Daily Papers

The precise timing of spikes emitted by neurons plays a crucial role in shaping the response of efferent biological neurons. This temporal dimension of neural activity holds significant importance in understanding information processing in neurobiology, especially for the performance of neuromorphic hardware, such as event-based cameras. Nonetheless, many artificial neural models disregard this critical temporal dimension of neural activity. In this study, we present a model designed to efficiently detect temporal spiking motifs using a layer of spiking neurons equipped with heterogeneous synaptic delays. Our model capitalizes on the diverse synaptic delays present on the dendritic tree, enabling specific arrangements of temporally precise synaptic inputs to synchronize upon reaching the basal dendritic tree. We formalize this process as a time-invariant logistic regression, which can be trained using labeled data. To demonstrate its practical efficacy, we apply the model to naturalistic videos transformed into event streams, simulating the output of the biological retina or event-based cameras. To evaluate the robustness of the model in detecting visual motion, we conduct experiments by selectively pruning weights and demonstrate that the model remains efficient even under significantly reduced workloads. In conclusion, by providing a comprehensive, event-driven computational building block, the incorporation of heterogeneous delays has the potential to greatly improve the performance of future spiking neural network algorithms, particularly in the context of neuromorphic chips.

This thesis presents and evaluates the Dilated Convolution with Learnable Spacings (DCLS) method. Through various supervised learning experiments in the fields of computer vision, audio, and speech processing, the DCLS method proves to outperform both standard and advanced convolution techniques. The research is organized into several steps, starting with an analysis of the literature and existing convolution techniques that preceded the development of the DCLS method. We were particularly interested in the methods that are closely related to our own and that remain essential to capture the nuances and uniqueness of our approach. The cornerstone of our study is the introduction and application of the DCLS method to convolutional neural networks (CNNs), as well as to hybrid architectures that rely on both convolutional and visual attention approaches. DCLS is shown to be particularly effective in tasks such as classification, semantic segmentation, and object detection. Initially using bilinear interpolation, the study also explores other interpolation methods, finding that Gaussian interpolation slightly improves performance. The DCLS method is further applied to spiking neural networks (SNNs) to enable synaptic delay learning within a neural network that could eventually be transferred to so-called neuromorphic chips. The results show that the DCLS method stands out as a new state-of-the-art technique in SNN audio classification for certain benchmark tasks in this field. These tasks involve datasets with a high temporal component. In addition, we show that DCLS can significantly improve the accuracy of artificial neural networks for the multi-label audio classification task. We conclude with a discussion of the chosen experimental setup, its limitations, the limitations of our method, and our results.

This work presents the Parallelized Hierarchical Connectome (PHC), a general architectural framework that upgrades temporal-only State-Space Models (SSMs) into spatiotemporal recurrent networks. Conventional SSMs achieve parallel-scan training but are limited to temporal recurrence, lacking lateral or feedback interactions within a single timestep. PHC maps the diagonal SSM core to a shared Neuron Layer and inter-neuronal communication to a shared Synapse Layer of hierarchical regions, reconnected by a Multi-Transmission Loop iterating spatial recurrence within each temporal window, at parameter complexity Theta(D^2) versus Theta(D^2 L) of stacked SSMs. This spatiotemporal framework enables the seamless integration of neuro-physical priors typically intractable for standard SSMs, including adaptive LIF, synaptic delay, STP, Dale's Law with E/I-asymmetric topology, and STDP. The framework is instantiated as PHCSSM, the first spiking SSM that integrates all five biological priors and is evaluated on long-sequence data, achieving test accuracy competitive with state-of-the-art SSM baselines at 1,312 to 4,891 trainable parameters (1 to 4 orders of magnitude smaller than every baseline). PHCSSM further admits a sequential recurrent spiking neural network (RSNN) deployment mode that converges asymptotically to the parallel-scan training mode without artificial-neural-network-to-spiking-neural-network (ANN-to-SNN) conversion, with cross-backend reproducibility verified across four hardware backends (x86 CPU, H100 GPU, Cortex-A76, Cortex-M4F) including end-to-end deployment on the Cortex-M4F microcontroller (40 KB SRAM, 128 KB Flash). PHCSSM thereby bridges parallel-scan SSM and biologically grounded RSNN, two paradigms with previously incompatible training regimes, into a single architecture and trained weights.

Spiking Neural Networks (SNNs) are a promising research direction for building power-efficient information processing systems, especially for temporal tasks such as speech recognition. In SNNs, delays refer to the time needed for one spike to travel from one neuron to another. These delays matter because they influence the spike arrival times, and it is well-known that spiking neurons respond more strongly to coincident input spikes. More formally, it has been shown theoretically that plastic delays greatly increase the expressivity in SNNs. Yet, efficient algorithms to learn these delays have been lacking. Here, we propose a new discrete-time algorithm that addresses this issue in deep feedforward SNNs using backpropagation, in an offline manner. To simulate delays between consecutive layers, we use 1D convolutions across time. The kernels contain only a few non-zero weights - one per synapse - whose positions correspond to the delays. These positions are learned together with the weights using the recently proposed Dilated Convolution with Learnable Spacings (DCLS). We evaluated our method on three datasets: the Spiking Heidelberg Dataset (SHD), the Spiking Speech Commands (SSC) and its non-spiking version Google Speech Commands v0.02 (GSC) benchmarks, which require detecting temporal patterns. We used feedforward SNNs with two or three hidden fully connected layers, and vanilla leaky integrate-and-fire neurons. We showed that fixed random delays help and that learning them helps even more. Furthermore, our method outperformed the state-of-the-art in the three datasets without using recurrent connections and with substantially fewer parameters. Our work demonstrates the potential of delay learning in developing accurate and precise models for temporal data processing. Our code is based on PyTorch / SpikingJelly and available at: https://github.com/Thvnvtos/SNN-delays

Human cognition emerges from coordinated spiking dynamics in distributed neural circuits, where information is encoded via both firing rates and precise spike timing determined by brain rhythms. Inspired by this notion, we propose a brain-inspired learning primitive in which cognition-level neural synchrony emerges through iterative bottom-up and top-down interactions between micro-scale dynamics of spiking neurons and a macro-scale mechanism of oscillatory synchronization. Specifically, we model each parcel (e.g., a cortical region or an image pixel) in the target system as a spiking neuron embedded in a predefined connectivity scaffold. Low-level information is encoded in a spatiotemporal domain, where neurons are selectively grouped and fire spontaneously over time through self-organized dynamics. In the bottom-up route, oscillatory synchronization is formed from past spiking activity accumulated over a finite memory window. Since brain dynamics operate in a regime of partial and transient synchronization rather than global phase locking, we model oscillatory coordination using a time-delayed synchronization formulation, which enables a top-down modulation of heterogeneous neural spiking for a large-scale distributed system. Together, we devise a spiking-by-synchronization neural network (S2-Net) that uses rhythmic timing as a control mechanism for efficient information processing. Promising results have been achieved across a broad range of tasks, including neural activity decoding, energy-efficient signal processing, temporal binding and semantic reasoning.

Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by non-ideal biological building blocks which can impose significant error. We explore quantitatively how the brain might cope with this inherent source of error by taking advantage of two ubiquitous mechanisms, redundancy and synchronization. In particular we consider a neural process whose goal is to learn a decision function by implementing a nonlinear gradient dynamics. The dynamics, however, are assumed to be corrupted by perturbations modeling the error which might be incurred due to limitations of the biology, intrinsic neuronal noise, and imperfect measurements. We show that error, and the associated uncertainty surrounding a learned solution, can be controlled in large part by trading off synchronization strength among multiple redundant neural systems against the noise amplitude. The impact of the coupling between such redundant systems is quantified by the spectrum of the network Laplacian, and we discuss the role of network topology in synchronization and in reducing the effect of noise. A range of situations in which the mechanisms we model arise in brain science are discussed, and we draw attention to experimental evidence suggesting that cortical circuits capable of implementing the computations of interest here can be found on several scales. Finally, simulations comparing theoretical bounds to the relevant empirical quantities show that the theoretical estimates we derive can be tight.

High-resolution brain imaging can now capture not just synapse locations but their molecular composition, with the cost of such mapping falling exponentially. Yet such ultrastructural data has so far told us little about local neuronal physiology - specifically, the parameters (e.g., synaptic efficacies, local conductances) that govern neural dynamics. We propose to translate molecularly annotated ultrastructure into physiology, introducing the concept of an ultrastructure-to-dynamics compiler: a learned mapping from molecularly annotated ultrastructure to simulator-ready, uncertainty-aware physiological parameters. The requirement is paired training data, with jointly acquired ultrastructure from imaging, and dynamical responses to perturbations from physiological experiments. With this data we can train models that predict local physiology directly from structure. Such a compiler would support biophysical simulations by turning anatomical maps into models of circuit dynamics, shifting structure-to-function from a descriptive program to a predictive one and opening routes to understanding neural computation and forecasting intervention effects.

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.

Why do neurons communicate through spikes? By definition, spikes are all-or-none neural events which occur at continuous times. In other words, spikes are on one side binary, existing or not without further details, and on the other can occur at any asynchronous time, without the need for a centralized clock. This stands in stark contrast to the analog representation of values and the discretized timing classically used in digital processing and at the base of modern-day neural networks. As neural systems almost systematically use this so-called event-based representation in the living world, a better understanding of this phenomenon remains a fundamental challenge in neurobiology in order to better interpret the profusion of recorded data. With the growing need for intelligent embedded systems, it also emerges as a new computing paradigm to enable the efficient operation of a new class of sensors and event-based computers, called neuromorphic, which could enable significant gains in computation time and energy consumption -- a major societal issue in the era of the digital economy and global warming. In this review paper, we provide evidence from biology, theory and engineering that the precise timing of spikes plays a crucial role in our understanding of the efficiency of neural networks.

Compared with rate-based artificial neural networks, Spiking Neural Networks (SNN) provide a more biological plausible model for the brain. But how they perform supervised learning remains elusive. Inspired by recent works of Bengio et al., we propose a supervised learning algorithm based on Spike-Timing Dependent Plasticity (STDP) for a hierarchical SNN consisting of Leaky Integrate-and-fire (LIF) neurons. A time window is designed for the presynaptic neuron and only the spikes in this window take part in the STDP updating process. The model is trained on the MNIST dataset. The classification accuracy approach that of a Multilayer Perceptron (MLP) with similar architecture trained by the standard back-propagation algorithm.

How neuronal circuits achieve credit assignment remains a central unsolved question in systems neuroscience. Various studies have suggested plausible solutions for back-propagating error signals through multi-layer networks. These purely functionally motivated models assume distinct neuronal compartments to represent local error signals that determine the sign of synaptic plasticity. However, this explicit error modulation is inconsistent with phenomenological plasticity models in which the sign depends primarily on postsynaptic activity. Here we show how a plausible microcircuit model and Hebbian learning rule derived within an adaptive control theory framework can resolve this discrepancy. Assuming errors are encoded in top-down dis-inhibitory synaptic afferents, we show that error-modulated learning emerges naturally at the circuit level when recurrent inhibition explicitly influences Hebbian plasticity. The same learning rule accounts for experimentally observed plasticity in the absence of inhibition and performs comparably to back-propagation of error (BP) on several non-linearly separable benchmarks. Our findings bridge the gap between functional and experimentally observed plasticity rules and make concrete predictions on inhibitory modulation of excitatory plasticity.

The Spiking Neural Network (SNN) has attracted more and more attention recently. It adopts binary spike signals to transmit information. Benefitting from the information passing paradigm of SNNs, the multiplications of activations and weights can be replaced by additions, which are more energy-efficient. However, its ``Hard Reset" mechanism for the firing activity would ignore the difference among membrane potentials when the membrane potential is above the firing threshold, causing information loss. Meanwhile, quantifying the membrane potential to 0/1 spikes at the firing instants will inevitably introduce the quantization error thus bringing about information loss too. To address these problems, we propose to use the ``Soft Reset" mechanism for the supervised training-based SNNs, which will drive the membrane potential to a dynamic reset potential according to its magnitude, and Membrane Potential Rectifier (MPR) to reduce the quantization error via redistributing the membrane potential to a range close to the spikes. Results show that the SNNs with the ``Soft Reset" mechanism and MPR outperform their vanilla counterparts on both static and dynamic datasets.

Learning synaptic weights of spiking neural network (SNN) models that can reproduce target spike trains from provided neural firing data is a central problem in computational neuroscience and spike-based computing. The discovery of the optimal weight values can be posed as a supervised learning task wherein the weights of the model network are chosen to maximize the similarity between the target spike trains and the model outputs. It is still largely unknown whether optimizing spike train similarity of highly recurrent SNNs produces weight matrices similar to those of the ground truth model. To this end, we propose flexible heuristic supervised learning rules, termed Pre-Synaptic Pool Modification (PSPM), that rely on stochastic weight updates in order to produce spikes within a short window of the desired times and eliminate spikes outside of this window. PSPM improves spike train similarity for all-to-all SNNs and makes no assumption about the post-synaptic potential of the neurons or the structure of the network since no gradients are required. We test whether optimizing for spike train similarity entails the discovery of accurate weights and explore the relative contributions of local and homeostatic weight updates. Although PSPM improves similarity between spike trains, the learned weights often differ from the weights of the ground truth model, implying that connectome inference from spike data may require additional constraints on connectivity statistics. We also find that spike train similarity is sensitive to local updates, but other measures of network activity such as avalanche distributions, can be learned through synaptic homeostasis.

