

Lookup-based memory has been a promising way to scale the parameters of large language models (LLMs). It retrieves learned representations of local token patterns, such as n-grams, instead of reconstructing them through successive layers of computation. However, existing designs such as Engram treat each retrieved embedding as a monolithic unit. Each embedding is stored in its own hashed slot and modulated by a single scalar gate. As a result, polysemous patterns cannot selectively read out the components of their memory that are relevant to the context. Moreover, parameters are shared only through hash collisions, which are largely unrelated to semantics. We propose FactorEngram, a factorized n-gram memory with basis-level contextual gating. FactorEngram retrieves sparsity-regularized coefficients over a dictionary of basis vectors shared across patterns, so related patterns can reuse common components. The same dictionary is also used for gating. The backbone hidden state is scored against each basis vector to gate the corresponding coefficient before reconstruction, which lets the context modulate each memory component individually. FactorEngram also covers both individual tokens and multi-token n-grams, and we systematically study where the memory branch should be inserted. On 340M- and 1B-parameter Transformer backbones, FactorEngram improves language modeling and downstream task performance. Ablation studies confirm the contribution of each component and identify insertion before the attention sublayer in the middle layers as an effective configuration.

While differentiable logic gates have shown promise in feedforward networks, their application to sequential modeling remains unexplored. This paper presents the first implementation of Recurrent Deep Differentiable Logic Gate Networks (RDDLGN), combining Boolean operations with recurrent architectures for sequence-to-sequence learning. Evaluated on WMT'14 English-German translation, RDDLGN achieves 5.00 BLEU and 30.9\% accuracy during training, approaching GRU performance (5.41 BLEU) and graceful degradation (4.39 BLEU) during inference. This work establishes recurrent logic-based neural computation as viable, opening research directions for FPGA acceleration in sequential modeling and other recursive network architectures.

Memory is fundamental to intelligence, enabling learning, reasoning, and adaptability across biological and artificial systems. While Transformer architectures excel at sequence modeling, they face critical limitations in long-range context retention, continual learning, and knowledge integration. This review presents a unified framework bridging neuroscience principles, including dynamic multi-timescale memory, selective attention, and consolidation, with engineering advances in Memory-Augmented Transformers. We organize recent progress through three taxonomic dimensions: functional objectives (context extension, reasoning, knowledge integration, adaptation), memory representations (parameter-encoded, state-based, explicit, hybrid), and integration mechanisms (attention fusion, gated control, associative retrieval). Our analysis of core memory operations (reading, writing, forgetting, and capacity management) reveals a shift from static caches toward adaptive, test-time learning systems. We identify persistent challenges in scalability and interference, alongside emerging solutions including hierarchical buffering and surprise-gated updates. This synthesis provides a roadmap toward cognitively-inspired, lifelong-learning Transformer architectures.

Learning arguably involves the discovery and memorization of abstract rules. The aim of this paper is to study associative memory mechanisms. Our model is based on high-dimensional matrices consisting of outer products of embeddings, which relates to the inner layers of transformer language models. We derive precise scaling laws with respect to sample size and parameter size, and discuss the statistical efficiency of different estimators, including optimization-based algorithms. We provide extensive numerical experiments to validate and interpret theoretical results, including fine-grained visualizations of the stored memory associations.

The capacity of a neural network to absorb information is limited by its number of parameters. Conditional computation, where parts of the network are active on a per-example basis, has been proposed in theory as a way of dramatically increasing model capacity without a proportional increase in computation. In practice, however, there are significant algorithmic and performance challenges. In this work, we address these challenges and finally realize the promise of conditional computation, achieving greater than 1000x improvements in model capacity with only minor losses in computational efficiency on modern GPU clusters. We introduce a Sparsely-Gated Mixture-of-Experts layer (MoE), consisting of up to thousands of feed-forward sub-networks. A trainable gating network determines a sparse combination of these experts to use for each example. We apply the MoE to the tasks of language modeling and machine translation, where model capacity is critical for absorbing the vast quantities of knowledge available in the training corpora. We present model architectures in which a MoE with up to 137 billion parameters is applied convolutionally between stacked LSTM layers. On large language modeling and machine translation benchmarks, these models achieve significantly better results than state-of-the-art at lower computational cost.

The human brain is a complex spiking neural network (SNN) that learns multimodal signals in a zero-shot manner by generalizing existing knowledge. Remarkably, the brain achieves this with minimal power consumption, using event-based signals that propagate within its structure. However, mimicking the human brain in neuromorphic hardware presents both hardware and software challenges. Hardware limitations, such as the slowdown of Moore's law and the von Neumann bottleneck, hinder the efficiency of digital computers. On the software side, SNNs are known for their difficult training, especially when learning multimodal signals. To overcome these challenges, we propose a hardware-software co-design that combines a fixed and random liquid state machine (LSM) SNN encoder with trainable artificial neural network (ANN) projections. The LSM is physically implemented using analogue resistive memory, leveraging the inherent stochasticity of resistive switching to generate random weights. This highly efficient and nanoscale in-memory computing approach effectively addresses the von Neumann bottleneck and the slowdown of Moore's law. The ANN projections are implemented digitally, allowing for easy optimization using contrastive loss, which helps to overcome the difficulties associated with SNN training. We experimentally implement this co-design on a 40nm 256Kb in-memory computing macro. We first demonstrate LSM-based event encoding through supervised classification and linear probing on the N-MNIST and N-TIDIGITS datasets.

Gated attention is an effective approach to mitigate attention sinks and enhance the representational capacity of attention. To further extend its effectiveness-efficiency Pareto frontier, we propose a Hybrid Gated Attention (HyGA) framework that contains three types of gating strategies. Specifically, these gates leverage diverse information from multiple stages of attention, and collaboratively build element-wise/head-wise gating from multiple perspectives, capturing intra-head and cross-head information interactions. Through our hybrid gating components, HyGA could provide multi-source modulation signals, enabling more comprehensive control over information flow and improving the representational capacity of attention. We also introduce low-rank matrix decomposition and learnable attention sink to further enhance training efficiency and stability. In experiments, we evaluate HyGA on widely-used benchmarks based on different backbones. The experimental results show that our HyGA comprehensively improves both training loss and various downstream performances compared with Gated attention. HyGA has also been verified to achieve the best performance at different computation costs, with comprehensive model analyses for better understanding. The proposed HyGA sheds light on a more effective, efficient, and stable attention mechanism.

Large Language Models (LLMs) face significant challenges in long-context processing, including quadratic computational costs, information forgetting, and the context fragmentation inherent in retrieval-augmented generation (RAG). We propose a cognitively inspired framework for efficient long-context inference based on chunk-wise compression and selective memory recall, rather than processing all raw tokens. The framework segments long inputs into chunks and encodes each chunk into compressed memory representations using a learned compressor. A gating module dynamically selects relevant memory blocks, which are then iteratively processed by a reasoning module with an evolving working memory to solve downstream tasks. The compressor and reasoner are jointly optimized via end-to-end reinforcement learning, while the gating module is trained separately as a classifier. Experimental results show that the proposed method achieves competitive accuracy on multi-hop reasoning benchmarks such as RULER-HQA, extrapolates context length from 7K to 1.75M tokens, and offers a favorable accuracy-efficiency trade-off compared to strong long-context baselines. In particular, it achieves up to a 2 times reduction in peak GPU memory usage and a 6 times inference speedup over MemAgent.

For over a decade, explicit memory architectures like the Neural Turing Machine have remained theoretically appealing yet practically intractable for language modeling due to catastrophic gradient instability during Backpropagation Through Time. In this work, we break this stalemate with Phasor Memory Network (PMNet), a novel architecture that structurally resolves memory volatility through Unitary Phasor Dynamics and Hierarchical Learnable Anchors. Rather than relying on brute-force scaling, we present a mechanistic proof-of-concept in a controlled byte-level setting. By constraining recurrent state updates to phase rotations on a complex unit circle, PMNet preserves gradient norms and inherently prevents divergence without the need for specialized initialization. We empirically demonstrate the active actuation of the memory module through a synthetic Copy-Paste task, where PMNet utilizes an expansive 85-slot hierarchical memory tree (=sum^{4}_{h=1}4^{h-1}) to achieve near 100\% exact retrieval across temporal distances that completely exceed the local sliding window attention's receptive field. Furthermore, despite being a compact 119M parameter model trained on 18.8B tokens, PMNet matches the zero-shot long-context robustness of a Mamba model that is three times larger. Our ablation studies and gradient analyses confirm that the historical failure of explicit memory was a structural alignment problem, which PMNet effectively overcomes, providing a theoretically grounded foundation for scalable sequence modeling.

