arXiv subjects

Terrence J. Sejnowski

Publications and source records attributed to Terrence J. Sejnowski.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical Mechanisms for Coordinating Long-term Working Memory Based on the Precision of Spike-timing in Cortical Neurons

In the last century, most sensorimotor studies of cortical neurons relied on average firing rates. Rate coding is efficient for fast sensorimotor processing that occurs within a few seconds. Much less is known about the neural mechanisms underlying long-term working memory with a time scale of hours. Cognitive states may not have sensory or motor correlates. For example, you can sit in a quiet room making plans without moving or sensory processing. You can also make plans while out walking. In this perspective, I make the case for a possible second tier of neural activity that coexists with the well-established sensorimotor tier. The prominent physiological feature of the second tier is coordinated spike timing activity. The interplay of data supporting this hypothesis involves three puzzling yet highly intriguing experimental observations, without any obvious indication that they might actually represent different aspects of a single functional organization. First, consider the precision of spiking in individual neurons. The discovery of millisecond-precision spike initiation in cortical neurons was unexpected (Mainen and Sejnowski, 1995). Even more striking was the precision of spiking in vivo, in response to rapidly fluctuating sensory inputs. Second, high temporal resolution can also mediate spike timing-dependent plasticity (STDP) by controlling the relative timing of presynaptic and postsynaptic spikes at the millisecond scale. Third, we observe waves across many frequency bands traveling across the cortex. Strikingly, their timing is highly precise. Gamma waves, for example, which are triggered by attention, can plausibly trigger STDP that lasts for hours in cortical neurons. This temporary cortical network, ostensibly a second tier of functionality, rides astride the long-term sensorimotor network and could support cognitive processing and long-term working memory.

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arXiv2026

Causal Dynamic Resonance

Many dynamical systems in nature, such as brains and weather systems, are highly nonlinear and complex. Determining information flow among the components that make up these dynamical systems is challenging. If the components are the result of a common process or become synchronized, causality measures typically fail. We previously introduced Cross-Dynamical Delay Differential Analysis (CD-DDA), a nonlinear method for assessing causal influence, along with a complementary approach for dynamical similarity between time series data, Dynamical Ergodicity Delay Differential Analysis (DE-DDA). Here, we show that ``Causal Dynamic Resonance (CDR)'' further improves the false positive rejection rate by adding white noise to the data, without perturbing the underlying dynamical system. This is followed by a study of CDR in coupled Rössler systems, where ground truth interactions are known and in invasive intracranial electroencephalographic (iEEG) data from drug-resistant epilepsy patients undergoing presurgical monitoring.

nlin.CD↗

arXiv2026

A Spatiotemporal Perspective on Dynamical Computation in Neural Information Processing Systems

Spatiotemporal flows of neural activity, such as traveling waves, have been observed throughout the brain since the earliest recordings; yet there is still little consensus on their functional role. Recent experiments and models have linked traveling waves to visual and physical motion, but these observations have been difficult to reconcile with standard accounts of topographically organized selectivity and feedforward receptive fields. Here, we introduce a theoretical framework that formalizes and generalizes the connection between 'motion' and flowing neural dynamics in the language of equivariant neural network theory. We consider 'motion' not only in physical or visual spaces, but also in more abstract representational spaces, and we argue that recurrent traveling-wave-like dynamics are not just useful but necessary for accurate and stable processing of any signal undergoing such motion. Formally, we show that for any non-trivial recurrent neural network to process a sequence undergoing a flow transformation (such as visual motion) in a structured equivariant manner, its hidden state dynamics must actively realize a homomorphic representation of the same flow through recurrent connectivity. In this ''spatiotemporal perspective on dynamical computation'', traveling waves and related flows are best understood as faithful dynamic representations of stimulus flows; and consequently the natural inclination of biological systems towards such dynamics may be viewed as an innate inductive bias towards efficiency and generalization in the spatiotemporally-structured dynamical world they inhabit.

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arXiv2026

Bridging Expressivity and Scalability with Adaptive Unitary SSMs

Recent work has revealed that state space models (SSMs), while efficient for long-sequence processing, are fundamentally limited in their ability to represent formal languages-particularly due to time-invariant and real-valued recurrence structures. In this work, we draw inspiration from adaptive and structured dynamics observed in biological neural systems and introduce the Adaptive Unitary State Space Model (AUSSM): a novel class of SSMs that leverages skew-symmetric, input-dependent recurrence to achieve unitary evolution and high expressive power. Using algebraic automata theory, we prove that AUSSM can perform modulo counting and simulate solvable group automata at precision logarithmically bounded in the input length, enabling SSMs to model a broad class of regular languages out of reach for other SSM architectures. To overcome the practical inefficiencies of adaptive recurrence, we develop a separable convolution formulation and a CUDA implementation that enables scalable parallel training. Empirically, we show that AUSSM and its hybrid variant-interleaved with Mamba-outperform prior SSMs on formal algorithmic tasks such as parity and modular arithmetic, and achieve competent performance on real-world long time-series classification benchmarks. Our results demonstrate that adaptive unitary recurrence provides a powerful and efficient inductive bias for both symbolic and continuous sequence modeling. The code is available at https://github.com/arjunkaruvally/AUSSM