The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors at different times. We introduce an unsupervised approach to learn the dynamic affinities between neurons in live, behaving animals, and to reveal which communities form among neurons at different times. The inference occurs in two major steps. First, pairwise non-linear affinities between neuronal traces from brain-wide calcium activity are organized by non-negative tensor factorization (NTF). Each factor specifies which groups of neurons are most likely interacting for an inferred interval in time, and for which animals. Finally, a generative model that allows for weighted community detection is applied to the functional motifs produced by NTF to reveal a dynamic functional connectome. Since time codes the different experimental variables (e.g., application of chemical stimuli), this provides an atlas of neural motifs active during separate stages of an experiment (e.g., stimulus application or spontaneous behaviors). Results from our analysis are experimentally validated, confirming that our method is able to robustly predict causal interactions between neurons to generate behavior. Code is available at https://github.com/dyballa/dynamic-connectomes.

Spiking Neural Networks (SNNs) have emerged as a promising substitute for Artificial Neural Networks (ANNs) due to their advantages of fast inference and low power consumption. However, the lack of efficient training algorithms has hindered their widespread adoption. Even efficient ANN-SNN conversion methods necessitate quantized training of ANNs to enhance the effectiveness of the conversion, incurring additional training costs. To address these challenges, we propose an efficient ANN-SNN conversion framework with only inference scale complexity. The conversion framework includes a local threshold balancing algorithm, which enables efficient calculation of the optimal thresholds and fine-grained adjustment of the threshold value by channel-wise scaling. We also introduce an effective delayed evaluation strategy to mitigate the influence of the spike propagation delays. We demonstrate the scalability of our framework in typical computer vision tasks: image classification, semantic segmentation, object detection, and video classification. Our algorithm outperforms existing methods, highlighting its practical applicability and efficiency. Moreover, we have evaluated the energy consumption of the converted SNNs, demonstrating their superior low-power advantage compared to conventional ANNs. This approach simplifies the deployment of SNNs by leveraging open-source pre-trained ANN models, enabling fast, low-power inference with negligible performance reduction. Code is available at https://github.com/putshua/Inference-scale-ANN-SNN.

The approximation capability of ANNs and their RNN instantiations, is strongly correlated with the number of parameters packed into these networks. However, the complexity barrier for human understanding, is arguably related to the number of neurons and synapses in the networks, and to the associated nonlinear transformations. In this paper we show that the use of biophysical synapses, as found in LTCs, have two main benefits. First, they allow to pack more parameters for a given number of neurons and synapses. Second, they allow to formulate the nonlinear-network transformation, as a linear system with state-dependent coefficients. Both increase interpretability, as for a given task, they allow to learn a system linear in its input features, that is smaller in size compared to the state of the art. We substantiate the above claims on various time-series prediction tasks, but we believe that our results are applicable to any feedforward or recurrent ANN.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point, or stationary distribution) towards a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged towards their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal 'back-propagated' during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not.

Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only occurring locally, over a node's immediate neighbours. Rewiring approaches attempting to make graphs 'more connected', and supposedly better suited to long-range tasks, often lose the inductive bias provided by distance on the graph since they make distant nodes communicate instantly at every layer. In this paper we propose a framework, applicable to any MPNN architecture, that performs a layer-dependent rewiring to ensure gradual densification of the graph. We also propose a delay mechanism that permits skip connections between nodes depending on the layer and their mutual distance. We validate our approach on several long-range tasks and show that it outperforms graph Transformers and multi-hop MPNNs.

Recent advances in artificial neural networks for machine learning, and language modeling in particular, have established a family of recurrent neural network (RNN) architectures that, unlike conventional RNNs with vector-form hidden states, use two-dimensional (2D) matrix-form hidden states. Such 2D-state RNNs, known as Fast Weight Programmers (FWPs), can be interpreted as a neural network whose synaptic weights (called fast weights) dynamically change over time as a function of input observations, and serve as short-term memory storage; corresponding synaptic weight modifications are controlled or programmed by another network (the programmer) whose parameters are trained (e.g., by gradient descent). In this Primer, we review the technical foundations of FWPs, their computational characteristics, and their connections to transformers and state space models. We also discuss connections between FWPs and models of synaptic plasticity in the brain, suggesting a convergence of natural and artificial intelligence.

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.

This article is about the neural conundrum behind the slowness of human behavior. The information throughput of a human being is about 10 bits/s. In comparison, our sensory systems gather data at ~10^9 bits/s. The stark contrast between these numbers remains unexplained and touches on fundamental aspects of brain function: What neural substrate sets this speed limit on the pace of our existence? Why does the brain need billions of neurons to process 10 bits/s? Why can we only think about one thing at a time? The brain seems to operate in two distinct modes: the "outer" brain handles fast high-dimensional sensory and motor signals, whereas the "inner" brain processes the reduced few bits needed to control behavior. Plausible explanations exist for the large neuron numbers in the outer brain, but not for the inner brain, and we propose new research directions to remedy this.

Motivated by the celebrated discrete-time model of nervous activity outlined by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the McCulloch-Pitts network (MPN), for sequence learning in spiking neural networks. Our model has a local learning rule, such that the synaptic weight updates depend only on the information directly accessible by the synapse. By exploiting asymmetry in the connections between binary neurons, we show that MPN can be trained to robustly memorize multiple spatiotemporal patterns of binary vectors, generalizing the ability of the symmetric Hopfield network to memorize static spatial patterns. In addition, we demonstrate that the model can efficiently learn sequences of binary pictures as well as generative models for experimental neural spike-train data. Our learning rule is consistent with spike-timing-dependent plasticity (STDP), thus providing a theoretical ground for the systematic design of biologically inspired networks with large and robust long-range sequence storage capacity.

Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled settings, such as DNNs initialized with large-norm parameters or transformers trained on algorithmic datasets. We demonstrate that grokking is actually much more widespread and materializes in a wide range of practical settings, such as training of a convolutional neural network (CNN) on CIFAR10 or a Resnet on Imagenette. We introduce the new concept of delayed robustness, whereby a DNN groks adversarial examples and becomes robust, long after interpolation and/or generalization. We develop an analytical explanation for the emergence of both delayed generalization and delayed robustness based on a new measure of the local complexity of a DNN's input-output mapping. Our local complexity measures the density of the so-called 'linear regions' (aka, spline partition regions) that tile the DNN input space, and serves as a utile progress measure for training. We provide the first evidence that for classification problems, the linear regions undergo a phase transition during training whereafter they migrate away from the training samples (making the DNN mapping smoother there) and towards the decision boundary (making the DNN mapping less smooth there). Grokking occurs post phase transition as a robust partition of the input space emerges thanks to the linearization of the DNN mapping around the training points. Website: https://bit.ly/grok-adversarial

Language models generate responses by producing a series of tokens in immediate succession: the (K+1)^{th} token is an outcome of manipulating K hidden vectors per layer, one vector per preceding token. What if instead we were to let the model manipulate say, K+10 hidden vectors, before it outputs the (K+1)^{th} token? We operationalize this idea by performing training and inference on language models with a (learnable) pause token, a sequence of which is appended to the input prefix. We then delay extracting the model's outputs until the last pause token is seen, thereby allowing the model to process extra computation before committing to an answer. We empirically evaluate pause-training on decoder-only models of 1B and 130M parameters with causal pretraining on C4, and on downstream tasks covering reasoning, question-answering, general understanding and fact recall. Our main finding is that inference-time delays show gains when the model is both pre-trained and finetuned with delays. For the 1B model, we witness gains on 8 of 9 tasks, most prominently, a gain of 18% EM score on the QA task of SQuAD, 8% on CommonSenseQA and 1% accuracy on the reasoning task of GSM8k. Our work raises a range of conceptual and practical future research questions on making delayed next-token prediction a widely applicable new paradigm.

As the prevalence of Alzheimer's disease (AD) rises, improving mechanistic insight from non-invasive biomarkers is increasingly critical. Recent work suggests that circuit-level brain alterations manifest as changes in electroencephalography (EEG) spectral features detectable by machine learning. However, conventional deep learning approaches for EEG-based AD detection are computationally intensive and mechanistically opaque. Spiking neural networks (SNNs) offer a biologically plausible and energy-efficient alternative, yet their application to AD diagnosis remains largely unexplored. We propose a neuro-bridge framework that links data-driven learning with minimal, biophysically grounded simulations, enabling bidirectional interpretation between machine learning signatures and circuit-level mechanisms in AD. Using resting-state clinical EEG, we train an SNN classifier that achieves competitive performance (AUC = 0.839) and identifies the aperiodic 1/f slope as a key discriminative marker. The 1/f slope reflects excitation-inhibition balance. To interpret this mechanistically, we construct spiking network simulations in which inhibitory-to-excitatory synaptic ratios are systematically varied to emulate healthy, mild cognitive impairment, and AD-like states. Using both membrane potential-based and synaptic current-based EEG proxies, we reproduce empirical spectral slowing and altered alpha organization. Incorporating empirical functional connectivity priors into multi-subnetwork simulations further enhances spectral differentiation, demonstrating that large-scale network topology constrains EEG signatures more strongly than excitation-inhibition balance alone. Overall, this neuro-bridge approach connects SNN-based classification with interpretable circuit simulations, advancing mechanistic understanding of EEG biomarkers while enabling scalable, explainable AD detection.

Contextual memory integration remains a high challenge in the development of language models, particularly in tasks that require maintaining coherence over extended sequences. Traditional approaches, such as self-attention mechanisms and memory-augmented architectures, often prioritize short-term dependencies, leading to fragmentation and inconsistency in long-range contextual understanding. Inspired by principles of synaptic plasticity observed in biological neural systems, a novel mechanism, Synaptic Resonance, is introduced to dynamically reinforce relevant memory pathways during training and inference. Unlike static memory representations, this mechanism continuously adjusts synaptic weight matrices based on contextual relevance, allowing for improved information retention without excessive computational overhead. Evaluations conducted on an open-source language model demonstrate reductions in perplexity, enhancements in contextual coherence, and increased robustness against input noise, highlighting the effectiveness of reinforcement-driven memory modulation. Comparative analysis against baseline models further reveals that the proposed approach achieves higher memory retention efficiency while maintaining computational feasibility. The architectural modifications integrate seamlessly into existing transformer-based frameworks, ensuring stable convergence and efficient inference without sacrificing scalability. Applications benefiting from improved long-term contextual consistency, such as dialogue systems and document summarization, stand to gain from this approach. Empirical findings suggest that dynamically reinforced memory pathways offer a promising alternative to conventional memory mechanisms, addressing longstanding limitations in extended sequence modeling.

Model Predictive Controllers (MPC) require a good model for the controlled process. In this paper I infer inductive biases about a physical system. I use these biases to derive a new neural network architecture that can model this real system that has noise and inertia. The main inductive biases exploited here are: the delayed impact of some inputs on the system and the separability between the temporal component and how the inputs interact to produce the output of a system. The inputs are independently delayed using shifted convolutional kernels. Feature interactions are modelled using a fully connected network that does not have access to temporal information. The available data and the problem setup allow the usage of Self Supervised Learning in order to train the models. The baseline architecture is an Attention based Reccurent network adapted to work with MPC like inputs. The proposed networks are faster, better at exploiting larger data volumes and are almost as good as baseline networks in terms of prediction performance. The proposed architecture family called Delay can be used in a real scenario to control systems with delayed responses with respect to its controls or inputs. Ablation studies show that the presence of delay kernels are vital to obtain any learning in proposed architecture. Code and some experimental data are available online.

We explore the effects of various plasticity functions on assemblies of neurons. To bridge the gap between experimental and computational theories we make use of a conceptual framework, the Assembly Calculus, which is a formal system for the description of brain function based on assemblies of neurons. The Assembly Calculus includes operations for projecting, associating, and merging assemblies of neurons. Our research is focused on simulating different plasticity functions with Assembly Calculus. Our main contribution is the modification and evaluation of the projection operation. We experiment with Oja's and Spike Time-Dependent Plasticity (STDP) rules and test the effect of various hyper-parameters.

Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost function these rules are nonlocal and hence biologically implausible. At the same time, biologically plausible local rules have been postulated rather than derived from a principled cost function. Here, to bridge this gap, we derive a biologically plausible network for subspace learning on streaming data by minimizing a principled cost function. In a departure from previous work, where cost was quantified by the representation, or reconstruction, error, we adopt a multidimensional scaling (MDS) cost function for streaming data. The resulting algorithm relies only on biologically plausible Hebbian and anti-Hebbian local learning rules. In a stochastic setting, synaptic weights converge to a stationary state which projects the input data onto the principal subspace. If the data are generated by a nonstationary distribution, the network can track the principal subspace. Thus, our result makes a step towards an algorithmic theory of neural computation.