The loss landscapes of neural networks contain minima and saddle points that may be connected in flat regions or appear in isolation. We identify and characterize a special structure in the loss landscape: channels along which the loss decreases extremely slowly, while the output weights of at least two neurons, a_i and a_j, diverge to pminfinity, and their input weight vectors, w_i and w_j, become equal to each other. At convergence, the two neurons implement a gated linear unit: a_iσ(w_i cdot x) + a_jσ(w_j cdot x) rightarrow σ(w cdot x) + (v cdot x) σ'(w cdot x). Geometrically, these channels to infinity are asymptotically parallel to symmetry-induced lines of critical points. Gradient flow solvers, and related optimization methods like SGD or ADAM, reach the channels with high probability in diverse regression settings, but without careful inspection they look like flat local minima with finite parameter values. Our characterization provides a comprehensive picture of these quasi-flat regions in terms of gradient dynamics, geometry, and functional interpretation. The emergence of gated linear units at the end of the channels highlights a surprising aspect of the computational capabilities of fully connected layers.

Memory-based Dynamic Graph Neural Networks (MDGNNs) are a family of dynamic graph neural networks that leverage a memory module to extract, distill, and memorize long-term temporal dependencies, leading to superior performance compared to memory-less counterparts. However, training MDGNNs faces the challenge of handling entangled temporal and structural dependencies, requiring sequential and chronological processing of data sequences to capture accurate temporal patterns. During the batch training, the temporal data points within the same batch will be processed in parallel, while their temporal dependencies are neglected. This issue is referred to as temporal discontinuity and restricts the effective temporal batch size, limiting data parallelism and reducing MDGNNs' flexibility in industrial applications. This paper studies the efficient training of MDGNNs at scale, focusing on the temporal discontinuity in training MDGNNs with large temporal batch sizes. We first conduct a theoretical study on the impact of temporal batch size on the convergence of MDGNN training. Based on the analysis, we propose PRES, an iterative prediction-correction scheme combined with a memory coherence learning objective to mitigate the effect of temporal discontinuity, enabling MDGNNs to be trained with significantly larger temporal batches without sacrificing generalization performance. Experimental results demonstrate that our approach enables up to a 4x larger temporal batch (3.4x speed-up) during MDGNN training.

Transformers with linear attention allow for efficient parallel training but can simultaneously be formulated as an RNN with 2D (matrix-valued) hidden states, thus enjoying linear (with respect to output length) inference complexity. Recent works such as RetNet (Sun et al., 2023) and TransNormerLLM (Qin et al., 2023a) observe that adding a global decay term to the additive RNN update rule greatly improves performance, sometimes outperforming standard Transformers with softmax attention when trained at scale. In this work we show that adding a data-dependent gating mechanism further improves performance. We derive a parallel form of this gated linear attention layer that enables efficient training. However, a straightforward, numerically stable implementation of this parallel form requires generalized matrix multiplications in log-space for numerical stability, and thus cannot take advantage of tensor cores on modern GPUs which are optimized for standard matrix multiplications. We develop a hardware-efficient version of the parallel form that can still make use of tensor cores through block-parallel computations over sequence chunks. Experiments on moderate-scale language modeling (340M-parameter models trained on 15B tokens, 1.3B-parameter models trained on 100B tokens) show that gated linear attention (GLA) Transformers perform competitively against a strong LLaMA-architecture Transformer baseline (Touvron et al., 2023) as well as Mamba (Gu & Dao, 2023), a recently introduced state-space model with a data-dependent state transition mechanism. For training speed, our Triton-based implementation performs comparably to CUDA-optimized FlashAttention-2 (Dao, 2023) under the regular 2048 training length setting, while outperforming FlashAttention-2 when training on longer sequences beyond 4096.

Conditional computation is a popular strategy to make Transformers more efficient. Existing methods often target individual modules (e.g., mixture-of-experts layers) or skip layers independently of one another. However, interpretability research has demonstrated that the middle layers of Transformers exhibit greater redundancy, and that early layers aggregate information into token positions. Guided by these insights, we propose a novel architecture that dynamically skips a variable number of layers from the middle outward. In particular, a learned gating mechanism determines whether to bypass a symmetric span of central blocks based on the input, and a gated attention mechanism prevents subsequent tokens from attending to skipped token positions. Residual norms are controlled with a 'sandwich' or 'perilayernorm' scheme and gate sparsity with an adaptive regularization loss. We had aimed to reduce compute requirements for 'simpler' tokens and potentially foster an emergent multi-level representational hierarchy but, at the scales investigated, our approach does not achieve improvements in the trade-off between validation cross-entropy and estimated FLOPs compared to dense baselines with fewer layers. We release our code at https://github.com/tim-lawson/skip-middle.

Making neural networks remember over the long term has been a longstanding issue. Although several external memory techniques have been introduced, most focus on retaining recent information in the short term. Regardless of its importance, information tends to be fatefully forgotten over time. We present Memoria, a memory system for artificial neural networks, drawing inspiration from humans and applying various neuroscientific and psychological theories. The experimental results prove the effectiveness of Memoria in the diverse tasks of sorting, language modeling, and classification, surpassing conventional techniques. Engram analysis reveals that Memoria exhibits the primacy, recency, and temporal contiguity effects which are characteristics of human memory.

Few algorithms for supervised training of spiking neural networks exist that can deal with patterns of multiple spikes, and their computational properties are largely unexplored. We demonstrate in a set of simulations that the ReSuMe learning algorithm can be successfully applied to layered neural networks. Input and output patterns are encoded as spike trains of multiple precisely timed spikes, and the network learns to transform the input trains into target output trains. This is done by combining the ReSuMe learning algorithm with multiplicative scaling of the connections of downstream neurons. We show in particular that layered networks with one hidden layer can learn the basic logical operations, including Exclusive-Or, while networks without hidden layer cannot, mirroring an analogous result for layered networks of rate neurons. While supervised learning in spiking neural networks is not yet fit for technical purposes, exploring computational properties of spiking neural networks advances our understanding of how computations can be done with spike trains.

Linear attention models allow a fixed state size and a fixed amount of compute per token. However, due to their limited state size, linear attention models fall behind in long-context recall compared to softmax-attention-based transformer architectures. Increasing the state size of linear attention improves recall performance but at the cost of higher FLOPs. In this work, we introduce Sparse Delta Memory (SDM), an architecture that scales the hidden state of gated linear RNNs to orders of magnitude higher capacity using a sparse addressing scheme. SDM extends the Gated DeltaNet architecture by replacing the dense key-value outer product with sparse reads and writes to a large explicit memory. We show that, under an isoFLOP constraint and with an identical number of parameters, a higher state memory capacity significantly improves performance on in-context learning and long-context retrieval tasks. Moreover, by learning the initial state of the SDM memory and therefore using it as a parametric memory, we show that the model further improves on a wide range of common-knowledge and reasoning tasks.

Attention mechanisms have revolutionized sequence learning but suffer from quadratic computational complexity. This paper introduces Lattice, a novel recurrent neural network (RNN) mechanism that leverages the inherent low-rank structure of K-V matrices to efficiently compress the cache into a fixed number of memory slots, achieving sub-quadratic complexity. We formulate this compression as an online optimization problem and derive a dynamic memory update rule based on a single gradient descent step. The resulting recurrence features a state- and input-dependent gating mechanism, offering an interpretable memory update process. The core innovation is the orthogonal update: each memory slot is updated exclusively with information orthogonal to its current state hence incorporation of only novel, non-redundant data, which minimizes the interference with previously stored information. The experimental results show that Lattice achieves the best perplexity compared to all baselines across diverse context lengths, with performance improvement becoming more pronounced as the context length increases.