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arXiv2025

Exponential Dynamic Energy Network for High Capacity Sequence Memory

The energy paradigm, exemplified by Hopfield networks, offers a principled framework for memory in neural systems by interpreting dynamics as descent on an energy surface. While powerful for static associative memories, it falls short in modeling sequential memory, where transitions between memories are essential. We introduce the Exponential Dynamic Energy Network (EDEN), a novel architecture that extends the energy paradigm to temporal domains by evolving the energy function over multiple timescales. EDEN combines a static high-capacity energy network with a slow, asymmetrically interacting modulatory population, enabling robust and controlled memory transitions. We formally derive short-timescale energy functions that govern local dynamics and use them to analytically compute memory escape times, revealing a phase transition between static and dynamic regimes. The analysis of capacity, defined as the number of memories that can be stored with minimal error rate as a function of the dimensions of the state space (number of feature neurons), for EDEN shows that it achieves exponential sequence memory capacity $O(γ^N)$, outperforming the linear capacity $O(N)$ of conventional models. Furthermore, EDEN's dynamics resemble the activity of time and ramping cells observed in the human brain during episodic memory tasks, grounding its biological relevance. By unifying static and sequential memory within a dynamic energy framework, EDEN offers a scalable and interpretable model for high-capacity temporal memory in both artificial and biological systems.

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arXiv2025

The Memory Paradox: Why Our Brains Need Knowledge in an Age of AI

In the age of generative AI and ubiquitous digital tools, human cognition faces a structural paradox: as external aids become more capable, internal memory systems risk atrophy. Drawing on neuroscience and cognitive psychology, this paper examines how heavy reliance on AI systems and discovery-based pedagogies may impair the consolidation of declarative and procedural memory -- systems essential for expertise, critical thinking, and long-term retention. We review how tools like ChatGPT and calculators can short-circuit the retrieval, error correction, and schema-building processes necessary for robust neural encoding. Notably, we highlight striking parallels between deep learning phenomena such as "grokking" and the neuroscience of overlearning and intuition. Empirical studies are discussed showing how premature reliance on AI during learning inhibits proceduralization and intuitive mastery. We argue that effective human-AI interaction depends on strong internal models -- biological "schemata" and neural manifolds -- that enable users to evaluate, refine, and guide AI output. The paper concludes with policy implications for education and workforce training in the age of large language models.

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arXiv2024

Transformers and Cortical Waves: Encoders for Pulling In Context Across Time

The capabilities of transformer networks such as ChatGPT and other Large Language Models (LLMs) have captured the world's attention. The crucial computational mechanism underlying their performance relies on transforming a complete input sequence - for example, all the words in a sentence - into a long "encoding vector" that allows transformers to learn long-range temporal dependencies in naturalistic sequences. Specifically, "self-attention" applied to this encoding vector enhances temporal context in transformers by computing associations between pairs of words in the input sequence. We suggest that waves of neural activity traveling across single cortical areas or multiple regions at the whole-brain scale could implement a similar encoding principle. By encapsulating recent input history into a single spatial pattern at each moment in time, cortical waves may enable temporal context to be extracted from sequences of sensory inputs, the same computational principle used in transformers.

cs.CL↗

arXiv2024

Hidden Traveling Waves bind Working Memory Variables in Recurrent Neural Networks

Traveling waves are a fundamental phenomenon in the brain, playing a crucial role in short-term information storage. In this study, we leverage the concept of traveling wave dynamics within a neural lattice to formulate a theoretical model of neural working memory, study its properties, and its real world implications in AI. The proposed model diverges from traditional approaches, which assume information storage in static, register-like locations updated by interference. Instead, the model stores data as waves that is updated by the wave's boundary conditions. We rigorously examine the model's capabilities in representing and learning state histories, which are vital for learning history-dependent dynamical systems. The findings reveal that the model reliably stores external information and enhances the learning process by addressing the diminishing gradient problem. To understand the model's real-world applicability, we explore two cases: linear boundary condition (LBC) and non-linear, self-attention-driven boundary condition (SBC). The model with the linear boundary condition results in a shift matrix plus low-rank matrix currently used in H3 state space RNN. Further, our experiments with LBC reveal that this matrix is effectively learned by Recurrent Neural Networks (RNNs) through backpropagation when modeling history-dependent dynamical systems. Conversely, the SBC parallels the autoregressive loop of an attention-only transformer with the context vector representing the wave substrate. Collectively, our findings suggest the broader relevance of traveling waves in AI and its potential in advancing neural network architectures.

cs.NE↗

arXiv2023

Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays

We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix associated to the system, leading to the emergence of waves with a preferred direction. We then create analytical predictions for the specific spatiotemporal patterns observed in individual simulations of time-delayed Kuramoto networks. This approach generalizes to systems with heterogeneous time delays at finite scales, which permits the study of spatiotemporal dynamics in a broad range of applications.