We show that in a drive-response coupling framework extreme events are suppressed in the response system by the dominance of a single driving signal. We validate this approach across three distinct response network topologies, namely (i) a pair of coupled neurons, (ii) a monolayer network of N coupled neurons and (iii) a two-layer multiplex network each composed of FitzHugh-Nagumo neuronal units. The response networks inherently exhibit extreme events. Our results demonstrate that influencing just one neuron in the response network with an appropriately tuned driving signal is sufficient to control extreme events across all three configurations. In the two-neuron case, suppression of extreme events occurs due to the breaking of phase-locking between the driving neuron and the targeted response neuron. In the case of monolayer and multiplex networks, suppression of extreme events results from the disruption of protoevent frequency dynamics and a subsequent frequency decoupling of the driven neuron from the rest of the network. We also observe that when the size of the neurons in response network connected to the drive increases, the onset of control occurs earlier indicating a scaling advantage of the method.

Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task, and, then, pruning neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning a large randomly initialized model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from a randomly initialized RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and temporal prediction. We experimentally show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.

Sensory systems across all modalities and species exhibit adaptation to continuously changing input statistics. Individual neurons have been shown to modulate their response gains so as to maximize information transmission in different stimulus contexts. Experimental measurements have revealed additional, nuanced sensory adaptation effects including changes in response maxima and minima, tuning curve repulsion from the adapter stimulus, and stimulus-driven response decorrelation. Existing explanations of these phenomena rely on changes in inter-neuronal synaptic efficacy, which, while more flexible, are unlikely to operate as rapidly or reversibly as single neuron gain modulations. Using published V1 population adaptation data, we show that propagation of single neuron gain changes in a recurrent network is sufficient to capture the entire set of observed adaptation effects. We propose a novel adaptive efficient coding objective with which single neuron gains are modulated, maximizing the fidelity of the stimulus representation while minimizing overall activity in the network. From this objective, we analytically derive a set of gains that optimize the trade-off between preserving information about the stimulus and conserving metabolic resources. Our model generalizes well-established concepts of single neuron adaptive gain control to recurrent populations, and parsimoniously explains experimental adaptation data.

The human brain is autonomously active, being characterized by a self-sustained neural activity which would be present even in the absence of external sensory stimuli. Here we study the interrelation between the self-sustained activity in autonomously active recurrent neural nets and external sensory stimuli. There is no a priori semantical relation between the influx of external stimuli and the patterns generated internally by the autonomous and ongoing brain dynamics. The question then arises when and how are semantic correlations between internal and external dynamical processes learned and built up? We study this problem within the paradigm of transient state dynamics for the neural activity in recurrent neural nets, i.e. for an autonomous neural activity characterized by an infinite time-series of transiently stable attractor states. We propose that external stimuli will be relevant during the sensitive periods, {\it viz} the transition period between one transient state and the subsequent semi-stable attractor. A diffusive learning signal is generated unsupervised whenever the stimulus influences the internal dynamics qualitatively. For testing we have presented to the model system stimuli corresponding to the bars and stripes problem. We found that the system performs a non-linear independent component analysis on its own, being continuously and autonomously active. This emergent cognitive capability results here from a general principle for the neural dynamics, the competition between neural ensembles.

The most popular framework for distributed training of machine learning models is the (synchronous) parameter server (PS). This paradigm consists of n workers, which iteratively compute updates of the model parameters, and a stateful PS, which waits and aggregates all updates to generate a new estimate of model parameters and sends it back to the workers for a new iteration. Transient computation slowdowns or transmission delays can intolerably lengthen the time of each iteration. An efficient way to mitigate this problem is to let the PS wait only for the fastest n-b updates, before generating the new parameters. The slowest b workers are called backup workers. The optimal number b of backup workers depends on the cluster configuration and workload, but also (as we show in this paper) on the hyper-parameters of the learning algorithm and the current stage of the training. We propose DBW, an algorithm that dynamically decides the number of backup workers during the training process to maximize the convergence speed at each iteration. Our experiments show that DBW 1) removes the necessity to tune b by preliminary time-consuming experiments, and 2) makes the training up to a factor 3 faster than the optimal static configuration.

Critical learning periods are periods early in development where temporary sensory deficits can have a permanent effect on behavior and learned representations. Despite the radical differences between biological and artificial networks, critical learning periods have been empirically observed in both systems. This suggests that critical periods may be fundamental to learning and not an accident of biology. Yet, why exactly critical periods emerge in deep networks is still an open question, and in particular it is unclear whether the critical periods observed in both systems depend on particular architectural or optimization details. To isolate the key underlying factors, we focus on deep linear network models, and show that, surprisingly, such networks also display much of the behavior seen in biology and artificial networks, while being amenable to analytical treatment. We show that critical periods depend on the depth of the model and structure of the data distribution. We also show analytically and in simulations that the learning of features is tied to competition between sources. Finally, we extend our analysis to multi-task learning to show that pre-training on certain tasks can damage the transfer performance on new tasks, and show how this depends on the relationship between tasks and the duration of the pre-training stage. To the best of our knowledge, our work provides the first analytically tractable model that sheds light into why critical learning periods emerge in biological and artificial networks.

Spiking Neural Networks (SNN) are a class of bio-inspired neural networks that promise to bring low-power and low-latency inference to edge devices through asynchronous and sparse processing. However, being temporal models, SNNs depend heavily on expressive states to generate predictions on par with classical artificial neural networks (ANNs). These states converge only after long transient periods, and quickly decay without input data, leading to higher latency, power consumption, and lower accuracy. This work addresses this issue by initializing the state with an auxiliary ANN running at a low rate. The SNN then uses the state to generate predictions with high temporal resolution until the next initialization phase. Our hybrid ANN-SNN model thus combines the best of both worlds: It does not suffer from long state transients and state decay thanks to the ANN, and can generate predictions with high temporal resolution, low latency, and low power thanks to the SNN. We show for the task of event-based 2D and 3D human pose estimation that our method consumes 88% less power with only a 4% decrease in performance compared to its fully ANN counterparts when run at the same inference rate. Moreover, when compared to SNNs, our method achieves a 74% lower error. This research thus provides a new understanding of how ANNs and SNNs can be used to maximize their respective benefits.

Biological cortical neurons are remarkably sophisticated computational devices, temporally integrating their vast synaptic input over an intricate dendritic tree, subject to complex, nonlinearly interacting internal biological processes. A recent study proposed to characterize this complexity by fitting accurate surrogate models to replicate the input-output relationship of a detailed biophysical cortical pyramidal neuron model and discovered it needed temporal convolutional networks (TCN) with millions of parameters. Requiring these many parameters, however, could stem from a misalignment between the inductive biases of the TCN and cortical neuron's computations. In light of this, and to explore the computational implications of leaky memory units and nonlinear dendritic processing, we introduce the Expressive Leaky Memory (ELM) neuron model, a biologically inspired phenomenological model of a cortical neuron. Remarkably, by exploiting such slowly decaying memory-like hidden states and two-layered nonlinear integration of synaptic input, our ELM neuron can accurately match the aforementioned input-output relationship with under ten thousand trainable parameters. To further assess the computational ramifications of our neuron design, we evaluate it on various tasks with demanding temporal structures, including the Long Range Arena (LRA) datasets, as well as a novel neuromorphic dataset based on the Spiking Heidelberg Digits dataset (SHD-Adding). Leveraging a larger number of memory units with sufficiently long timescales, and correspondingly sophisticated synaptic integration, the ELM neuron displays substantial long-range processing capabilities, reliably outperforming the classic Transformer or Chrono-LSTM architectures on LRA, and even solving the Pathfinder-X task with over 70% accuracy (16k context length).

Biological brains demonstrate complex neural activity, where the timing and interplay between neurons is critical to how brains process information. Most deep learning architectures simplify neural activity by abstracting away temporal dynamics. In this paper we challenge that paradigm. By incorporating neuron-level processing and synchronization, we can effectively reintroduce neural timing as a foundational element. We present the Continuous Thought Machine (CTM), a model designed to leverage neural dynamics as its core representation. The CTM has two core innovations: (1) neuron-level temporal processing, where each neuron uses unique weight parameters to process a history of incoming signals; and (2) neural synchronization employed as a latent representation. The CTM aims to strike a balance between oversimplified neuron abstractions that improve computational efficiency, and biological realism. It operates at a level of abstraction that effectively captures essential temporal dynamics while remaining computationally tractable for deep learning. We demonstrate the CTM's strong performance and versatility across a range of challenging tasks, including ImageNet-1K classification, solving 2D mazes, sorting, parity computation, question-answering, and RL tasks. Beyond displaying rich internal representations and offering a natural avenue for interpretation owing to its internal process, the CTM is able to perform tasks that require complex sequential reasoning. The CTM can also leverage adaptive compute, where it can stop earlier for simpler tasks, or keep computing when faced with more challenging instances. The goal of this work is to share the CTM and its associated innovations, rather than pushing for new state-of-the-art results. To that end, we believe the CTM represents a significant step toward developing more biologically plausible and powerful artificial intelligence systems.

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.

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of SNNs remains relatively limited compared to the ever-growing body of literature on ANNs. In this paper, we study a discrete-time model of SNNs based on leaky integrate-and-fire (LIF) neurons, referred to as discrete-time LIF-SNNs, a widely used framework that still lacks solid theoretical foundations. We demonstrate that discrete-time LIF-SNNs with static inputs and outputs realize piecewise constant functions defined on polyhedral regions, and more importantly, we quantify the network size required to approximate continuous functions. Moreover, we investigate the impact of latency (number of time steps) and depth (number of layers) on the complexity of the input space partitioning induced by discrete-time LIF-SNNs. Our analysis highlights the importance of latency and contrasts these networks with ANNs employing piecewise linear activation functions. Finally, we present numerical experiments to support our theoretical findings.

The standard formulation of Markov decision processes (MDPs) assumes that the agent's decisions are executed immediately. However, in numerous realistic applications such as robotics or healthcare, actions are performed with a delay whose value can even be stochastic. In this work, we introduce stochastic delayed execution MDPs, a new formalism addressing random delays without resorting to state augmentation. We show that given observed delay values, it is sufficient to perform a policy search in the class of Markov policies in order to reach optimal performance, thus extending the deterministic fixed delay case. Armed with this insight, we devise DEZ, a model-based algorithm that optimizes over the class of Markov policies. DEZ leverages Monte-Carlo tree search similar to its non-delayed variant EfficientZero to accurately infer future states from the action queue. Thus, it handles delayed execution while preserving the sample efficiency of EfficientZero. Through a series of experiments on the Atari suite, we demonstrate that although the previous baseline outperforms the naive method in scenarios with constant delay, it underperforms in the face of stochastic delays. In contrast, our approach significantly outperforms the baselines, for both constant and stochastic delays. The code is available at http://github.com/davidva1/Delayed-EZ .

The brain is the perfect place to look for inspiration to develop more efficient neural networks. The inner workings of our synapses and neurons provide a glimpse at what the future of deep learning might look like. This paper serves as a tutorial and perspective showing how to apply the lessons learnt from several decades of research in deep learning, gradient descent, backpropagation and neuroscience to biologically plausible spiking neural neural networks. We also explore the delicate interplay between encoding data as spikes and the learning process; the challenges and solutions of applying gradient-based learning to spiking neural networks (SNNs); the subtle link between temporal backpropagation and spike timing dependent plasticity, and how deep learning might move towards biologically plausible online learning. Some ideas are well accepted and commonly used amongst the neuromorphic engineering community, while others are presented or justified for the first time here. The fields of deep learning and spiking neural networks evolve very rapidly. We endeavour to treat this document as a 'dynamic' manuscript that will continue to be updated as the common practices in training SNNs also change. A series of companion interactive tutorials complementary to this paper using our Python package, snnTorch, are also made available. See https://snntorch.readthedocs.io/en/latest/tutorials/index.html .

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.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

Spiking Neural Networks (SNNs) as one of the biology-inspired models have received much attention recently. It can significantly reduce energy consumption since they quantize the real-valued membrane potentials to 0/1 spikes to transmit information thus the multiplications of activations and weights can be replaced by additions when implemented on hardware. However, this quantization mechanism will inevitably introduce quantization error, thus causing catastrophic information loss. To address the quantization error problem, we propose a regularizing membrane potential loss (RMP-Loss) to adjust the distribution which is directly related to quantization error to a range close to the spikes. Our method is extremely simple to implement and straightforward to train an SNN. Furthermore, it is shown to consistently outperform previous state-of-the-art methods over different network architectures and datasets.