Training large neural networks with end-to-end backpropagation creates significant memory bottlenecks, limiting accessibility to state-of-the-art AI research. We propose DiffusionBlocks, a novel training framework that interprets neural network blocks as performing denoising operations in a continuous-time diffusion process. By partitioning the network into independently trainable blocks and optimizing noise level assignments based on equal cumulative probability mass, our approach achieves significant memory efficiency while maintaining competitive performance compared to traditional backpropagation in generative tasks. Experiments on image generation and language modeling tasks demonstrate memory reduction proportional to the number of blocks while achieving superior performance. DiffusionBlocks provides a promising pathway for democratizing access to large-scale neural network training with limited computational resources.

We prove theoretically that generalization improves not only through data scaling but also by compressing internal representations. To operationalize this insight, we introduce the Information Bottleneck Language Modeling (IBLM) objective, which reframes language modeling as a constrained optimization problem: minimizing representation entropy subject to optimal prediction performance. Empirically, we observe an emergent memorization-compression cycle during LLM pretraining, evidenced by oscillation positive/negative gradient alignment between cross-entropy and Matrix-Based Entropy (MBE), a measure of representation entropy. This pattern closely mirrors the predictive-compressive trade-off prescribed by IBLM and also parallels the biological alternation between awake learning and sleep consolidation. Motivated by this observation, we propose Gated Phase Transition (GAPT), a training algorithm that adaptively switches between memorization and compression phases. When applied to GPT-2 pretraining on FineWeb dataset, GAPT reduces MBE by 50% and improves cross-entropy by 4.8%. GAPT improves OOD generalizatino by 35% in a pretraining task on arithmetic multiplication. In a setting designed to simulate catastrophic forgetting, GAPT reduces interference by compressing and separating representations, achieving a 97% improvement in separation - paralleling the functional role of sleep consolidation.

This article summarizes principles and ideas from the emerging area of applying conditional computation methods to the design of neural networks. In particular, we focus on neural networks that can dynamically activate or de-activate parts of their computational graph conditionally on their input. Examples include the dynamic selection of, e.g., input tokens, layers (or sets of layers), and sub-modules inside each layer (e.g., channels in a convolutional filter). We first provide a general formalism to describe these techniques in an uniform way. Then, we introduce three notable implementations of these principles: mixture-of-experts (MoEs) networks, token selection mechanisms, and early-exit neural networks. The paper aims to provide a tutorial-like introduction to this growing field. To this end, we analyze the benefits of these modular designs in terms of efficiency, explainability, and transfer learning, with a focus on emerging applicative areas ranging from automated scientific discovery to semantic communication.

State-of-the-art neural network architectures such as ResNet, MobileNet, and DenseNet have achieved outstanding accuracy over low MACs and small model size counterparts. However, these metrics might not be accurate for predicting the inference time. We suggest that memory traffic for accessing intermediate feature maps can be a factor dominating the inference latency, especially in such tasks as real-time object detection and semantic segmentation of high-resolution video. We propose a Harmonic Densely Connected Network to achieve high efficiency in terms of both low MACs and memory traffic. The new network achieves 35%, 36%, 30%, 32%, and 45% inference time reduction compared with FC-DenseNet-103, DenseNet-264, ResNet-50, ResNet-152, and SSD-VGG, respectively. We use tools including Nvidia profiler and ARM Scale-Sim to measure the memory traffic and verify that the inference latency is indeed proportional to the memory traffic consumption and the proposed network consumes low memory traffic. We conclude that one should take memory traffic into consideration when designing neural network architectures for high-resolution applications at the edge.

Autoregressive sequence modeling stands as the cornerstone of modern Generative AI, powering results across diverse modalities ranging from text generation to image generation. However, a fundamental limitation of this paradigm is the rigid structural coupling of model capacity to computational cost: expanding a model's parametric memory -- its repository of factual knowledge or visual patterns -- traditionally requires deepening or widening the network, which incurs a proportional rise in active FLOPs. In this work, we introduce MoVE (Mixture of Value Embeddings), a mechanism that breaks this coupling and establishes a new axis for scaling capacity. MoVE decouples memory from compute by introducing a global bank of learnable value embeddings shared across all attention layers. For every step in the sequence, the model employs a differentiable soft gating mechanism to dynamically mix retrieved concepts from this bank into the standard value projection. This architecture allows parametric memory to be scaled independently of network depth by simply increasing the number of embedding slots. We validate MoVE through strictly controlled experiments on two representative applications of autoregressive modeling: Text Generation and Image Generation. In both domains, MoVE yields consistent performance improvements over standard and layer-wise memory baselines, enabling the construction of "memory-dense" models that achieve lower perplexity and higher fidelity than their dense counterparts at comparable compute budgets.

Long contexts challenge transformers: attention scores dilute across thousands of tokens, critical information is often lost in the middle, and models struggle to adapt to novel patterns at inference time. Recent work on test-time adaptation addresses this by maintaining a form of working memory -- transient parameters updated on the current context -- but existing approaches rely on uniform write policies that waste computation on low-utility regions and suffer from high gradient variance across semantically heterogeneous contexts. In this work, we reframe test-time adaptation as a budget-constrained memory consolidation problem, focusing on which parts of the context should be consolidated into working memory under limited computation. We propose Gdwm (Gated Differentiable Working Memory), a framework that introduces a write controller to gate the consolidation process. The controller estimates Contextual Utility, an information-theoretic measure of long-range contextual dependence, and allocates gradient steps accordingly while maintaining global coverage. Experiments on ZeroSCROLLS and LongBench v2 demonstrate that Gdwm achieves comparable or superior performance with 4times fewer gradient steps than uniform baselines, establishing a new efficiency-performance Pareto frontier for test-time adaptation.

Gated Linear Units (GLUs) have become essential components in the feed-forward networks of state-of-the-art Large Language Models (LLMs). However, they require twice as many memory reads compared to feed-forward layers without gating, due to the use of separate weight matrices for the gate and value streams. To address this bottleneck, we introduce Masked Gated Linear Units (MGLUs), a novel family of GLUs with an efficient kernel implementation. The core contribution of MGLUs include: (1) the Mixture of Element-wise Gating (MoEG) architecture that learns multiple binary masks, each determining gate or value assignments at the element level on a single shared weight matrix resulting in reduced memory transfer, and (2) FlashMGLU, a hardware-friendly kernel that yields up to a 19.7 times inference-time speed-up over a naive PyTorch MGLU and is 47% more memory-efficient and 34% faster than standard GLUs despite added architectural complexity on an RTX5090 GPU. In LLM experiments, the Swish-activated variant SwiMGLU preserves its memory advantages while matching - or even surpassing - the downstream accuracy of the SwiGLU baseline.

Linear Recurrence has proven to be a powerful tool for modeling long sequences efficiently. In this work, we show that existing models fail to take full advantage of its potential. Motivated by this finding, we develop GateLoop, a foundational sequence model that generalizes linear recurrent models such as S4, S5, LRU and RetNet, by employing data-controlled state transitions. Utilizing this theoretical advance, GateLoop empirically outperforms existing models for auto-regressive language modeling. Our method comes with a low-cost O(l) recurrent mode and an efficient O(l log_{2} l) parallel mode making use of highly optimized associative scan implementations. Furthermore, we derive an O(l^2) surrogate attention mode, revealing remarkable implications for Transformer and recently proposed architectures. Specifically, we prove that our approach can be interpreted as providing data-controlled relative-positional information to Attention. While many existing models solely rely on data-controlled cumulative sums for context aggregation, our findings suggest that incorporating data-controlled complex cumulative products may be a crucial step towards more powerful sequence models.

Gating mechanisms have been widely utilized, from early models like LSTMs and Highway Networks to recent state space models, linear attention, and also softmax attention. Yet, existing literature rarely examines the specific effects of gating. In this work, we conduct comprehensive experiments to systematically investigate gating-augmented softmax attention variants. Specifically, we perform a comprehensive comparison over 30 variants of 15B Mixture-of-Experts (MoE) models and 1.7B dense models trained on a 3.5 trillion token dataset. Our central finding is that a simple modification-applying a head-specific sigmoid gate after the Scaled Dot-Product Attention (SDPA)-consistently improves performance. This modification also enhances training stability, tolerates larger learning rates, and improves scaling properties. By comparing various gating positions and computational variants, we attribute this effectiveness to two key factors: (1) introducing non-linearity upon the low-rank mapping in the softmax attention, and (2) applying query-dependent sparse gating scores to modulate the SDPA output. Notably, we find this sparse gating mechanism mitigates 'attention sink' and enhances long-context extrapolation performance, and we also release related https://github.com/qiuzh20/gated_attention{codes} and https://huggingface.co/QwQZh/gated_attention{models} to facilitate future research.