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arXiv2023

Internal feedback in the cortical perception-action loop enables fast and accurate behavior

Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single, unidirectional perception-action loop. This loop contains internal delays in sensory and motor pathways, which can lead to unstable control. We show here that these delays can be compensated by internal feedback signals that flow backwards, from motor towards sensory areas. Internal feedback is ubiquitous in neural sensorimotor systems and recent advances in control theory show how internal feedback compensates internal delays. This is accomplished by filtering out self-generated and other predictable changes in early sensory areas so that unpredicted, actionable information can be rapidly transmitted toward action by the fastest components. For example, fast, giant neurons are necessarily less accurate than smaller neurons, but they are crucial for fast and accurate behavior. We use a mathematically tractable control model to show that internal feedback has an indispensable role in achieving state estimation, localization of function -- how different parts of cortex control different parts of the body -- and attention, all of which are crucial for effective sensorimotor control. This control model can explain anatomical, physiological and behavioral observations, including motor signals in visual cortex, heterogeneous kinetics of sensory receptors and the presence of giant Betz cells in motor cortex, Meynert cells in visual cortex and giant von Economo cells in the prefrontal cortex of humans as well as internal feedback patterns and unexplained heterogeneity in other neural systems.

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arXiv2022

Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks

One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding complex-valued system that permits describing the system in terms of a linear operator and iterative update rule. We now use this description to investigate three major synchronization phenomena in Kuramoto networks (phase synchronization, chimera states, and traveling waves), not only in terms of steady state solutions but also in terms of transient dynamics and individual simulations. These results provide new mathematical insight into how sophisticated behaviors arise from connection patterns in nonlinear networked systems.

math.DS↗

arXiv2021

Replay in Deep Learning: Current Approaches and Missing Biological Elements

Replay is the reactivation of one or more neural patterns, which are similar to the activation patterns experienced during past waking experiences. Replay was first observed in biological neural networks during sleep, and it is now thought to play a critical role in memory formation, retrieval, and consolidation. Replay-like mechanisms have been incorporated into deep artificial neural networks that learn over time to avoid catastrophic forgetting of previous knowledge. Replay algorithms have been successfully used in a wide range of deep learning methods within supervised, unsupervised, and reinforcement learning paradigms. In this paper, we provide the first comprehensive comparison between replay in the mammalian brain and replay in artificial neural networks. We identify multiple aspects of biological replay that are missing in deep learning systems and hypothesize how they could be utilized to improve artificial neural networks.

q-bio.NC↗

arXiv2021

Diversity-enabled sweet spots in layered architectures and speed-accuracy trade-offs in sensorimotor control

Nervous systems sense, communicate, compute and actuate movement using distributed components with severe trade-offs in speed, accuracy, sparsity, noise and saturation. Nevertheless, brains achieve remarkably fast, accurate, and robust control performance due to a highly effective layered control architecture. Here we introduce a driving task to study how a mountain biker mitigates the immediate disturbance of trail bumps and responds to changes in trail direction. We manipulated the time delays and accuracy of the control input from the wheel as a surrogate for manipulating the characteristics of neurons in the control loop. The observed speed-accuracy trade-offs (SATs) motivated a theoretical framework consisting of layers of control loops with components having diverse speeds and accuracies within each physical level, such as nerve bundles containing axons with a wide range of sizes. Our model explains why the errors from two control loops -- one fast but inaccurate reflexive layer that corrects for bumps, and a planning layer that is slow but accurate -- are additive, and show how the errors in each control loop can be decomposed into the errors caused by the limited speeds and accuracies of the components. These results demonstrate that an appropriate diversity in the properties of neurons across layers helps to create "diversity-enabled sweet spots" (DESSs) so that both fast and accurate control is achieved using slow or inaccurate components.

math.OC↗

arXiv2020

Assessing observability of chaotic systems using Delay Differential Analysis

Observability can determine which recorded variables of a given system are optimal for discriminating its different states. Quantifying observability requires knowledge of the equations governing the dynamics. These equations are often unknown when experimental data are considered. Consequently, we propose an approach for numerically assessing observability using Delay Differential Analysis (DDA). Given a time series, DDA uses a delay differential equation for approximating the measured data. The lower the least squares error between the predicted and recorded data, the higher the observability. We thus rank the variables of several chaotic systems according to their corresponding least square error to assess observability. The performance of our approach is evaluated by comparison with the ranking provided by the symbolic observability coefficients as well as with two other data-based approaches using reservoir computing and singular value decomposition of the reconstructed space. We investigate the robustness of our approach against noise contamination.