Activation sparsity improves compute efficiency and resource utilization in sparsity-aware neural network accelerators. As the predominant operation in DNNs is multiply-accumulate (MAC) of activations with weights to compute inner products, skipping operations where (at least) one of the two operands is zero can make inference more efficient in terms of latency and power. Spatial sparsification of activations is a popular topic in DNN literature and several methods have already been established to bias a DNN for it. On the other hand, temporal sparsity is an inherent feature of bio-inspired spiking neural networks (SNNs), which neuromorphic processing exploits for hardware efficiency. Introducing and exploiting spatio-temporal sparsity, is a topic much less explored in DNN literature, but in perfect resonance with the trend in DNN, to shift from static signal processing to more streaming signal processing. Towards this goal, in this paper we introduce a new DNN layer (called Delta Activation Layer), whose sole purpose is to promote temporal sparsity of activations during training. A Delta Activation Layer casts temporal sparsity into spatial activation sparsity to be exploited when performing sparse tensor multiplications in hardware. By employing delta inference and ``the usual'' spatial sparsification heuristics during training, the resulting model learns to exploit not only spatial but also temporal activation sparsity (for a given input data distribution). One may use the Delta Activation Layer either during vanilla training or during a refinement phase. We have implemented Delta Activation Layer as an extension of the standard Tensoflow-Keras library, and applied it to train deep neural networks on the Human Action Recognition (UCF101) dataset. We report an almost 3x improvement of activation sparsity, with recoverable loss of model accuracy after longer training.

Significant work has been recently dedicated to the stochastic delayed bandit setting because of its relevance in applications. The applicability of existing algorithms is however restricted by the fact that strong assumptions are often made on the delay distributions, such as full observability, restrictive shape constraints, or uniformity over arms. In this work, we weaken them significantly and only assume that there is a bound on the tail of the delay. In particular, we cover the important case where the delay distributions vary across arms, and the case where the delays are heavy-tailed. Addressing these difficulties, we propose a simple but efficient UCB-based algorithm called the PatientBandits. We provide both problems-dependent and problems-independent bounds on the regret as well as performance lower bounds.

The brain understands the external world through an internal model that generates predictions and refines them based on prediction errors. A complete prediction specifies what will happen, when it will happen, and with what probability, which we refer to as a "prediction object". Existing models typically capture only what and when, omit probabilities, and rely on biologically-implausible algorithms. Here we show that a single population of spiking neurons can jointly encode the prediction object through a biologically grounded learning mechanism. We implement a heterogeneous Izhikevich spiking reservoir with readouts trained by an error-modulated, attention-gated three-factor Hebbian rule and test it on a novel paradigm that controls both the timing and probability of upcoming stimuli. By integrating real-time learning of "when" with offline consolidation of "what", the model encodes the complete prediction object, firing at the correct times with magnitudes proportional to the probabilities. Critically, it rapidly adapts to changes in both stimulus timing and probability, an ability that global least-squares methods such as FORCE lack without explicit resets. During learning, the model self-organizes its readout weights into near-orthogonal subspaces for "what" and "when," showing that multiplexed encoding arises naturally from generic recurrent dynamics under local, error-gated modulation. These results challenge the view that "what" and "when" predictions require separate modules, suggesting instead that mixed selectivity within shared populations supports flexible predictive cognition. The model also predicts phase-specific neuromodulation and overlapping neural subspaces, offering a parsimonious alternative to hierarchical predictive-coding accounts.

Convolutional Neural Networks (CNNs) have demonstrated superiority in learning patterns, but are sensitive to label noises and may overfit noisy labels during training. The early stopping strategy averts updating CNNs during the early training phase and is widely employed in the presence of noisy labels. Motivated by biological findings that the amplitude spectrum (AS) and phase spectrum (PS) in the frequency domain play different roles in the animal's vision system, we observe that PS, which captures more semantic information, can increase the robustness of DNNs to label noise, more so than AS can. We thus propose early stops at different times for AS and PS by disentangling the features of some layer(s) into AS and PS using Discrete Fourier Transform (DFT) during training. Our proposed Phase-AmplituDe DisentangLed Early Stopping (PADDLES) method is shown to be effective on both synthetic and real-world label-noise datasets. PADDLES outperforms other early stopping methods and obtains state-of-the-art performance.

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g. naturalistic) stimulus distribution, we review several inference methods, focussing in particular on two information-theory-based approaches (maximization of stimulus energy or of noise entropy) and a likelihood-based approach (Bayesian spike-triggered covariance, extensions of generalized linear models). We analyze the formal connection between the likelihood-based and information-based approaches to show how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

The measurement of time is central to intelligent behavior. We know that both animals and artificial agents can successfully use temporal dependencies to select actions. In artificial agents, little work has directly addressed (1) which architectural components are necessary for successful development of this ability, (2) how this timing ability comes to be represented in the units and actions of the agent, and (3) whether the resulting behavior of the system converges on solutions similar to those of biology. Here we studied interval timing abilities in deep reinforcement learning agents trained end-to-end on an interval reproduction paradigm inspired by experimental literature on mechanisms of timing. We characterize the strategies developed by recurrent and feedforward agents, which both succeed at temporal reproduction using distinct mechanisms, some of which bear specific and intriguing similarities to biological systems. These findings advance our understanding of how agents come to represent time, and they highlight the value of experimentally inspired approaches to characterizing agent abilities.

One puzzling artifact in machine learning dubbed grokking is where delayed generalization is achieved tenfolds of iterations after near perfect overfitting to the training data. Focusing on the long delay itself on behalf of machine learning practitioners, our goal is to accelerate generalization of a model under grokking phenomenon. By regarding a series of gradients of a parameter over training iterations as a random signal over time, we can spectrally decompose the parameter trajectories under gradient descent into two components: the fast-varying, overfitting-yielding component and the slow-varying, generalization-inducing component. This analysis allows us to accelerate the grokking phenomenon more than times 50 with only a few lines of code that amplifies the slow-varying components of gradients. The experiments show that our algorithm applies to diverse tasks involving images, languages, and graphs, enabling practical availability of this peculiar artifact of sudden generalization. Our code is available at https://github.com/ironjr/grokfast.

Within the complex neuroarchitecture of the brain, astrocytes play crucial roles in development, structure, and metabolism. These cells regulate neural activity through tripartite synapses, directly impacting cognitive processes such as learning and memory. Despite the growing recognition of astrocytes' significance, traditional Spiking Neural Network (SNN) models remain predominantly neuron-centric, overlooking the profound influence of astrocytes on neural dynamics. Inspired by these biological insights, we have developed an Astrocyte-Modulated Spiking Unit (AM-SU), an innovative framework that integrates neuron-astrocyte interactions into the computational paradigm, demonstrating wide applicability across various hardware platforms. Our Astrocyte-Modulated Spiking Neural Network (AstroSNN) exhibits exceptional performance in tasks involving memory retention and natural language generation, particularly in handling long-term dependencies and complex linguistic structures. The design of AstroSNN not only enhances its biological authenticity but also introduces novel computational dynamics, enabling more effective processing of complex temporal dependencies. Furthermore, AstroSNN shows low latency, high throughput, and reduced memory usage in practical applications, making it highly suitable for resource-constrained environments. By successfully integrating astrocytic dynamics into intelligent neural networks, our work narrows the gap between biological plausibility and neural modeling, laying the groundwork for future biologically-inspired neural computing research that includes both neurons and astrocytes.

Spiking Neural Networks (SNNs) are computational models inspired by the structure and dynamics of biological neuronal networks. Their event-driven nature enables them to achieve high energy efficiency, particularly when deployed on neuromorphic hardware platforms. Unlike conventional Artificial Neural Networks (ANNs), which primarily rely on layered architectures, SNNs naturally support a wide range of connectivity patterns, from traditional layered structures to small-world graphs characterized by locally dense and globally sparse connections. In this work, we introduce NeuroCoreX, an FPGA-based emulator designed for the flexible co-design and testing of SNNs. NeuroCoreX supports all-to-all connectivity, providing the capability to implement diverse network topologies without architectural restrictions. It features a biologically motivated local learning mechanism based on Spike-Timing-Dependent Plasticity (STDP). The neuron model implemented within NeuroCoreX is the Leaky Integrate-and-Fire (LIF) model, with current-based synapses facilitating spike integration and transmission . A Universal Asynchronous Receiver-Transmitter (UART) interface is provided for programming and configuring the network parameters, including neuron, synapse, and learning rule settings. Users interact with the emulator through a simple Python-based interface, streamlining SNN deployment from model design to hardware execution. NeuroCoreX is released as an open-source framework, aiming to accelerate research and development in energy-efficient, biologically inspired computing.

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.

Spiking neural networks (SNNs) possess energy-efficient potential due to event-based computation. However, supervised training of SNNs remains a challenge as spike activities are non-differentiable. Previous SNNs training methods can be generally categorized into two basic classes, i.e., backpropagation-like training methods and plasticity-based learning methods. The former methods are dependent on energy-inefficient real-valued computation and non-local transmission, as also required in artificial neural networks (ANNs), whereas the latter are either considered to be biologically implausible or exhibit poor performance. Hence, biologically plausible (bio-plausible) high-performance supervised learning (SL) methods for SNNs remain deficient. In this paper, we proposed a novel bio-plausible SNN model for SL based on the symmetric spike-timing dependent plasticity (sym-STDP) rule found in neuroscience. By combining the sym-STDP rule with bio-plausible synaptic scaling and intrinsic plasticity of the dynamic threshold, our SNN model implemented SL well and achieved good performance in the benchmark recognition task (MNIST dataset). To reveal the underlying mechanism of our SL model, we visualized both layer-based activities and synaptic weights using the t-distributed stochastic neighbor embedding (t-SNE) method after training and found that they were well clustered, thereby demonstrating excellent classification ability. Furthermore, to verify the robustness of our model, we trained it on another more realistic dataset (Fashion-MNIST), which also showed good performance. As the learning rules were bio-plausible and based purely on local spike events, our model could be easily applied to neuromorphic hardware for online training and may be helpful for understanding SL information processing at the synaptic level in biological neural systems.

Nowadays, neural networks act as a synonym for artificial intelligence. Present neural network models, although remarkably powerful, are inefficient both in terms of data and energy. Several alternative forms of neural networks have been proposed to address some of these problems. Specifically, spiking neural networks are suitable for efficient hardware implementations. However, effective learning algorithms for spiking networks remain elusive, although it is suspected that effective plasticity mechanisms could alleviate the problem of data efficiency. Here, we present a new framework for spiking neural networks - Spark - built upon the idea of modular design, from simple components to entire models. The aim of this framework is to provide an efficient and streamlined pipeline for spiking neural networks. We showcase this framework by solving the sparse-reward cartpole problem with simple plasticity mechanisms. We hope that a framework compatible with traditional ML pipelines may accelerate research in the area, specifically for continuous and unbatched learning, akin to the one animals exhibit.

This paper presents a new methodology to alleviate the fundamental trade-off between accuracy and latency in spiking neural networks (SNNs). The approach involves decoding confidence information over time from the SNN outputs and using it to develop a decision-making agent that can dynamically determine when to terminate each inference. The proposed method, Dynamic Confidence, provides several significant benefits to SNNs. 1. It can effectively optimize latency dynamically at runtime, setting it apart from many existing low-latency SNN algorithms. Our experiments on CIFAR-10 and ImageNet datasets have demonstrated an average 40% speedup across eight different settings after applying Dynamic Confidence. 2. The decision-making agent in Dynamic Confidence is straightforward to construct and highly robust in parameter space, making it extremely easy to implement. 3. The proposed method enables visualizing the potential of any given SNN, which sets a target for current SNNs to approach. For instance, if an SNN can terminate at the most appropriate time point for each input sample, a ResNet-50 SNN can achieve an accuracy as high as 82.47% on ImageNet within just 4.71 time steps on average. Unlocking the potential of SNNs needs a highly-reliable decision-making agent to be constructed and fed with a high-quality estimation of ground truth. In this regard, Dynamic Confidence represents a meaningful step toward realizing the potential of SNNs.