We introduce GateSkip, a simple residual-stream gating mechanism that enables token-wise layer skipping in decoder-only LMs. Each Attention/MLP branch is equipped with a sigmoid-linear gate that condenses the branch's output before it re-enters the residual stream. During inference we rank tokens by the gate values and skip low-importance ones using a per-layer budget. While early-exit or router-based Mixture-of-Depths models are known to be unstable and need extensive retraining, our smooth, differentiable gates fine-tune stably on top of pretrained models. On long-form reasoning, we save up to 15\% compute while retaining over 90\% of baseline accuracy. On instruction-tuned models we see accuracy gains at full compute and match baseline quality near 50\% savings. The learned gates give insight into transformer information flow (e.g., BOS tokens act as anchors), and the method combines easily with quantization, pruning, and self-speculative decoding.

While Attention Residuals has shown some effectiveness in addressing the widespread issue of unbounded activation growth across deep residual layers, it inevitably incurs significant communication overhead. To circumvent this bottleneck, we propose Multi-Gate Residuals (MGR), which stabilizes activation scales without additional communication burden. It utilizes a straightforward scoring and gating mechanism to maintain multi-stream context, coupled with Attention Pooling to extract hidden states from the stream states. Empirical experiments demonstrate that MGR is practical for large-scale training and deployment, offering tangible performance improvements over existing architectures.

In this paper, we introduce a novel layer designed to be used as the output of pre-trained neural networks in the context of classification. Based on Associative Memories, this layer can help design Deep Neural Networks which support incremental learning and that can be (partially) trained in real time on embedded devices. Experiments on the ImageNet dataset and other different domain specific datasets show that it is possible to design more flexible and faster-to-train Neural Networks at the cost of a slight decrease in accuracy.

Large pretrained models, coupled with fine-tuning, are slowly becoming established as the dominant architecture in machine learning. Even though these models offer impressive performance, their practical application is often limited by the prohibitive amount of resources required for every inference. Early-exiting dynamic neural networks (EDNN) circumvent this issue by allowing a model to make some of its predictions from intermediate layers (i.e., early-exit). Training an EDNN architecture is challenging as it consists of two intertwined components: the gating mechanism (GM) that controls early-exiting decisions and the intermediate inference modules (IMs) that perform inference from intermediate representations. As a result, most existing approaches rely on thresholding confidence metrics for the gating mechanism and strive to improve the underlying backbone network and the inference modules. Although successful, this approach has two fundamental shortcomings: 1) the GMs and the IMs are decoupled during training, leading to a train-test mismatch; and 2) the thresholding gating mechanism introduces a positive bias into the predictive probabilities, making it difficult to readily extract uncertainty information. We propose a novel architecture that connects these two modules. This leads to significant performance improvements on classification datasets and enables better uncertainty characterization capabilities.

The deployment of Large Language Models (LLMs) on edge devices is fundamentally constrained by the "Memory Wall" -- a hardware limitation where memory bandwidth, not compute, becomes the bottleneck. Recent 1.58-bit quantization techniques (e.g., BitNet b1.58) dramatically reduce memory footprint but typically incur a perplexity degradation of 20-25% compared to FP16 baselines. In this work, we introduce Hybrid Gated Flow (HGF), a dual-stream architecture that couples a 1.58-bit ternary backbone with a learnable, low-rank FP16 correction path controlled by adaptive gates. Through extensive experiments on the TinyStories dataset across two training regimes (2500 and 3500 steps), we demonstrate that HGF 5.4 achieves a validation loss of 0.9306 compared to BitNet's 1.0294, recovering approximately 55% of the quality gap between pure ternary quantization and the FP16 baseline (0.8490). This recovery is achieved with only ~12-15% memory overhead beyond the ternary backbone. Furthermore, we provide empirical evidence for an emergent phenomenon: quantization as structural regularization. While a full-precision differential attention baseline (Diff_Only) exhibited training instability with validation loss exceeding 1.68, the ternary-anchored HGF maintained robust convergence throughout training. Finally, we report preliminary results extending this architecture to 1.2B and 3B parameter models trained on SlimPajama and FineWeb-Edu. These larger-scale experiments confirm that the architectural stability and quality recovery observed in small-scale proxies scale linearly to production-grade language modeling regimes.

We present Analogical Networks, a model that encodes domain knowledge explicitly, in a collection of structured labelled 3D scenes, in addition to implicitly, as model parameters, and segments 3D object scenes with analogical reasoning: instead of mapping a scene to part segments directly, our model first retrieves related scenes from memory and their corresponding part structures, and then predicts analogous part structures for the input scene, via an end-to-end learnable modulation mechanism. By conditioning on more than one retrieved memories, compositions of structures are predicted, that mix and match parts across the retrieved memories. One-shot, few-shot or many-shot learning are treated uniformly in Analogical Networks, by conditioning on the appropriate set of memories, whether taken from a single, few or many memory exemplars, and inferring analogous parses. We show Analogical Networks are competitive with state-of-the-art 3D segmentation transformers in many-shot settings, and outperform them, as well as existing paradigms of meta-learning and few-shot learning, in few-shot settings. Analogical Networks successfully segment instances of novel object categories simply by expanding their memory, without any weight updates. Our code and models are publicly available in the project webpage: http://analogicalnets.github.io/.

Driven by the development of persistent, self-adapting autonomous agents, equipping these systems with high-fidelity memory access for long-horizon reasoning has emerged as a critical requirement. However, prevalent retrieval-based memory frameworks often follow an incremental processing paradigm that continuously extracts and updates conversational memories into vector databases, relying on semantic retrieval when queried. While this approach is fast, it inherently relies on lossy abstraction, frequently missing contextually critical information and struggling to resolve queries that rely on fine-grained contextual understanding. To address this, we introduce D-Mem, a dual-process memory system. It retains lightweight vector retrieval for routine queries while establishing an exhaustive Full Deliberation module as a high-fidelity fallback. To achieve cognitive economy without sacrificing accuracy, D-Mem employs a Multi-dimensional Quality Gating policy to dynamically bridge these two processes. Experiments on the LoCoMo and RealTalk benchmarks using GPT-4o-mini and Qwen3-235B-Instruct demonstrate the efficacy of our approach. Notably, our Multi-dimensional Quality Gating policy achieves an F1 score of 53.5 on LoCoMo with GPT-4o-mini. This outperforms our static retrieval baseline, Mem0^ast (51.2), and recovers 96.7\% of the Full Deliberation's performance (55.3), while incurring significantly lower computational costs.

Fine-tuning pretrained large models to downstream tasks is an important problem, which however suffers from huge memory overhead due to large-scale parameters. This work strives to reduce memory overhead in fine-tuning from perspectives of activation function and layer normalization. To this end, we propose the Approximate Backpropagation (Approx-BP) theory, which provides the theoretical feasibility of decoupling the forward and backward passes. We apply our Approx-BP theory to backpropagation training and derive memory-efficient alternatives of GELU and SiLU activation functions, which use derivative functions of ReLUs in the backward pass while keeping their forward pass unchanged. In addition, we introduce a Memory-Sharing Backpropagation strategy, which enables the activation memory to be shared by two adjacent layers, thereby removing activation memory usage redundancy. Our method neither induces extra computation nor reduces training efficiency. We conduct extensive experiments with pretrained vision and language models, and the results demonstrate that our proposal can reduce up to sim30% of the peak memory usage. Our code is released at https://github.com/yyyyychen/LowMemoryBP.

We introduce and train distributed neural architectures (DNA) in vision and language domains. DNAs are initialized with a proto-architecture that consists of (transformer, MLP, attention, etc.) modules and routers. Any token (or patch) can traverse any series of modules in any order. DNAs are a natural generalization of the sparse methods such as Mixture-of-Experts, Mixture-of-Depths, parameter sharing, etc. Computation and communication patterns of DNA modules are learnt end-to-end during training and depend on the content and context of each token (or patch). These patterns can be shaped by further requirements added to the optimization objective such as compute/memory efficiency or load balancing. We empirically show that (i) trained DNAs are competitive with the dense baselines in both domains and (ii) compute efficiency/parameter sharing can be learnt from data. Next, we analyze the emergent connectivity and computation patterns in the trained DNAs. We find that the paths that tokens take through the models are themselves distributed according to a power-law. We show that some paths (or, equivalently, groups of modules) show emergent specialization. Finally, we demonstrate that models learn to allocate compute and active parameters in an interpretable way.