nlin.AO↗

arXiv2020

The Unreasonable Effectiveness of Deep Learning in Artificial Intelligence

Deep learning networks have been trained to recognize speech, caption photographs and translate text between languages at high levels of performance. Although applications of deep learning networks to real world problems have become ubiquitous, our understanding of why they are so effective is lacking. These empirical results should not be possible according to sample complexity in statistics and non-convex optimization theory. However, paradoxes in the training and effectiveness of deep learning networks are being investigated and insights are being found in the geometry of high-dimensional spaces. A mathematical theory of deep learning would illuminate how they function, allow us to assess the strengths and weaknesses of different network architectures and lead to major improvements. Deep learning has provided natural ways for humans to communicate with digital devices and is foundational for building artificial general intelligence. Deep learning was inspired by the architecture of the cerebral cortex and insights into autonomy and general intelligence may be found in other brain regions that are essential for planning and survival, but major breakthroughs will be needed to achieve these goals.

q-bio.NC↗

arXiv2019

Fitts' Law for speed-accuracy trade-off describes a diversity-enabled sweet spot in sensorimotor control

Human sensorimotor control exhibits remarkable speed and accuracy, and the tradeoff between them is encapsulated in Fitts' Law for reaching and pointing. While Fitts related this to Shannon's channel capacity theorem, despite widespread study of Fitts' Law, a theory that connects implementation of sensorimotor control at the system and hardware level has not emerged. Here we describe a theory that connects hardware (neurons and muscles with inherent severe speed-accuracy tradeoffs) with system level control to explain Fitts' Law for reaching and related laws. The results supporting the theory show that diversity between hardware components is exploited to achieve both fast and accurate control performance despite slow or inaccurate hardware. Such "diversity-enabled sweet spots" (DESSs) are ubiquitous in biology and technology, and explain why large heterogeneities exist in biological and technical components and how both engineers and natural selection routinely evolve fast and accurate systems using imperfect hardware.

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arXiv2019

Utilizing Deep Learning Towards Multi-modal Bio-sensing and Vision-based Affective Computing

In recent years, the use of bio-sensing signals such as electroencephalogram (EEG), electrocardiogram (ECG), etc. have garnered interest towards applications in affective computing. The parallel trend of deep-learning has led to a huge leap in performance towards solving various vision-based research problems such as object detection. Yet, these advances in deep-learning have not adequately translated into bio-sensing research. This work applies novel deep-learning-based methods to various bio-sensing and video data of four publicly available multi-modal emotion datasets. For each dataset, we first individually evaluate the emotion-classification performance obtained by each modality. We then evaluate the performance obtained by fusing the features from these modalities. We show that our algorithms outperform the results reported by other studies for emotion/valence/arousal/liking classification on DEAP and MAHNOB-HCI datasets and set up benchmarks for the newer AMIGOS and DREAMER datasets. We also evaluate the performance of our algorithms by combining the datasets and by using transfer learning to show that the proposed method overcomes the inconsistencies between the datasets. Hence, we do a thorough analysis of multi-modal affective data from more than 120 subjects and 2,800 trials. Finally, utilizing a convolution-deconvolution network, we propose a new technique towards identifying salient brain regions corresponding to various affective states.

cs.LG↗

arXiv2018

MCell-R: A particle-resolution network-free spatial modeling framework

Spatial heterogeneity can have dramatic effects on the biochemical networks that drive cell regulation and decision-making. For this reason, a number of methods have been developed to model spatial heterogeneity and incorporated into widely used modeling platforms. Unfortunately, the standard approaches for specifying and simulating chemical reaction networks become untenable when dealing with multi-state, multi-component systems that are characterized by combinatorial complexity. To address this issue, we developed MCell-R, a framework that extends the particle-based spatial Monte Carlo simulator, MCell, with the rule-based model specification and simulation capabilities provided by BioNetGen and NFsim. The BioNetGen syntax enables the specification of biomolecules as structured objects whose components can have different internal states that represent such features as covalent modification and conformation and which can bind components of other molecules to form molecular complexes. The network-free simulation algorithm used by NFsim enables efficient simulation of rule-based models even when the size of the network implied by the biochemical rules is too large to enumerate explicitly, which frequently occurs in detailed models of biochemical signaling. The result is a framework that can efficiently simulate systems characterized by combinatorial complexity at the level of spatially-resolved individual molecules over biologically relevant time and length scales.

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