Artificial Neural Networks (ANN) have gained significant popularity thanks to their ability to learn using the well-known backpropagation algorithm. Conversely, Spiking Neural Networks (SNNs), despite having broader capabilities than ANNs, have always posed challenges in the training phase. This paper shows a new method to perform supervised learning on SNNs, using Spike Timing Dependent Plasticity (STDP) and homeostasis, aiming at training the network to identify spatial patterns. Spatial patterns refer to spike patterns without a time component, where all spike events occur simultaneously. The method is tested using the SpiNNaker digital architecture. A SNN is trained to recognise one or multiple patterns and performance metrics are extracted to measure the performance of the network. Some considerations are drawn from the results showing that, in the case of a single trained pattern, the network behaves as the ideal detector, with 100% accuracy in detecting the trained pattern. However, as the number of trained patterns on a single network increases, the accuracy of identification is linked to the similarities between these patterns. This method of training an SNN to detect spatial patterns may be applied to pattern recognition in static images or traffic analysis in computer networks, where each network packet represents a spatial pattern. It will be stipulated that the homeostatic factor may enable the network to detect patterns with some degree of similarity, rather than only perfectly matching patterns.The principles outlined in this article serve as the fundamental building blocks for more complex systems that utilise both spatial and temporal patterns by converting specific features of input signals into spikes.One example of such a system is a computer network packet classifier, tasked with real-time identification of packet streams based on features within the packet content

Predictive coding networks are neuroscience-inspired models with roots in both Bayesian statistics and neuroscience. Training such models, however, is quite inefficient and unstable. In this work, we show how by simply changing the temporal scheduling of the update rule for the synaptic weights leads to an algorithm that is much more efficient and stable than the original one, and has theoretical guarantees in terms of convergence. The proposed algorithm, that we call incremental predictive coding (iPC) is also more biologically plausible than the original one, as it it fully automatic. In an extensive set of experiments, we show that iPC constantly performs better than the original formulation on a large number of benchmarks for image classification, as well as for the training of both conditional and masked language models, in terms of test accuracy, efficiency, and convergence with respect to a large set of hyperparameters.

Traveling waves of neural activity have been observed throughout the brain at a diversity of regions and scales; however, their precise computational role is still debated. One physically inspired hypothesis suggests that the cortical sheet may act like a wave-propagating system capable of invertibly storing a short-term memory of sequential stimuli through induced waves traveling across the cortical surface, and indeed many experimental results from neuroscience correlate wave activity with memory tasks. To date, however, the computational implications of this idea have remained hypothetical due to the lack of a simple recurrent neural network architecture capable of exhibiting such waves. In this work, we introduce a model to fill this gap, which we denote the Wave-RNN (wRNN), and demonstrate how such an architecture indeed efficiently encodes the recent past through a suite of synthetic memory tasks where wRNNs learn faster and reach significantly lower error than wave-free counterparts. We further explore the implications of this memory storage system on more complex sequence modeling tasks such as sequential image classification and find that wave-based models not only again outperform comparable wave-free RNNs while using significantly fewer parameters, but additionally perform comparably to more complex gated architectures such as LSTMs and GRUs.

Regarded as the third generation of neural networks, Spiking Neural Networks (SNNs) have garnered significant traction due to their biological plausibility and energy efficiency. Recent advancements in large models necessitate spiking neurons capable of high performance, adaptability, and training efficiency. In this work, we first propose a novel functional perspective that provides general guidance for designing the new generation of spiking neurons. Following the insightful guidelines, we propose the Adaptive Spiking Neuron (ASN), which incorporates trainable parameters to learn membrane potential dynamics and enable adaptive firing. ASN adopts an integer training and spike inference paradigm, facilitating efficient SNN training. To further enhance robustness, we propose a specialized variant of ASN, the Normalized Adaptive Spiking Neuron (NASN), which integrates normalization to stabilize training. We evaluate our neuron model on 19 datasets spanning five distinct tasks in both vision and language modalities, demonstrating the effectiveness and versatility of the ASN family. Our ASN family is expected to become the new generation of general-purpose spiking neurons.

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to gain mechanistic insights into the phenomenon of abrupt learning by studying RNNs trained to perform diverse short-term memory tasks. In these tasks, RNN training begins with an initial search phase. Following a long period of plateau in accuracy, the values of the loss function suddenly drop, indicating abrupt learning. Analyzing the neural computation performed by these RNNs reveals geometric restructuring (GR) in their phase spaces prior to the drop. To promote these GR events, we introduce a temporal consistency regularization that accelerates (bioplausible) training, facilitates attractor formation, and enables efficient learning in strongly connected networks. Our findings offer testable predictions for neuroscientists and emphasize the need for goal-agnostic secondary mechanisms to facilitate learning in biological and artificial networks.

Spiking Neural Networks (SNNs) are well known as a promising energy-efficient alternative to conventional artificial neural networks. Subject to the preconceived impression that SNNs are sparse firing, the analysis and optimization of inherent redundancy in SNNs have been largely overlooked, thus the potential advantages of spike-based neuromorphic computing in accuracy and energy efficiency are interfered. In this work, we pose and focus on three key questions regarding the inherent redundancy in SNNs. We argue that the redundancy is induced by the spatio-temporal invariance of SNNs, which enhances the efficiency of parameter utilization but also invites lots of noise spikes. Further, we analyze the effect of spatio-temporal invariance on the spatio-temporal dynamics and spike firing of SNNs. Then, motivated by these analyses, we propose an Advance Spatial Attention (ASA) module to harness SNNs' redundancy, which can adaptively optimize their membrane potential distribution by a pair of individual spatial attention sub-modules. In this way, noise spike features are accurately regulated. Experimental results demonstrate that the proposed method can significantly drop the spike firing with better performance than state-of-the-art SNN baselines. Our code is available in https://github.com/BICLab/ASA-SNN.

It has long been known in both neuroscience and AI that ``binding'' between neurons leads to a form of competitive learning where representations are compressed in order to represent more abstract concepts in deeper layers of the network. More recently, it was also hypothesized that dynamic (spatiotemporal) representations play an important role in both neuroscience and AI. Building on these ideas, we introduce Artificial Kuramoto Oscillatory Neurons (AKOrN) as a dynamical alternative to threshold units, which can be combined with arbitrary connectivity designs such as fully connected, convolutional, or attentive mechanisms. Our generalized Kuramoto updates bind neurons together through their synchronization dynamics. We show that this idea provides performance improvements across a wide spectrum of tasks such as unsupervised object discovery, adversarial robustness, calibrated uncertainty quantification, and reasoning. We believe that these empirical results show the importance of rethinking our assumptions at the most basic neuronal level of neural representation, and in particular show the importance of dynamical representations.

This study explores the interference in temporal processing within a dual-task paradigm from an artificial intelligence (AI) perspective. In this context, the dual-task setup is implemented as a simplified version of the Overcooked environment with two variations, single task (T) and dual task (T+N). Both variations involve an embedded time production task, but the dual task (T+N) additionally involves a concurrent number comparison task. Two deep reinforcement learning (DRL) agents were separately trained for each of these tasks. These agents exhibited emergent behavior consistent with human timing research. Specifically, the dual task (T+N) agent exhibited significant overproduction of time relative to its single task (T) counterpart. This result was consistent across four target durations. Preliminary analysis of neural dynamics in the agents' LSTM layers did not reveal any clear evidence of a dedicated or intrinsic timer. Hence, further investigation is needed to better understand the underlying time-keeping mechanisms of the agents and to provide insights into the observed behavioral patterns. This study is a small step towards exploring parallels between emergent DRL behavior and behavior observed in biological systems in order to facilitate a better understanding of both.

This study introduces BrainTransformers, an innovative Large Language Model (LLM) implemented using Spiking Neural Networks (SNN). Our key contributions include: (1) designing SNN-compatible Transformer components such as SNNMatmul, SNNSoftmax, and SNNSiLU; (2) implementing an SNN approximation of the SiLU activation function; and (3) developing a Synapsis module to simulate synaptic plasticity. Our 3-billion parameter model, BrainTransformers-3B-Chat, demonstrates competitive performance across various benchmarks, including MMLU (63.2), BBH (54.1), ARC-C (54.3), and GSM8K (76.3), while potentially offering improved energy efficiency and biological plausibility. The model employs a three-stage training approach, including SNN-specific neuronal synaptic plasticity training. This research opens new avenues for brain-like AI systems in natural language processing and neuromorphic computing. Future work will focus on hardware optimization, developing specialized SNN fine-tuning tools, and exploring practical applications in energy-efficient computing environments.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Recent years have witnessed Spiking Neural Networks (SNNs) gaining attention for their ultra-low energy consumption and high biological plausibility compared with traditional Artificial Neural Networks (ANNs). Despite their distinguished properties, the application of SNNs in the computationally intensive field of image generation is still under exploration. In this paper, we propose the Spiking Diffusion Models (SDMs), an innovative family of SNN-based generative models that excel in producing high-quality samples with significantly reduced energy consumption. In particular, we propose a Temporal-wise Spiking Mechanism (TSM) that allows SNNs to capture more temporal features from a bio-plasticity perspective. In addition, we propose a threshold-guided strategy that can further improve the performances by up to 16.7% without any additional training. We also make the first attempt to use the ANN-SNN approach for SNN-based generation tasks. Extensive experimental results reveal that our approach not only exhibits comparable performance to its ANN counterpart with few spiking time steps, but also outperforms previous SNN-based generative models by a large margin. Moreover, we also demonstrate the high-quality generation ability of SDM on large-scale datasets, e.g., LSUN bedroom. This development marks a pivotal advancement in the capabilities of SNN-based generation, paving the way for future research avenues to realize low-energy and low-latency generative applications. Our code is available at https://github.com/AndyCao1125/SDM.

Spiking neural networks (SNNs) are well suited for spatio-temporal learning and implementations on energy-efficient event-driven neuromorphic processors. However, existing SNN error backpropagation (BP) methods lack proper handling of spiking discontinuities and suffer from low performance compared with the BP methods for traditional artificial neural networks. In addition, a large number of time steps are typically required to achieve decent performance, leading to high latency and rendering spike-based computation unscalable to deep architectures. We present a novel Temporal Spike Sequence Learning Backpropagation (TSSL-BP) method for training deep SNNs, which breaks down error backpropagation across two types of inter-neuron and intra-neuron dependencies and leads to improved temporal learning precision. It captures inter-neuron dependencies through presynaptic firing times by considering the all-or-none characteristics of firing activities and captures intra-neuron dependencies by handling the internal evolution of each neuronal state in time. TSSL-BP efficiently trains deep SNNs within a much shortened temporal window of a few steps while improving the accuracy for various image classification datasets including CIFAR10.

Dynamic neuroimaging data, such as emission tomography measurements of radiotracer transport in blood or cerebrospinal fluid, often exhibit diffusion-like properties. These introduce distance-dependent temporal delays, scale-differences, and stretching effects that limit the effectiveness of conventional linear modeling and decomposition methods. To address this, we present the shift- and stretch-invariant non-negative matrix factorization framework. Our approach estimates both integer and non-integer temporal shifts as well as temporal stretching, all implemented in the frequency domain, where shifts correspond to phase modifications, and where stretching is handled via zero-padding or truncation. The model is implemented in PyTorch (https://github.com/anders-s-olsen/shiftstretchNMF). We demonstrate on synthetic data and brain emission tomography data that the model is able to account for stretching to provide more detailed characterization of brain tissue structure.

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.

Many learning algorithms used as normative models in neuroscience or as candidate approaches for learning on neuromorphic chips learn by contrasting one set of network states with another. These Contrastive Learning (CL) algorithms are traditionally implemented with rigid, temporally non-local, and periodic learning dynamics that could limit the range of physical systems capable of harnessing CL. In this study, we build on recent work exploring how CL might be implemented by biological or neurmorphic systems and show that this form of learning can be made temporally local, and can still function even if many of the dynamical requirements of standard training procedures are relaxed. Thanks to a set of general theorems corroborated by numerical experiments across several CL models, our results provide theoretical foundations for the study and development of CL methods for biological and neuromorphic neural networks.

This study introduces a novel approach by replacing the traditional perceptron neuron model with a biologically inspired probabilistic meta neuron, where the internal neuron parameters are jointly learned, leading to improved classification accuracy of spiking neural networks (SNNs). To validate this innovation, we implement and compare two SNN architectures: one based on standard leaky integrate-and-fire (LIF) neurons and another utilizing the proposed probabilistic meta neuron model. As a second key contribution, we present a new biologically inspired classification framework that uniquely integrates SNNs with Lempel-Ziv complexity (LZC) a measure closely related to entropy rate. By combining the temporal precision and biological plausibility of SNNs with the capacity of LZC to capture structural regularity, the proposed approach enables efficient and interpretable classification of spatiotemporal neural data, an aspect not addressed in existing works. We consider learning algorithms such as backpropagation, spike-timing-dependent plasticity (STDP), and the Tempotron learning rule. To explore neural dynamics, we use Poisson processes to model neuronal spike trains, a well-established method for simulating the stochastic firing behavior of biological neurons. Our results reveal that depending on the training method, the classifier's efficiency can improve by up to 11.00%, highlighting the advantage of learning additional neuron parameters beyond the traditional focus on weighted inputs alone.

Recent studies show that LLM hidden states encode reward-related information, such as answer correctness and model confidence. However, existing approaches typically fit black-box probes on the full hidden states, offering little insight into how this information is structured across neurons. In this paper, we show that reward-related information is concentrated in a sparse subset of neurons. Using simple probing, we identify two types of neurons: value neurons, whose activations predict state value, and dopamine neurons, whose activations encode step-level temporal difference (TD) errors. Together, these neurons form a sparse reward subsystem within LLM hidden states. These names are drawn by analogy with neuroscience, where value neurons and dopamine neurons in the biological reward subsystem also encode value and reward prediction errors, respectively. We demonstrate that value neurons are robust and transferable across diverse datasets and models, and provide causal evidence that they encode reward-related information. Finally, we show applications of the reward subsystem: value neurons serve as effective predictors of model confidence, and dopamine neurons can function as a process reward model (PRM) to guide inference-time search.