We introduce a novel class of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) paradigm, called Residual Reservoir Memory Networks (ResRMNs). ResRMN combines a linear memory reservoir with a non-linear reservoir, where the latter is based on residual orthogonal connections along the temporal dimension for enhanced long-term propagation of the input. The resulting reservoir state dynamics are studied through the lens of linear stability analysis, and we investigate diverse configurations for the temporal residual connections. The proposed approach is empirically assessed on time-series and pixel-level 1-D classification tasks. Our experimental results highlight the advantages of the proposed approach over other conventional RC models.

With the emergence of pre-trained vision-language models like CLIP, how to adapt them to various downstream classification tasks has garnered significant attention in recent research. The adaptation strategies can be typically categorized into three paradigms: zero-shot adaptation, few-shot adaptation, and the recently-proposed training-free few-shot adaptation. Most existing approaches are tailored for a specific setting and can only cater to one or two of these paradigms. In this paper, we introduce a versatile adaptation approach that can effectively work under all three settings. Specifically, we propose the dual memory networks that comprise dynamic and static memory components. The static memory caches training data knowledge, enabling training-free few-shot adaptation, while the dynamic memory preserves historical test features online during the testing process, allowing for the exploration of additional data insights beyond the training set. This novel capability enhances model performance in the few-shot setting and enables model usability in the absence of training data. The two memory networks employ the same flexible memory interactive strategy, which can operate in a training-free mode and can be further enhanced by incorporating learnable projection layers. Our approach is tested across 11 datasets under the three task settings. Remarkably, in the zero-shot scenario, it outperforms existing methods by over 3\% and even shows superior results against methods utilizing external training data. Additionally, our method exhibits robust performance against natural distribution shifts. Codes are available at https://github.com/YBZh/DMN.

Scaling transformer language models creates an inherent tension between expressivity and memory efficiency. While unique weights across layers preserve functional specialization---from input-grounding to abstract refinement---they incur a substantial memory footprint. Conversely, standard depth-sharing enforces uniform transformations that collapse representational diversity and degrade modeling quality. We introduce Gated Recurrent Transformer, a recurrent depth transformer where fixed-depth prelude and coda blocks bracket a single shared core iterated R times. Inspired by gated recurrent neural networks, we employ a lightweight projection and an elementwise update gate---conditioned on the hidden state, the fixed prelude output, and noise resampled at every step---to modulate the recurrent update. This allows the model to specialize the input to the same few layers across recurrences, rather than requiring many unique layers to achieve functional diversity. Under an isoFLOPS constraint, a 3-layer Gated Recurrent Transformer matches the accuracy of a 12-layer GPT-2 Small baseline with similar training and inference FLOPs, and leads MoR and heavy-tail depth sampling in all nine scale-by-budget cells; at medium and large scale it approaches dense quality at the standard token budget and overtakes it at medium scale once that budget is doubled. Under an isoPARAMS constraint, deeper recurrence achieves a 2.76 validation loss versus 2.84 for a non-recurrent counterpart at matched parameter and data budget. Our results demonstrate that adaptive depth reuse is a principled strategy for trading parameters for quality: at large scale, 63% fewer parameters and 59% less peak decoding memory for a 10% increase in compiled generation latency.

Designing efficient and effective architectural backbones has been in the core of research efforts to enhance the capability of foundation models. Inspired by the human cognitive phenomenon of attentional bias-the natural tendency to prioritize certain events or stimuli-we reconceptualize neural architectures, including Transformers, Titans, and modern linear recurrent neural networks as associative memory modules that learn a mapping of keys and values using an internal objective, referred to as attentional bias. Surprisingly, we observed that most existing sequence models leverage either (1) dot-product similarity, or (2) L2 regression objectives as their attentional bias. Going beyond these objectives, we present a set of alternative attentional bias configurations along with their effective approximations to stabilize their training procedure. We then reinterpret forgetting mechanisms in modern deep learning architectures as a form of retention regularization, providing a novel set of forget gates for sequence models. Building upon these insights, we present Miras, a general framework to design deep learning architectures based on four choices of: (i) associative memory architecture, (ii) attentional bias objective, (iii) retention gate, and (iv) memory learning algorithm. We present three novel sequence models-Moneta, Yaad, and Memora-that go beyond the power of existing linear RNNs while maintaining a fast parallelizable training process. Our experiments show different design choices in Miras yield models with varying strengths. For example, certain instances of Miras achieve exceptional performance in special tasks such as language modeling, commonsense reasoning, and recall intensive tasks, even outperforming Transformers and other modern linear recurrent models.

There is a concerted effort to build domain-general artificial intelligence in the form of universal neural network models with sufficient computational flexibility to solve a wide variety of cognitive tasks but without requiring fine-tuning on individual problem spaces and domains. To do this, models need appropriate priors and inductive biases, such that trained models can generalise to out-of-distribution examples and new problem sets. Here we provide an overview of the hallmarks endowing biological neural networks with the functionality needed for flexible cognition, in order to establish which features might also be important to achieve similar functionality in artificial systems. We specifically discuss the role of system-level distribution of network communication and recurrence, in addition to the role of short-term topological changes for efficient local computation. As machine learning models become more complex, these principles may provide valuable directions in an otherwise vast space of possible architectures. In addition, testing these inductive biases within artificial systems may help us to understand the biological principles underlying domain-general cognition.

Neural networks for image recognition have evolved through extensive manual design from simple chain-like models to structures with multiple wiring paths. The success of ResNets and DenseNets is due in large part to their innovative wiring plans. Now, neural architecture search (NAS) studies are exploring the joint optimization of wiring and operation types, however, the space of possible wirings is constrained and still driven by manual design despite being searched. In this paper, we explore a more diverse set of connectivity patterns through the lens of randomly wired neural networks. To do this, we first define the concept of a stochastic network generator that encapsulates the entire network generation process. Encapsulation provides a unified view of NAS and randomly wired networks. Then, we use three classical random graph models to generate randomly wired graphs for networks. The results are surprising: several variants of these random generators yield network instances that have competitive accuracy on the ImageNet benchmark. These results suggest that new efforts focusing on designing better network generators may lead to new breakthroughs by exploring less constrained search spaces with more room for novel design.

Long-context language modeling remains central to modern sequence modeling, but the quadratic cost of Transformer attention makes scaling computationally prohibitive. Linear recurrent models address this bottleneck by compressing the context into a fixed-size state, making the rule that forgets, writes, and edits information a central design problem. To address state maintenance, Gated DeltaNet (GDN) combines gated state decay with delta-rule residual writes, using a learnable coefficient to balance forgetting and update magnitude. However, this coefficient is learned empirically rather than derived from the underlying objective, which can lead to suboptimal update magnitudes. We revisit the online-regression objective underlying GDN and, inspired by the Kaczmarz projection method, derive the key-norm-normalized dynamic step size β_t = η_t / (|k_t|_2^2 + ε) for residual updates. We propose Kaczmarz Linear Attention (KLA), a one-scalar modification of GDN that preserves the state shape, gates, linear recurrence, and chunkwise parallel algorithm. At the 0.4B scale with a 1B-token budget, KLA achieves the lowest validation perplexity among evaluated linear-time baselines, 8.09 versus 8.50 for GDN, and remains stable up to 65K tokens. On controlled tasks, KLA reaches 100% on single-needle-in-a-haystack retrieval, improves 8x multi-query associative recall by 7.03 points over GDN, and delivers 2.1x higher decode throughput at 32K context. These results suggest that the key-norm-normalized Kaczmarz coefficient is a first-order design axis for delta-rule sequence models: it improves accuracy, extrapolation, and decoding efficiency without changing the recurrent state or hardware kernel.