Recurrent Neural Networks (RNNs) are popular models of brain function. The typical training strategy is to adjust their input-output behavior so that it matches that of the biological circuit of interest. Even though this strategy ensures that the biological and artificial networks perform the same computational task, it does not guarantee that their internal activity dynamics match. This suggests that the trained RNNs might end up performing the task employing a different internal computational mechanism, which would make them a suboptimal model of the biological circuit. In this work, we introduce a novel training strategy that allows learning not only the input-output behavior of an RNN but also its internal network dynamics, based on sparse neural recordings. We test the proposed method by training an RNN to simultaneously reproduce internal dynamics and output signals of a physiologically-inspired neural model. Specifically, this model generates the multiphasic muscle-like activity patterns typically observed during the execution of reaching movements, based on the oscillatory activation patterns concurrently observed in the motor cortex. Remarkably, we show that the reproduction of the internal dynamics is successful even when the training algorithm relies on the activities of a small subset of neurons sampled from the biological network. Furthermore, we show that training the RNNs with this method significantly improves their generalization performance. Overall, our results suggest that the proposed method is suitable for building powerful functional RNN models, which automatically capture important computational properties of the biological circuit of interest from sparse neural recordings.

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations whose training dynamics and dependence on training set size can be predicted by our effective theory in a toy setting. We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. We find on transformers the grokking phase stays closer to the memorization phase (compared to the comprehension phase), leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.

The brain solves the credit assignment problem remarkably well. For credit to be assigned across neural networks they must, in principle, wait for specific neural computations to finish. How the brain deals with this inherent locking problem has remained unclear. Deep learning methods suffer from similar locking constraints both on the forward and feedback phase. Recently, decoupled neural interfaces (DNIs) were introduced as a solution to the forward and feedback locking problems in deep networks. Here we propose that a specialised brain region, the cerebellum, helps the cerebral cortex solve similar locking problems akin to DNIs. To demonstrate the potential of this framework we introduce a systems-level model in which a recurrent cortical network receives online temporal feedback predictions from a cerebellar module. We test this cortico-cerebellar recurrent neural network (ccRNN) model on a number of sensorimotor (line and digit drawing) and cognitive tasks (pattern recognition and caption generation) that have been shown to be cerebellar-dependent. In all tasks, we observe that ccRNNs facilitates learning while reducing ataxia-like behaviours, consistent with classical experimental observations. Moreover, our model also explains recent behavioural and neuronal observations while making several testable predictions across multiple levels. Overall, our work offers a novel perspective on the cerebellum as a brain-wide decoupling machine for efficient credit assignment and opens a new avenue between deep learning and neuroscience.

Large-scale recordings of neural activity are providing new opportunities to study neural population dynamics. A powerful method for analyzing such high-dimensional measurements is to deploy an algorithm to learn the low-dimensional latent dynamics. LFADS (Latent Factor Analysis via Dynamical Systems) is a deep learning method for inferring latent dynamics from high-dimensional neural spiking data recorded simultaneously in single trials. This method has shown a remarkable performance in modeling complex brain signals with an average inference latency in milliseconds. As our capacity of simultaneously recording many neurons is increasing exponentially, it is becoming crucial to build capacity for deploying low-latency inference of the computing algorithms. To improve the real-time processing ability of LFADS, we introduce an efficient implementation of the LFADS models onto Field Programmable Gate Arrays (FPGA). Our implementation shows an inference latency of 41.97 mus for processing the data in a single trial on a Xilinx U55C.

This position and survey paper identifies the emerging convergence of neuroscience, artificial general intelligence (AGI), and neuromorphic computing toward a unified research paradigm. Using a framework grounded in brain physiology, we highlight how synaptic plasticity, sparse spike-based communication, and multimodal association provide design principles for next-generation AGI systems that potentially combine both human and machine intelligences. The review traces this evolution from early connectionist models to state-of-the-art large language models, demonstrating how key innovations like transformer attention, foundation-model pre-training, and multi-agent architectures mirror neurobiological processes like cortical mechanisms, working memory, and episodic consolidation. We then discuss emerging physical substrates capable of breaking the von Neumann bottleneck to achieve brain-scale efficiency in silicon: memristive crossbars, in-memory compute arrays, and emerging quantum and photonic devices. There are four critical challenges at this intersection: 1) integrating spiking dynamics with foundation models, 2) maintaining lifelong plasticity without catastrophic forgetting, 3) unifying language with sensorimotor learning in embodied agents, and 4) enforcing ethical safeguards in advanced neuromorphic autonomous systems. This combined perspective across neuroscience, computation, and hardware offers an integrative agenda for in each of these fields.

Emergence of deep neural networks (DNNs) has raised enormous attention towards artificial neural networks (ANNs) once again. They have become the state-of-the-art models and have won different machine learning challenges. Although these networks are inspired by the brain, they lack biological plausibility, and they have structural differences compared to the brain. Spiking neural networks (SNNs) have been around for a long time, and they have been investigated to understand the dynamics of the brain. However, their application in real-world and complicated machine learning tasks were limited. Recently, they have shown great potential in solving such tasks. Due to their energy efficiency and temporal dynamics there are many promises in their future development. In this work, we reviewed the structures and performances of SNNs on image classification tasks. The comparisons illustrate that these networks show great capabilities for more complicated problems. Furthermore, the simple learning rules developed for SNNs, such as STDP and R-STDP, can be a potential alternative to replace the backpropagation algorithm used in DNNs.

We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural field model with a simple functional form that still able to predict or reproduce empirical findings. Each neural unit was modelled using a neural mass and the accompanying field theory was derived in the continuum limit. The field theory comprised coupled (real) Klein-Gordon fields, where predictions of the model fall within the range of experimental findings. These predictions included the frequency spectrum of electric activity measured from the cortex, which was derived using an equipartition of energy over eigenfunctions of the neural fields. Moreover, the neural field model was invariant, within a set of parameters, to the dynamical system used to model each neuronal mass. Specifically, topologically equivalent dynamical systems resulted in the same neural field model when connected in a lattice; indicating that the fields derived could be read as a canonical cortical field theory. We specifically investigated non-dispersive fields that provide a structure for the coding (or representation) of afferent information. Further elaboration of the ensuing neural field theory, including the effect of dispersive forces, could be of importance in the understanding of the cortical processing of information.

Recent Continuous Thought Machine architecture decouples internal computation from external inputs via neural dynamics, but relies on multi-layer perceptrons without stability guarantees. We propose to model neural dynamics using asymmetric Excitatory-Inhibitory (E-I) networks, which can be stabilized via principles from network theory and can be expressed as energy-based systems optimized through a game-theoretic loss. Building on this perspective, we introduce Temporal Inhibitory-Excitatory Dynamic Engine (TIDE), a neuro-inspired architecture that computes internal representations through neural dynamics stabilized by incorporating the Wilson-Cowan dynamics and lateral inhibition. TIDE balances biological realism by, for instance, using Hierarchical Receptive Fields and enforcing Dale's principle to ensure a realistic 80:20 E-I balance ratio with an end-to-end trainable architecture. The aim of this paper is to introduce a new architecture that brings neuro-inspired learning to the forefront. We present proofs of convergence, stability, and complexity bounds, along with empirical ablation studies. Overall, TIDE surpasses CTM with under 50% of the training time and improves top-1 accuracy by an average of +1.65% on ImageNet under various perturbations.

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional interactions. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional interactions can change over time. To model dynamically changing functional interactions, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional interactions are shaped and confined by the underlying anatomical connectome. Here, we propose a novel prior-informed state-switching GLM. We introduce both a Gaussian prior and a one-hot prior over the GLM in each state. The priors are learnable. We will show that the learned prior should capture the state-constant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood with real neural datasets, and render interaction structures and hidden states more interpretable when applied to real neural data.

There is renewed interest in modeling and understanding the nervous system of the nematode Caenorhabditis elegans (C. elegans), as this small model system provides a path to bridge the gap between nervous system structure (connectivity) and function (physiology). However, existing physiology datasets, whether involving passive recording or stimulation, are in distinct formats, and connectome datasets require preprocessing before analysis can commence. Here we compile and homogenize datasets of neural activity and connectivity. Our neural activity dataset is derived from 11 C. elegans neuroimaging experiments, while our connectivity dataset is compiled from 9 connectome annotations based on 3 primary electron microscopy studies and 1 signal propagation study. Physiology datasets, collected under varying protocols, measure calcium fluorescence in labeled subsets of the worm's 300 neurons. Our preprocessing pipeline standardizes these datasets by consistently ordering labeled neurons and resampling traces to a common sampling rate, yielding recordings from approximately 900 worms and 250 uniquely labeled neurons. The connectome datasets, collected from electron microscopy reconstructions, represent the entire nervous system as a graph of connections. Our collection is accessible on HuggingFace, facilitating analysis of the structure-function relationship in biology using modern neural network architectures and enabling cross-lab and cross-animal comparisons.

Continuous-time neural processes are performant sequential decision-makers that are built by differential equations (DE). However, their expressive power when they are deployed on computers is bottlenecked by numerical DE solvers. This limitation has significantly slowed down the scaling and understanding of numerous natural physical phenomena such as the dynamics of nervous systems. Ideally, we would circumvent this bottleneck by solving the given dynamical system in closed form. This is known to be intractable in general. Here, we show it is possible to closely approximate the interaction between neurons and synapses -- the building blocks of natural and artificial neural networks -- constructed by liquid time-constant networks (LTCs) efficiently in closed-form. To this end, we compute a tightly-bounded approximation of the solution of an integral appearing in LTCs' dynamics, that has had no known closed-form solution so far. This closed-form solution substantially impacts the design of continuous-time and continuous-depth neural models; for instance, since time appears explicitly in closed-form, the formulation relaxes the need for complex numerical solvers. Consequently, we obtain models that are between one and five orders of magnitude faster in training and inference compared to differential equation-based counterparts. More importantly, in contrast to ODE-based continuous networks, closed-form networks can scale remarkably well compared to other deep learning instances. Lastly, as these models are derived from liquid networks, they show remarkable performance in time series modeling, compared to advanced recurrent models.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Neural networks acquire structured representations at specific moments during training, yet identifying these transitions typically relies on retrospective, label-dependent metrics. We introduce a bifurcation theory of representation dynamics to detect these moments in real time. Analyzing a passive GMM probe attached to the evolving encoder, we show the onset of structure corresponds to a supercritical pitchfork bifurcation driven by the loss Hessian. The system exhibits a theoretically predictable zero-crossing (β_c) that, compared to the network's current state (β), yields a dynamic ratio β(t)/β_c(t): a universal, label-free phase coordinate for representation dynamics, computable entirely from hidden states. We empirically validate four distinct transition regimes predicted by this coordinate across diverse settings: SAEs on language models (Pythia), SSL (CIFAR), and grokking (modular arithmetic). Crucially, under finite dissipation, macroscopic symmetry-breaking can lag the initial zero-crossing by orders of magnitude, which providing a rigorous dynamical account of the delayed escape observed in grokking. Microscopically, the bifurcation creates a shared unstable subspace, forcing collective symmetry breaking. We term this the "feature lottery" in SAE training: a feature's terminal interpretability becomes predictable remarkably early. By only 5% of training, early atom purity robustly predicts final convergence purity, with top-decile early atoms achieving over 12x the baseline purity at convergence. Beyond explaining concept emergence, β/β_c provides a practical early-warning indicator for training health, detecting the onset of usable structure, the crystallization of feature identity, and representational collapse epochs before downstream metrics react.

Large language models deployed in the wild must adapt to evolving data, user behavior, and task mixtures without erasing previously acquired capabilities. In practice, this remains difficult: sequential updates induce catastrophic forgetting, while many stabilization methods rely on external procedures that are costly, brittle, or difficult to scale. We present TRC^{2} (Thalamically Routed Cortical Columns), a decoder-only architecture that makes continual adaptation a property of the backbone itself. TRC^{2} combines stacked cortical columns with a thalamic modulatory pathway for selective inter-column communication and a hippocampal pathway for event-selective retrieval, delayed surprise-based writing, and replay-driven consolidation. This design localizes fast plasticity while preserving a slower stable computation pathway. We further introduce a causal memory-update scheme and an online replay controller that adjusts consolidation strength from measured forgetting. Across a task-sequential language-modeling stream over C4, WikiText-103, and GSM8K, TRC^{2} consistently improves task-boundary modeling quality and substantially reduces cumulative forgetting relative to Transformer, Mamba, MoE, and DeepSeek baselines trained under the same pipeline. Ablations show that the thalamic and hippocampal components are central to the retention gains, while the full model remains competitive in throughput and training cost.

Reservoir computers (RCs) provide a computationally efficient alternative to deep learning while also offering a framework for incorporating brain-inspired computational principles. By using an internal neural network with random, fixed connections-the 'reservoir'-and training only the output weights, RCs simplify the training process but remain sensitive to the choice of hyperparameters that govern activation functions and network architecture. Moreover, typical RC implementations overlook a critical aspect of neuronal dynamics: the balance between excitatory and inhibitory (E-I) signals, which is essential for robust brain function. We show that RCs characteristically perform best in balanced or slightly over-inhibited regimes, outperforming excitation-dominated ones. To reduce the need for precise hyperparameter tuning, we introduce a self-adapting mechanism that locally adjusts E/I balance to achieve target neuronal firing rates, improving performance by up to 130% in tasks like memory capacity and time series prediction compared with globally tuned RCs. Incorporating brain-inspired heterogeneity in target neuronal firing rates further reduces the need for fine-tuning hyperparameters and enables RCs to excel across linear and non-linear tasks. These results support a shift from static optimization to dynamic adaptation in reservoir design, demonstrating how brain-inspired mechanisms improve RC performance and robustness while deepening our understanding of neural computation.

We present PyCARL, a PyNN-based common Python programming interface for hardware-software co-simulation of spiking neural network (SNN). Through PyCARL, we make the following two key contributions. First, we provide an interface of PyNN to CARLsim, a computationally-efficient, GPU-accelerated and biophysically-detailed SNN simulator. PyCARL facilitates joint development of machine learning models and code sharing between CARLsim and PyNN users, promoting an integrated and larger neuromorphic community. Second, we integrate cycle-accurate models of state-of-the-art neuromorphic hardware such as TrueNorth, Loihi, and DynapSE in PyCARL, to accurately model hardware latencies that delay spikes between communicating neurons and degrade performance. PyCARL allows users to analyze and optimize the performance difference between software-only simulation and hardware-software co-simulation of their machine learning models. We show that system designers can also use PyCARL to perform design-space exploration early in the product development stage, facilitating faster time-to-deployment of neuromorphic products. We evaluate the memory usage and simulation time of PyCARL using functionality tests, synthetic SNNs, and realistic applications. Our results demonstrate that for large SNNs, PyCARL does not lead to any significant overhead compared to CARLsim. We also use PyCARL to analyze these SNNs for a state-of-the-art neuromorphic hardware and demonstrate a significant performance deviation from software-only simulations. PyCARL allows to evaluate and minimize such differences early during model development.

We introduce a mathematically rigorous framework based on rough path theory to model stochastic spiking neural networks (SSNNs) as stochastic differential equations with event discontinuities (Event SDEs) and driven by c\`adl\`ag rough paths. Our formalism is general enough to allow for potential jumps to be present both in the solution trajectories as well as in the driving noise. We then identify a set of sufficient conditions ensuring the existence of pathwise gradients of solution trajectories and event times with respect to the network's parameters and show how these gradients satisfy a recursive relation. Furthermore, we introduce a general-purpose loss function defined by means of a new class of signature kernels indexed on c\`adl\`ag rough paths and use it to train SSNNs as generative models. We provide an end-to-end autodifferentiable solver for Event SDEs and make its implementation available as part of the diffrax library. Our framework is, to our knowledge, the first enabling gradient-based training of SSNNs with noise affecting both the spike timing and the network's dynamics.

As one of the energy-efficient alternatives of conventional neural networks (CNNs), spiking neural networks (SNNs) have gained more and more interest recently. To train the deep models, some effective batch normalization (BN) techniques are proposed in SNNs. All these BNs are suggested to be used after the convolution layer as usually doing in CNNs. However, the spiking neuron is much more complex with the spatio-temporal dynamics. The regulated data flow after the BN layer will be disturbed again by the membrane potential updating operation before the firing function, i.e., the nonlinear activation. Therefore, we advocate adding another BN layer before the firing function to normalize the membrane potential again, called MPBN. To eliminate the induced time cost of MPBN, we also propose a training-inference-decoupled re-parameterization technique to fold the trained MPBN into the firing threshold. With the re-parameterization technique, the MPBN will not introduce any extra time burden in the inference. Furthermore, the MPBN can also adopt the element-wised form, while these BNs after the convolution layer can only use the channel-wised form. Experimental results show that the proposed MPBN performs well on both popular non-spiking static and neuromorphic datasets. Our code is open-sourced at https://github.com/yfguo91/MPBN{MPBN}.

While Large Language Models (LLMs) excel at generalized reasoning, standard retrieval-augmented approaches fail to address the disconnected nature of long-term agentic memory. To bridge this gap, we introduce Synapse (Synergistic Associative Processing Semantic Encoding), a unified memory architecture that transcends static vector similarity. Drawing from cognitive science, Synapse models memory as a dynamic graph where relevance emerges from spreading activation rather than pre-computed links. By integrating lateral inhibition and temporal decay, the system dynamically highlights relevant sub-graphs while filtering interference. We implement a Triple Hybrid Retrieval strategy that fuses geometric embeddings with activation-based graph traversal. Comprehensive evaluations on the LoCoMo benchmark show that Synapse significantly outperforms state-of-the-art methods in complex temporal and multi-hop reasoning tasks, offering a robust solution to the "Contextual Tunneling" problem. Our code and data will be made publicly available upon acceptance.

Redundancies and correlations in the responses of sensory neurons seem to waste neural resources but can carry cues about structured stimuli and may help the brain to correct for response errors. To assess how the retina negotiates this tradeoff, we measured simultaneous responses from populations of ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure. We found that pairwise correlations in the retinal output remained similar across stimuli with widely different spatio-temporal correlations including white noise and natural movies. Meanwhile, purely spatial correlations tended to increase correlations in the retinal response. Responding to more correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the similarity of pairwise correlations across stimuli where receptive field measurements were possible.

Spiking Neural Networks (SNNs) are energy efficient alternatives to commonly used deep neural networks (DNNs). Through event-driven information processing, SNNs can reduce the expensive compute requirements of DNNs considerably, while achieving comparable performance. However, high inference latency is a significant hindrance to the edge deployment of deep SNNs. Computation over multiple timesteps not only increases latency as well as overall energy budget due to higher number of operations, but also incurs memory access overhead of fetching membrane potentials, both of which lessen the energy benefits of SNNs. To overcome this bottleneck and leverage the full potential of SNNs, we propose an Iterative Initialization and Retraining method for SNNs (IIR-SNN) to perform single shot inference in the temporal axis. The method starts with an SNN trained with T timesteps (T>1). Then at each stage of latency reduction, the network trained at previous stage with higher timestep is utilized as initialization for subsequent training with lower timestep. This acts as a compression method, as the network is gradually shrunk in the temporal domain. In this paper, we use direct input encoding and choose T=5, since as per literature, it is the minimum required latency to achieve satisfactory performance on ImageNet. The proposed scheme allows us to obtain SNNs with up to unit latency, requiring a single forward pass during inference. We achieve top-1 accuracy of 93.05%, 70.15% and 67.71% on CIFAR-10, CIFAR-100 and ImageNet, respectively using VGG16, with just 1 timestep. In addition, IIR-SNNs perform inference with 5-2500X reduced latency compared to other state-of-the-art SNNs, maintaining comparable or even better accuracy. Furthermore, in comparison with standard DNNs, the proposed IIR-SNNs provide25-33X higher energy efficiency, while being comparable to them in classification performance.

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.

The neurons of artificial neural networks were originally invented when much less was known about biological neurons than is known today. Our work explores a modification to the core neuron unit to make it more parallel to a biological neuron. The modification is made with the knowledge that biological dendrites are not simply passive activation funnels, but also compute complex non-linear functions as they transmit activation to the cell body. The paper explores a novel system of "Perforated" backpropagation empowering the artificial neurons of deep neural networks to achieve better performance coding for the same features they coded for in the original architecture. After an initial network training phase, additional "Dendrite Nodes" are added to the network and separately trained with a different objective: to correlate their output with the remaining error of the original neurons. The trained Dendrite Nodes are then frozen, and the original neurons are further trained, now taking into account the additional error signals provided by the Dendrite Nodes. The cycle of training the original neurons and then adding and training Dendrite Nodes can be repeated several times until satisfactory performance is achieved. Our algorithm was successfully added to modern state-of-the-art PyTorch networks across multiple domains, improving upon original accuracies and allowing for significant model compression without a loss in accuracy.

Memory systems can store vastly different amounts of information despite similar hardware constraints. Here, we show that superior spatial memory emerges from a discrete stiffening of hippocampal population geometry-a transition from disorganized to crystalline collective coding. Comparing food-caching chickadees to non-caching zebra finches, we found that the caching hippocampus maintains a topologically rigid, "crystalline" geometry with significantly higher geometric stability (Shesha 0.245 v 0.166) and nearly two-fold greater temporal coherence (Shesha 0.393 v 0.209), while the non-caching hippocampus resembles a disorganized "mist." This stability is actively constructed by synergistic circuit dynamics: excitatory neurons form the spatial scaffold while inhibitory populations contribute orthogonal decorrelation, a circuit motif in which excitatory and inhibitory populations occupy largely non-overlapping representational subspaces. A double dissociation with Valiant's Stable Memory Allocator, a model predicting that dedicated neuron ensembles underlie each memory, confirms this advantage reflects continuous topological organization rather than discrete neuron allocation: caching networks exhibit near-zero split-half allocation reliability despite their geometric superiority. Computational modeling across 10k configurations reveals topological rigidity as the mathematical prerequisite for scale: crystalline codes sustain high-fidelity readout beyond M=1k locations while mist codes fail below M=10, a >100-fold capacity advantage. This capacity requires a 169fold representational redundancy: a "geometric tax" stabilizing the manifold against biological noise. These results establish geometric stability as a candidate organizing principle of biological memory: evolution achieves high-capacity memory not by proliferating neurons, but by engineering the geometry of the neural code itself.

Statistical whitening transformations play a fundamental role in many computational systems, and may also play an important role in biological sensory systems. Existing neural circuit models of adaptive whitening operate by modifying synaptic interactions; however, such modifications would seem both too slow and insufficiently reversible. Motivated by the extensive neuroscience literature on gain modulation, we propose an alternative model that adaptively whitens its responses by modulating the gains of individual neurons. Starting from a novel whitening objective, we derive an online algorithm that whitens its outputs by adjusting the marginal variances of an overcomplete set of projections. We map the algorithm onto a recurrent neural network with fixed synaptic weights and gain-modulating interneurons. We demonstrate numerically that sign-constraining the gains improves robustness of the network to ill-conditioned inputs, and a generalization of the circuit achieves a form of local whitening in convolutional populations, such as those found throughout the visual or auditory systems.

We analyze a family of large language models in such a lightweight manner that can be done on a single GPU. Specifically, we focus on the OPT family of models ranging from 125m to 66b parameters and rely only on whether an FFN neuron is activated or not. First, we find that the early part of the network is sparse and represents many discrete features. Here, many neurons (more than 70% in some layers of the 66b model) are "dead", i.e. they never activate on a large collection of diverse data. At the same time, many of the alive neurons are reserved for discrete features and act as token and n-gram detectors. Interestingly, their corresponding FFN updates not only promote next token candidates as could be expected, but also explicitly focus on removing the information about triggering them tokens, i.e., current input. To the best of our knowledge, this is the first example of mechanisms specialized at removing (rather than adding) information from the residual stream. With scale, models become more sparse in a sense that they have more dead neurons and token detectors. Finally, some neurons are positional: them being activated or not depends largely (or solely) on position and less so (or not at all) on textual data. We find that smaller models have sets of neurons acting as position range indicators while larger models operate in a less explicit manner.

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We provide an asymptotic theoretical description of the grokking dynamics in this model using dynamical mean field theory (DMFT) for high dimensional data. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function y(x). We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels y(x) are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

Historically, artificial intelligence has drawn much inspiration from neuroscience to fuel advances in the field. However, current progress in reinforcement learning is largely focused on benchmark problems that fail to capture many of the aspects that are of interest in neuroscience today. We illustrate this point by extending a T-maze task from neuroscience for use with reinforcement learning algorithms, and show that state-of-the-art algorithms are not capable of solving this problem. Finally, we point out where insights from neuroscience could help explain some of the issues encountered.

How can we build agents that keep learning from experience, quickly and efficiently, after their initial training? Here we take inspiration from the main mechanism of learning in biological brains: synaptic plasticity, carefully tuned by evolution to produce efficient lifelong learning. We show that plasticity, just like connection weights, can be optimized by gradient descent in large (millions of parameters) recurrent networks with Hebbian plastic connections. First, recurrent plastic networks with more than two million parameters can be trained to memorize and reconstruct sets of novel, high-dimensional 1000+ pixels natural images not seen during training. Crucially, traditional non-plastic recurrent networks fail to solve this task. Furthermore, trained plastic networks can also solve generic meta-learning tasks such as the Omniglot task, with competitive results and little parameter overhead. Finally, in reinforcement learning settings, plastic networks outperform a non-plastic equivalent in a maze exploration task. We conclude that differentiable plasticity may provide a powerful novel approach to the learning-to-learn problem.