As giant dense models advance quality but require large amounts of GPU budgets for training, the sparsely gated Mixture-of-Experts (MoE), a kind of conditional computation architecture, is proposed to scale models while keeping their computation constant. Specifically, the input tokens are routed by the gate network and only activates part of the expert network. Existing MoE training systems only support part of mainstream MoE models (e.g. Top k) training under expensive high-bandwidth GPU clusters. In this paper, we present HetuMoE, a high-performance large-scale sparse MoE training system built on Hetu. HetuMoE provides multiple gating strategies and efficient GPU kernel implementations. To further improve the training efficiency on commodity GPU clusters (e.g, with only 1 NiC), we introduce the hierarchical AllToAll communication that combines hierarchical networks and aggregating messages. Compared with existing state-of-the-art MoE systems, HetuMoE obtains at least 15% speedup. Specifically, HetuMoE outperforms DeepSpeed-MoE up to 8.1x under the switch gate with a batch size of 32. Our code is available at: https://github.com/PKU-DAIR/Hetu.

Recurrent neural networks (RNNs) have fast inference and scale efficiently on long sequences, but they are difficult to train and hard to scale. We propose Hawk, an RNN with gated linear recurrences, and Griffin, a hybrid model that mixes gated linear recurrences with local attention. Hawk exceeds the reported performance of Mamba on downstream tasks, while Griffin matches the performance of Llama-2 despite being trained on over 6 times fewer tokens. We also show that Griffin can extrapolate on sequences significantly longer than those seen during training. Our models match the hardware efficiency of Transformers during training, and during inference they have lower latency and significantly higher throughput. We scale Griffin up to 14B parameters, and explain how to shard our models for efficient distributed training.

Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for various cost functions. We also propose several new cost functions suitable for learning. We discuss the role of biases (the external inputs) in the learning process in Hopfield networks. Furthermore, we apply Newtons method for learning memories, and experimentally compare the performances of various learning rules. Finally, to add to the debate whether allowing connections of a neuron to itself enhances memory capacity, we numerically investigate the effects of self coupling. Keywords: Hopfield Networks, associative memory, content addressable memory, learning rules, gradient descent, attractor networks

Autonomous LLM agents require structured long-term memory, yet current "append-and-evolve" systems like A-MEM face O(N^2) write-latency and excessive token costs. We introduce D-MEM (Dopamine-Gated Agentic Memory), a biologically inspired architecture that decouples short-term interaction from cognitive restructuring via a Fast/Slow routing system based on Reward Prediction Error (RPE). A lightweight Critic Router evaluates stimuli for Surprise and Utility. Routine, low-RPE inputs are bypassed or cached in an O(1) fast-access buffer. Conversely, high-RPE inputs, such as factual contradictions or preference shifts, trigger a "dopamine" signal, activating the O(N) memory evolution pipeline to reshape the agent's knowledge graph. To evaluate performance under realistic conditions, we introduce the LoCoMo-Noise benchmark, which injects controlled conversational noise into long-term sessions. Evaluations demonstrate that D-MEM reduces token consumption by over 80%, eliminates O(N^2) bottlenecks, and outperforms baselines in multi-hop reasoning and adversarial resilience. By selectively gating cognitive restructuring, D-MEM provides a scalable, cost-efficient foundation for lifelong agentic memory.

Training a neural network is a monolithic endeavor, akin to carving knowledge into stone: once the process is completed, editing the knowledge in a network is nearly impossible, since all information is distributed across the network's weights. We here explore a simple, compelling alternative by marrying the representational power of deep neural networks with the flexibility of a database. Decomposing the task of image classification into image similarity (from a pre-trained embedding) and search (via fast nearest neighbor retrieval from a knowledge database), we build a simple and flexible visual memory that has the following key capabilities: (1.) The ability to flexibly add data across scales: from individual samples all the way to entire classes and billion-scale data; (2.) The ability to remove data through unlearning and memory pruning; (3.) An interpretable decision-mechanism on which we can intervene to control its behavior. Taken together, these capabilities comprehensively demonstrate the benefits of an explicit visual memory. We hope that it might contribute to a conversation on how knowledge should be represented in deep vision models -- beyond carving it in ``stone'' weights.

Self-attention lets each token retrieve information from the full context, but its quadratic cost in sequence length limits training and inference at long context. This paper presents a comparative study of softmax attention and four recent recurrent linear-attention architectures: DeltaNet, Gated DeltaNet, Kimi Delta Attention, and Gated DeltaNet-2. We express these mechanisms in a common recurrent-memory notation, making explicit how they differ in expressivity, memory decay, erase and write control, training throughput, and implementation complexity. Our experiments center on 350M-parameter models trained for 15B tokens, and include optimizer and learning-rate comparisons, hybrid-versus-pure stack comparisons, sequence-length runtime measurements, larger DeltaNet runs at 1.3B and 3B parameters, and a small set of downstream evaluations. The reported speed results measure training throughput and iteration time; we do not provide an empirical inference-speed benchmark. Within the reported 350M-parameter, 15B-token sweep, Kimi Delta Attention with Muon reaches the lowest final validation loss, a pure Gated DeltaNet stack trained with AdamW has the highest normalized training throughput, hybrid stacks generally improve loss at a throughput cost, and Muon consistently lowers final validation loss relative to AdamW in the matched architecture settings we evaluate. We introduce and evaluate lightweight cross-layer routing mechanisms for DeltaNet-style memories. The most natural DeltaNet-inspired formulation, forwarding a lower layer's delta-rule write error into the next layer's value target, does not improve over matched baselines. Routing into the aligned hidden stream and forwarding the write value instead yields a modest improvement in the matched runs we report: Cross-Layer Value Routing (CLVR) lowers final validation loss for both DeltaNet and Gated DeltaNet.

Robotic manipulation tasks exhibit varying memory requirements, ranging from Markovian tasks that require no memory to non-Markovian tasks that depend on historical information spanning single or multiple interaction trials. Surprisingly, simply extending observation histories of a visuomotor policy often leads to a significant performance drop due to distribution shift and overfitting. To address these issues, we propose Gated Memory Policy (GMP), a visuomotor policy that learns both when to recall memory and what to recall. To learn when to recall memory, GMP employs a learned memory gate mechanism that selectively activates history context only when necessary, improving robustness and reactivity. To learn what to recall efficiently, GMP introduces a lightweight cross-attention module that constructs effective latent memory representations. To further enhance robustness, GMP injects diffusion noise into historical actions, mitigating sensitivity to noisy or inaccurate histories during both training and inference. On our proposed non-Markovian benchmark MemMimic, GMP achieves a 30.1% average success rate improvement over long-history baselines, while maintaining competitive performance on Markovian tasks in RoboMimic. All code, data and in-the-wild deployment instructions are available on our project website https://gated-memory-policy.github.io/.

Transformers have been established as the de-facto backbones for most recent advances in sequence modeling, mainly due to their growing memory capacity that scales with the context length. While plausible for retrieval tasks, it causes quadratic complexity and so has motivated recent studies to explore viable subquadratic recurrent alternatives. Despite showing promising preliminary results in diverse domains, such recurrent architectures underperform Transformers in recall-intensive tasks, often attributed to their fixed-size memory. In this paper, we introduce Memory Caching (MC), a simple yet effective technique that enhances recurrent models by caching checkpoints of their memory states (a.k.a. hidden states). Memory Caching allows the effective memory capacity of RNNs to grow with sequence length, offering a flexible trade-off that interpolates between the fixed memory (i.e., O(L) complexity) of RNNs and the growing memory (i.e., O(L^2) complexity) of Transformers. We propose four variants of MC, including gated aggregation and sparse selective mechanisms, and discuss their implications on both linear and deep memory modules. Our experimental results on language modeling, and long-context understanding tasks show that MC enhances the performance of recurrent models, supporting its effectiveness. The results of in-context recall tasks indicate that while Transformers achieve the best accuracy, our MC variants show competitive performance, close the gap with Transformers, and performs better than state-of-the-art recurrent models.

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In this work, we propose a novel algorithm to find efficient low-rank subnetworks. Remarkably, these subnetworks are determined and adapted already during the training phase and the overall time and memory resources required by both training and evaluating them are significantly reduced. The main idea is to restrict the weight matrices to a low-rank manifold and to update the low-rank factors rather than the full matrix during training. To derive training updates that are restricted to the prescribed manifold, we employ techniques from dynamic model order reduction for matrix differential equations. This allows us to provide approximation, stability, and descent guarantees. Moreover, our method automatically and dynamically adapts the ranks during training to achieve the desired approximation accuracy. The efficiency of the proposed method is demonstrated through a variety of numerical experiments on fully-connected and convolutional networks.

Memory layers use a trainable key-value lookup mechanism to add extra parameters to a model without increasing FLOPs. Conceptually, sparsely activated memory layers complement compute-heavy dense feed-forward layers, providing dedicated capacity to store and retrieve information cheaply. This work takes memory layers beyond proof-of-concept, proving their utility at contemporary scale. On downstream tasks, language models augmented with our improved memory layer outperform dense models with more than twice the computation budget, as well as mixture-of-expert models when matched for both compute and parameters. We find gains are especially pronounced for factual tasks. We provide a fully parallelizable memory layer implementation, demonstrating scaling laws with up to 128B memory parameters, pretrained to 1 trillion tokens, comparing to base models with up to 8B parameters.

Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature. For many years this bottleneck has persisted, as many thought sequential models could not be parallelized. We challenge this long-held belief with our parallel algorithm that accelerates GPU evaluation of sequential models by up to 3 orders of magnitude faster without compromising output accuracy. The algorithm does not need any special structure in the sequential models' architecture, making it applicable to a wide range of architectures. Using our method, training sequential models can be more than 10 times faster than the common sequential method without any meaningful difference in the training results. Leveraging this accelerated training, we discovered the efficacy of the Gated Recurrent Unit in a long time series classification problem with 17k time samples. By overcoming the training bottleneck, our work serves as the first step to unlock the potential of non-linear sequential models for long sequence problems.

The structure of biological neural circuits-modular, hierarchical, and sparsely interconnected-reflects an efficient trade-off between wiring cost, functional specialization, and robustness. These principles offer valuable insights for artificial neural network (ANN) design, especially as networks grow in depth and scale. Sparsity, in particular, has been widely explored for reducing memory and computation, improving speed, and enhancing generalization. Motivated by systems neuroscience findings, we explore how patterns of functional connectivity in the mouse visual cortex-specifically, ensemble-to-ensemble communication, can inform ANN design. We introduce G2GNet, a novel architecture that imposes sparse, modular connectivity across feedforward layers. Despite having significantly fewer parameters than fully connected models, G2GNet achieves superior accuracy on standard vision benchmarks. To our knowledge, this is the first architecture to incorporate biologically observed functional connectivity patterns as a structural bias in ANN design. We complement this static bias with a dynamic sparse training (DST) mechanism that prunes and regrows edges during training. We also propose a Hebbian-inspired rewiring rule based on activation correlations, drawing on principles of biological plasticity. G2GNet achieves up to 75% sparsity while improving accuracy by up to 4.3% on benchmarks, including Fashion-MNIST, CIFAR-10, and CIFAR-100, outperforming dense baselines with far fewer computations.

Efficient key-value (KV) cache management is crucial for the practical deployment of large language models (LLMs), yet existing compression techniques often incur a trade-off between performance degradation and computational overhead. We propose a novel gating-based KV cache eviction method for frozen-weight LLMs that achieves high compression ratios with negligible computational cost. Our approach introduces lightweight sink-attention gating modules to identify and retain critical KV pairs, and integrates seamlessly into both the prefill and decoding stages. The proposed gate training algorithm relies on forward passes of an LLM, avoiding expensive backpropagation, while achieving strong task generalization through a task-agnostic reconstruction objective. Extensive experiments across the Qwen2.5-1M, Qwen3, and Gemma3 families show that our method maintains near-lossless performance while evicting up to 70% of the KV cache. The results are consistent across a wide range of tasks, including long-context understanding, code comprehension, and mathematical reasoning, demonstrating the generality of our approach.

Large language model (LLM)-based multi-agent systems tackle complex reasoning by orchestrating how multiple agents are configured and how they collaborate. A central challenge is to adapt orchestration to the evolving collaboration state. Routing from the query alone cannot adapt to intermediate progress or errors, which hurts accuracy. Routing from the complete execution history supplies this missing context, but forces later decisions to process every prior step, including redundant or low-utility ones. This creates an execution-history overload that inflates cost. Effective orchestration instead requires a compact state that captures useful progress without accumulating redundant context. We propose Gated-Memory Routing, which conditions each decision on the query and a learned execution memory. A learned Memory Write Gate commits only non-redundant reasoning steps, and a learned Retrieval Gate supplies each agent a compact, relevant subset, so every decision conditions on a clean, informative state. At each step, the system selects the next role and backbone from this memory, while an Adaptive Halting Controller stops execution once the memory contains sufficient evidence for answering. Across five reasoning and code-generation benchmarks, our framework is both effective and efficient: it attains the best average accuracy, exceeding the strongest baseline by 2.44 points, while reducing HumanEval inference cost by 31.9% relative to that baseline. Code is available at https://github.com/rajibrhasan/gated-memory-routing

Spiking Neural Networks (SNNs) have been widely praised for their high energy efficiency and immense potential. However, comprehensive research that critically contrasts and correlates SNNs with quantized Artificial Neural Networks (ANNs) remains scant, often leading to skewed comparisons lacking fairness towards ANNs. This paper introduces a unified perspective, illustrating that the time steps in SNNs and quantized bit-widths of activation values present analogous representations. Building on this, we present a more pragmatic and rational approach to estimating the energy consumption of SNNs. Diverging from the conventional Synaptic Operations (SynOps), we champion the "Bit Budget" concept. This notion permits an intricate discourse on strategically allocating computational and storage resources between weights, activation values, and temporal steps under stringent hardware constraints. Guided by the Bit Budget paradigm, we discern that pivoting efforts towards spike patterns and weight quantization, rather than temporal attributes, elicits profound implications for model performance. Utilizing the Bit Budget for holistic design consideration of SNNs elevates model performance across diverse data types, encompassing static imagery and neuromorphic datasets. Our revelations bridge the theoretical chasm between SNNs and quantized ANNs and illuminate a pragmatic trajectory for future endeavors in energy-efficient neural computations.

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

Linear recurrent neural networks have emerged as efficient alternatives to the original Transformer's softmax attention mechanism, thanks to their highly parallelizable training and constant memory and computation requirements at inference. Iterative refinements of these models have introduced an increasing number of architectural mechanisms, leading to increased complexity and computational costs. Nevertheless, systematic direct comparisons among these models remain limited. Existing benchmark tasks are either too simplistic to reveal substantial differences or excessively resource-intensive for experimentation. In this work, we propose a refined taxonomy of linear recurrent models and introduce SelectivBench, a set of lightweight and customizable synthetic benchmark tasks for systematically evaluating sequence models. SelectivBench specifically evaluates selectivity in sequence models at small to medium scale, such as the capacity to focus on relevant inputs while ignoring context-based distractors. It employs rule-based grammars to generate sequences with adjustable complexity, incorporating irregular gaps that intentionally violate transition rules. Evaluations of linear recurrent models on SelectivBench reveal performance patterns consistent with results from large-scale language tasks. Our analysis clarifies the roles of essential architectural features: gating and rapid forgetting mechanisms facilitate recall, in-state channel mixing is unnecessary for selectivity, but critical for generalization, and softmax attention remains dominant due to its memory capacity scaling with sequence length. Our benchmark enables targeted, efficient exploration of linear recurrent models and provides a controlled setting for studying behaviors observed in large-scale evaluations. Code is available at https://github.com/symseqbench/selectivbench

Memory footprint is one of the main limiting factors for large neural network training. In backpropagation, one needs to store the input to each operation in the computational graph. Every modern neural network model has quite a few pointwise nonlinearities in its architecture, and such operation induces additional memory costs which -- as we show -- can be significantly reduced by quantization of the gradients. We propose a systematic approach to compute optimal quantization of the retained gradients of the pointwise nonlinear functions with only a few bits per each element. We show that such approximation can be achieved by computing optimal piecewise-constant approximation of the derivative of the activation function, which can be done by dynamic programming. The drop-in replacements are implemented for all popular nonlinearities and can be used in any existing pipeline. We confirm the memory reduction and the same convergence on several open benchmarks.