Models for low-latency, streaming applications could benefit from the knowledge capacity of larger models, but edge devices cannot run these models due to resource constraints. A possible solution is to transfer hints during inference from a large model running remotely to a small model running on-device. However, this incurs a communication delay that breaks real-time requirements and does not guarantee that both models will operate on the same data at the same time. We propose knowledge boosting, a novel technique that allows a large model to operate on time-delayed input during inference, while still boosting small model performance. Using a streaming neural network that processes 8 ms chunks, we evaluate different speech separation and enhancement tasks with communication delays of up to six chunks or 48 ms. Our results show larger gains where the performance gap between the small and large models is wide, demonstrating a promising method for large-small model collaboration for low-latency applications. Code, dataset, and audio samples available at https://knowledgeboosting.cs.washington.edu/.

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.

Learning to remember over long timescales is fundamentally challenging for recurrent neural networks (RNNs). While much prior work has explored why RNNs struggle to learn long timescales and how to mitigate this, we still lack a clear understanding of the dynamics involved when RNNs learn long timescales via gradient descent. Here we build a mathematical theory of the learning dynamics of linear RNNs trained to integrate white noise. We show that when the initial recurrent weights are small, the dynamics of learning are described by a low-dimensional system that tracks a single outlier eigenvalue of the recurrent weights. This reveals the precise manner in which the long timescale associated with white noise integration is learned. We extend our analyses to RNNs learning a damped oscillatory filter, and find rich dynamical equations for the evolution of a conjugate pair of outlier eigenvalues. Taken together, our analyses build a rich mathematical framework for studying dynamical learning problems salient for both machine learning and neuroscience.

Artificial neural networks for motor control usually adopt generic architectures like fully connected MLPs. While general, these tabula rasa architectures rely on large amounts of experience to learn, are not easily transferable to new bodies, and have internal dynamics that are difficult to interpret. In nature, animals are born with highly structured connectivity in their nervous systems shaped by evolution; this innate circuitry acts synergistically with learning mechanisms to provide inductive biases that enable most animals to function well soon after birth and learn efficiently. Convolutional networks inspired by visual circuitry have encoded useful biases for vision. However, it is unknown the extent to which ANN architectures inspired by neural circuitry can yield useful biases for other AI domains. In this work, we ask what advantages biologically inspired ANN architecture can provide in the domain of motor control. Specifically, we translate C. elegans locomotion circuits into an ANN model controlling a simulated Swimmer agent. On a locomotion task, our architecture achieves good initial performance and asymptotic performance comparable with MLPs, while dramatically improving data efficiency and requiring orders of magnitude fewer parameters. Our architecture is interpretable and transfers to new body designs. An ablation analysis shows that constrained excitation/inhibition is crucial for learning, while weight initialization contributes to good initial performance. Our work demonstrates several advantages of biologically inspired ANN architecture and encourages future work in more complex embodied control.

Vital to primary visual processing, retinal circuitry shows many similar structures across a very broad array of species, both vertebrate and non-vertebrate, especially functional components such as lateral inhibition. This surprisingly conservative pattern raises a question of how evolution leads to it, and whether there is any alternative that can also prompt helpful preprocessing. Here we design a method using genetic algorithm that, with many degrees of freedom, leads to architectures whose functions are similar to biological retina, as well as effective alternatives that are different in structures and functions. We compare this model to natural evolution and discuss how our framework can come into goal-driven search and sustainable enhancement of neural network models in machine learning.

Spiking neural networks (SNN) are a biologically inspired model of neural networks with certain brain-like properties. In the past few decades, this model has received increasing attention in computer science community, owing also to the successful phenomenon of deep learning. In SNN, communication between neurons takes place through the spikes and spike trains. This differentiates these models from the ``standard'' artificial neural networks (ANN) where the frequency of spikes is replaced by real-valued signals. Spiking neural P systems (SNPS) can be considered a branch of SNN based more on the principles of formal automata, with many variants developed within the framework of the membrane computing theory. In this paper, we first briefly compare structure and function, advantages and drawbacks of SNN and SNPS. A key part of the article is a survey of recent results and applications of machine learning and deep learning models of both SNN and SNPS formalisms.

Gradient-based algorithms are a cornerstone of artificial neural network training, yet it remains unclear whether biological neural networks use similar gradient-based strategies during learning. Experiments often discover a diversity of synaptic plasticity rules, but whether these amount to an approximation to gradient descent is unclear. Here we investigate a previously overlooked possibility: that learning dynamics may include fundamentally non-gradient "curl"-like components while still being able to effectively optimize a loss function. Curl terms naturally emerge in networks with inhibitory-excitatory connectivity or Hebbian/anti-Hebbian plasticity, resulting in learning dynamics that cannot be framed as gradient descent on any objective. To investigate the impact of these curl terms, we analyze feedforward networks within an analytically tractable student-teacher framework, systematically introducing non-gradient dynamics through neurons exhibiting rule-flipped plasticity. Small curl terms preserve the stability of the original solution manifold, resulting in learning dynamics similar to gradient descent. Beyond a critical value, strong curl terms destabilize the solution manifold. Depending on the network architecture, this loss of stability can lead to chaotic learning dynamics that destroy performance. In other cases, the curl terms can counterintuitively speed learning compared to gradient descent by allowing the weight dynamics to escape saddles by temporarily ascending the loss. Our results identify specific architectures capable of supporting robust learning via diverse learning rules, providing an important counterpoint to normative theories of gradient-based learning in neural networks.

Cells that collide with each other repolarize away from contact, in a process called contact inhibition of locomotion (CIL), which is necessary for correct development of the embryo. CIL can occur even when cells make a micron-scale contact with a neighbor - much smaller than their size. How precisely can a cell sense cell-cell contact and repolarize in the correct direction? What factors control whether a cell recognizes it has contacted a neighbor? We propose a theoretical model for the limits of CIL where cells recognize the presence of another cell by binding the protein ephrin with the Eph receptor. This recognition is made difficult by the presence of interfering ligands that bind nonspecifically. Both theoretical predictions and simulation results show that it becomes more difficult to sense cell-cell contact when it is difficult to distinguish ephrin from the interfering ligands, or when there are more interfering ligands, or when the contact width decreases. However, the error of estimating contact position remains almost constant when the contact width changes. This happens because the cell gains spatial information largely from the boundaries of cell-cell contact. We study using statistical decision theory the likelihood of a false positive CIL event in the absence of cell-cell contact, and the likelihood of a false negative where CIL does not occur when another cell is present. Our results suggest that the cell is more likely to make incorrect decisions when the contact width is very small or so large that it nears the cell's perimeter. However, in general, we find that cells have the ability to make reasonably reliable CIL decisions even for very narrow (micron-scale) contacts, even if the concentration of interfering ligands is ten times that of the correct ligands.

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105 585-593 (2003), Annu. Rev. Phys. Chem. 58 113-142 (2007)], emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models, and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential triangle G=0, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in phosphorylation-dephosphorylation cycle respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by "dissociation constants", which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule which can not be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein which can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon.

The electron microscope (EM) remains the predominant technique for elucidating intricate details of the animal nervous system at the nanometer scale. However, accurately reconstructing the complex morphology of axons and myelin sheaths poses a significant challenge. Furthermore, the absence of publicly available, large-scale EM datasets encompassing complete cross sections of the corpus callosum, with dense ground truth segmentation for axons and myelin sheaths, hinders the advancement and evaluation of holistic corpus callosum reconstructions. To surmount these obstacles, we introduce the AxonCallosumEM dataset, comprising a 1.83 times 5.76mm EM image captured from the corpus callosum of the Rett Syndrome (RTT) mouse model, which entail extensive axon bundles. We meticulously proofread over 600,000 patches at a resolution of 1024 times 1024, thus providing a comprehensive ground truth for myelinated axons and myelin sheaths. Additionally, we extensively annotated three distinct regions within the dataset for the purposes of training, testing, and validation. Utilizing this dataset, we develop a fine-tuning methodology that adapts Segment Anything Model (SAM) to EM images segmentation tasks, called EM-SAM, enabling outperforms other state-of-the-art methods. Furthermore, we present the evaluation results of EM-SAM as a baseline.

Recent advancements in the direct training of Spiking Neural Networks (SNNs) have demonstrated high-quality outputs even at early timesteps, paving the way for novel energy-efficient AI paradigms. However, the inherent non-linearity and temporal dependencies in SNNs introduce persistent challenges, such as temporal covariate shift (TCS) and unstable gradient flow with learnable neuron thresholds. In this paper, we present two key innovations: MP-Init (Membrane Potential Initialization) and TrSG (Threshold-robust Surrogate Gradient). MP-Init addresses TCS by aligning the initial membrane potential with its stationary distribution, while TrSG stabilizes gradient flow with respect to threshold voltage during training. Extensive experiments validate our approach, achieving state-of-the-art accuracy on both static and dynamic image datasets. The code is available at: https://github.com/kookhh0827/SNN-MP-Init-TRSG

Networks capture our intuition about relationships in the world. They describe the friendships between Facebook users, interactions in financial markets, and synapses connecting neurons in the brain. These networks are richly structured with cliques of friends, sectors of stocks, and a smorgasbord of cell types that govern how neurons connect. Some networks, like social network friendships, can be directly observed, but in many cases we only have an indirect view of the network through the actions of its constituents and an understanding of how the network mediates that activity. In this work, we focus on the problem of latent network discovery in the case where the observable activity takes the form of a mutually-excitatory point process known as a Hawkes process. We build on previous work that has taken a Bayesian approach to this problem, specifying prior distributions over the latent network structure and a likelihood of observed activity given this network. We extend this work by proposing a discrete-time formulation and developing a computationally efficient stochastic variational inference (SVI) algorithm that allows us to scale the approach to long sequences of observations. We demonstrate our algorithm on the calcium imaging data used in the Chalearn neural connectomics challenge.

Does structure in representations imply structure in computation? We study how Llama-3.1-8B reasons over cyclic concepts (e.g., "what month is six months after August?"). Even though Llama-3.1-8B's representations for these concepts are circularly structured, we find that instead of directly computing modular addition in the period of the cyclic concept (e.g., 12 for months), the model re-uses a generic addition mechanism across tasks that operates independently of concept-specific geometry. First, it computes the sum of its two inputs using base-10 addition (six + August=14). Then, it maps this sum back to cyclic concept space (14->February). We show that Llama-3.1-8B uses task-agnostic Fourier features to compute these sums--in fact, these features have periods that respect standard base-10 addition, e.g., 2, 5, and 10, rather than the cyclic concept period (e.g., 12 for months). Furthermore, we identify a sparse set of 28 MLP neurons re-used across all tasks (approximately 0.2% of the MLP at layer 18) that can be partitioned into disjoint clusters, each computing the sum for a Fourier feature with a different period. Our work highlights how an interplay between causal abstraction and feature geometry can deepen our mechanistic understanding of LMs.

There is an analogy that is often made between deep neural networks and actual brains, suggested by the nomenclature itself: the "neurons" in deep neural networks should correspond to neurons (or nerve cells, to avoid confusion) in the brain. We claim, however, that this analogy doesn't even type check: it is structurally flawed. In agreement with the slightly glib summary of Hebbian learning as "cells that fire together wire together", this article makes the case that the analogy should be different. Since the "neurons" in deep neural networks are managing the changing weights, they are more akin to the synapses in the brain; instead, it is the wires in deep neural networks that are more like nerve cells, in that they are what cause the information to flow. An intuition that nerve cells seem like more than mere wires is exactly right, and is justified by a precise category-theoretic analogy which we will explore in this article. Throughout, we will continue to highlight the error in equating artificial neurons with nerve cells by leaving "neuron" in quotes or by calling them artificial neurons. We will first explain how to view deep neural networks as nested dynamical systems with a very restricted sort of interaction pattern, and then explain a more general sort of interaction for dynamical systems that is useful throughout engineering, but which fails to adapt to changing circumstances. As mentioned, an analogy is then forced upon us by the mathematical formalism in which they are both embedded. We call the resulting encompassing generalization deeply interacting learning systems: they have complex interaction as in control theory, but adaptation to circumstances as in deep neural networks.

Neural network training is commonly accelerated by using multiple synchronized workers to compute gradient updates in parallel. Asynchronous methods remove synchronization overheads and improve hardware utilization at the cost of introducing gradient delay, which impedes optimization and can lead to lower final model performance. We introduce Adaptive Braking (AB), a modification for momentum-based optimizers that mitigates the effects of gradient delay. AB dynamically scales the gradient based on the alignment of the gradient and the velocity. This can dampen oscillations along high curvature directions of the loss surface, stabilizing and accelerating asynchronous training. We show that applying AB on top of SGD with momentum enables training ResNets on CIFAR-10 and ImageNet-1k with delays D geq 32 update steps with minimal drop in final test accuracy.