Random Neural Networks (RNNs) are a class of Neural Networks (NNs) that can also be seen as a specific type of queuing network. They have been successfully used in several domains during the last 25 years, as queuing networks to analyze the performance of resource sharing in many engineering areas, as learning tools and in combinatorial optimization, where they are seen as neural systems, and also as models of neurological aspects of living beings. In this article we focus on their learning capabilities, and more specifically, we present a practical guide for using the RNN to solve supervised learning problems. We give a general description of these models using almost indistinctly the terminology of Queuing Theory and the neural one. We present the standard learning procedures used by RNNs, adapted from similar well-established improvements in the standard NN field. We describe in particular a set of learning algorithms covering techniques based on the use of first order and, then, of second order derivatives. We also discuss some issues related to these objects and present new perspectives about their use in supervised learning problems. The tutorial describes their most relevant applications, and also provides a large bibliography.

This paper tackles the problem of semi-supervised video object segmentation on resource-constrained devices, such as mobile phones. We formulate this problem as a distillation task, whereby we demonstrate that small space-time-memory networks with finite memory can achieve competitive results with state of the art, but at a fraction of the computational cost (32 milliseconds per frame on a Samsung Galaxy S22). Specifically, we provide a theoretically grounded framework that unifies knowledge distillation with supervised contrastive representation learning. These models are able to jointly benefit from both pixel-wise contrastive learning and distillation from a pre-trained teacher. We validate this loss by achieving competitive J&F to state of the art on both the standard DAVIS and YouTube benchmarks, despite running up to 5x faster, and with 32x fewer parameters.

Over more than a decade there has been an extensive research effort on how to effectively utilize recurrent models and attention. While recurrent models aim to compress the data into a fixed-size memory (called hidden state), attention allows attending to the entire context window, capturing the direct dependencies of all tokens. This more accurate modeling of dependencies, however, comes with a quadratic cost, limiting the model to a fixed-length context. We present a new neural long-term memory module that learns to memorize historical context and helps attention to attend to the current context while utilizing long past information. We show that this neural memory has the advantage of fast parallelizable training while maintaining a fast inference. From a memory perspective, we argue that attention due to its limited context but accurate dependency modeling performs as a short-term memory, while neural memory due to its ability to memorize the data, acts as a long-term, more persistent, memory. Based on these two modules, we introduce a new family of architectures, called Titans, and present three variants to address how one can effectively incorporate memory into this architecture. Our experimental results on language modeling, common-sense reasoning, genomics, and time series tasks show that Titans are more effective than Transformers and recent modern linear recurrent models. They further can effectively scale to larger than 2M context window size with higher accuracy in needle-in-haystack tasks compared to baselines.

The prevalent approach to sequence to sequence learning maps an input sequence to a variable length output sequence via recurrent neural networks. We introduce an architecture based entirely on convolutional neural networks. Compared to recurrent models, computations over all elements can be fully parallelized during training and optimization is easier since the number of non-linearities is fixed and independent of the input length. Our use of gated linear units eases gradient propagation and we equip each decoder layer with a separate attention module. We outperform the accuracy of the deep LSTM setup of Wu et al. (2016) on both WMT'14 English-German and WMT'14 English-French translation at an order of magnitude faster speed, both on GPU and CPU.

The pre-dominant approach to language modeling to date is based on recurrent neural networks. Their success on this task is often linked to their ability to capture unbounded context. In this paper we develop a finite context approach through stacked convolutions, which can be more efficient since they allow parallelization over sequential tokens. We propose a novel simplified gating mechanism that outperforms Oord et al (2016) and investigate the impact of key architectural decisions. The proposed approach achieves state-of-the-art on the WikiText-103 benchmark, even though it features long-term dependencies, as well as competitive results on the Google Billion Words benchmark. Our model reduces the latency to score a sentence by an order of magnitude compared to a recurrent baseline. To our knowledge, this is the first time a non-recurrent approach is competitive with strong recurrent models on these large scale language tasks.

In-Context Learning (ICL) in transformers acts as an online associative memory and is believed to underpin their high performance on complex sequence processing tasks. However, in gated linear attention models, this memory has a fixed capacity and is prone to interference, especially for long sequences. We propose Palimpsa, a self-attention model that views ICL as a continual learning problem that must address a stability-plasticity dilemma. Palimpsa uses Bayesian metaplasticity, where the plasticity of each attention state is tied to an importance state grounded by a prior distribution that captures accumulated knowledge. We demonstrate that various gated linear attention models emerge as specific architecture choices and posterior approximations, and that Mamba2 is a special case of Palimpsa where forgetting dominates. This theoretical link enables the transformation of any non-metaplastic model into a metaplastic one, significantly expanding its memory capacity. Our experiments show that Palimpsa consistently outperforms baselines on the Multi-Query Associative Recall (MQAR) benchmark and on Commonsense Reasoning tasks.

Recent research developing neural network architectures with external memory have often used the benchmark bAbI question and answering dataset which provides a challenging number of tasks requiring reasoning. Here we employed a classic associative inference task from the memory-based reasoning neuroscience literature in order to more carefully probe the reasoning capacity of existing memory-augmented architectures. This task is thought to capture the essence of reasoning -- the appreciation of distant relationships among elements distributed across multiple facts or memories. Surprisingly, we found that current architectures struggle to reason over long distance associations. Similar results were obtained on a more complex task involving finding the shortest path between nodes in a path. We therefore developed MEMO, an architecture endowed with the capacity to reason over longer distances. This was accomplished with the addition of two novel components. First, it introduces a separation between memories (facts) stored in external memory and the items that comprise these facts in external memory. Second, it makes use of an adaptive retrieval mechanism, allowing a variable number of "memory hops" before the answer is produced. MEMO is capable of solving our novel reasoning tasks, as well as match state of the art results in bAbI.

Recent works have suggested that finite Bayesian neural networks may sometimes outperform their infinite cousins because finite networks can flexibly adapt their internal representations. However, our theoretical understanding of how the learned hidden layer representations of finite networks differ from the fixed representations of infinite networks remains incomplete. Perturbative finite-width corrections to the network prior and posterior have been studied, but the asymptotics of learned features have not been fully characterized. Here, we argue that the leading finite-width corrections to the average feature kernels for any Bayesian network with linear readout and Gaussian likelihood have a largely universal form. We illustrate this explicitly for three tractable network architectures: deep linear fully-connected and convolutional networks, and networks with a single nonlinear hidden layer. Our results begin to elucidate how task-relevant learning signals shape the hidden layer representations of wide Bayesian neural networks.

Self-attention gives LLMs fine-grained, query-dependent access to context, but dense token interactions incur quadratic prefill cost and a key--value cache growing with context length. Research thus spans explicit-memory compression, sparse access, recurrent state construction, structured state dynamics, and heterogeneous mechanism composition. This survey analyzes these developments as model-internal contextual memory. We introduce a five-dimensional lens---Memory Representation, Memory Update, Access, Readout, and Integration---describing what is represented, how it changes, what is query-eligible, how it is read, and how readouts form outputs. This lens compares overlapping research lines without imposing one computational model. We reconstruct mechanism-level developments and architectural adoption using 59 release-level records from 14 major model lineages and 11 high-performing open-weight endpoints. First, explicit-memory and recurrent-state methods retain distinct interfaces but increasingly control overlapping memory functions. Second, heterogeneous architectures increasingly coordinate across network depth: layer-wise composition distributes complementary memory processing across representational stages, while cross-layer reuse carries selected memory and routing artifacts forward. Depth thus becomes a dimension along which contextual memory is constructed and managed. Third, these developments motivate a stateful multidimensional memory-routing hypothesis: persistent memory is organized across temporal scope, network depth, substrate type, and representation granularity, while coordinated Sparse Write and Sparse Read determine what is maintained and what contributes to each query. Overall, efficient sequence architecture design increasingly concerns the organization, lifecycle, and selective use of contextual memory rather than an isolated Attention operator.

This paper introduces a structured memory which can be easily integrated into a neural network. The memory is very large by design and significantly increases the capacity of the architecture, by up to a billion parameters with a negligible computational overhead. Its design and access pattern is based on product keys, which enable fast and exact nearest neighbor search. The ability to increase the number of parameters while keeping the same computational budget lets the overall system strike a better trade-off between prediction accuracy and computation efficiency both at training and test time. This memory layer allows us to tackle very large scale language modeling tasks. In our experiments we consider a dataset with up to 30 billion words, and we plug our memory layer in a state-of-the-art transformer-based architecture. In particular, we found that a memory augmented model with only 12 layers outperforms a baseline transformer model with 24 layers, while being twice faster at inference time. We release our code for reproducibility purposes.