arXiv subjects

Marc W. Howard

Publications and source records attributed to Marc W. Howard.

15 recordsLinked to original sources

arXiv2026

Hierarchical temporal receptive windows and zero-shot timescale generalization in biologically constrained scale-invariant deep networks

Human cognition integrates information across nested timescales. While the cortex exhibits hierarchical Temporal Receptive Windows (TRWs), local circuits often display heterogeneous time constants. To reconcile this, we trained biologically constrained deep networks, based on scale-invariant hippocampal time cells, on a language classification task mimicking the hierarchical structure of language (e.g., 'letters' forming 'words'). First, using a feedforward model (SITHCon), we found that a hierarchy of TRWs emerged naturally across layers, despite the network having an identical spectrum of time constants within layers. We then distilled these inductive priors into a biologically plausible recurrent architecture, SITH-RNN. Training a sequence of architectures ranging from generic RNNs to this restricted subset showed that the scale-invariant SITH-RNN learned faster with orders-of-magnitude fewer parameters, and generalized zero-shot to out-of-distribution timescales. These results suggest the brain employs scale-invariant, sequential priors - coding "what" happened "when" - making recurrent networks with such priors particularly well-suited to describe human cognition.

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arXiv2025

"What" x "When" working memory representations using Laplace Neural Manifolds

Working memory - the ability to remember recent events as they recede continuously into the past - requires the ability to represent any stimulus at any time delay. This property requires neurons coding working memory to show mixed selectivity, with conjunctive receptive fields (RFs) for stimuli and time, forming a representation of 'what' x 'when'. We study the properties of such a working memory in simple experiments where a single stimulus must be remembered for a short time. The requirement of conjunctive receptive fields allows the covariance matrix of the network to decouple neatly, allowing an understanding of the low-dimensional dynamics of the population. Different choices of temporal basis functions lead to qualitatively different dynamics. We study a specific choice - a Laplace space with exponential basis functions for time coupled to an "Inverse Laplace" space with circumscribed basis functions in time. We refer to this choice with basis functions that evenly tile log time as a Laplace Neural Manifold. Despite the fact that they are related to one another by a linear projection, the Laplace population shows a stable stimulus-specific subspace whereas the Inverse Laplace population shows rotational dynamics. The growth of the rank of the covariance matrix with time depends on the density of the temporal basis set; logarithmic tiling shows good agreement with data. We sketch a continuous attractor CANN that constructs a Laplace Neural Manifold. The attractor in the Laplace space appears as an edge; the attractor for the inverse space appears as a bump. This work provides a map for going from more abstract cognitive models of WM to circuit-level implementation using continuous attractor neural networks, and places constraints on the types of neural dynamics that support working memory.

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arXiv2024

Learning temporal relationships between symbols with Laplace Neural Manifolds

Firing across populations of neurons in many regions of the mammalian brain maintains a temporal memory, a neural timeline of the recent past. Behavioral results demonstrate that people can both remember the past and anticipate the future over an analogous internal timeline. This paper presents a mathematical framework for building this timeline of the future. We assume that the input to the system is a time series of symbols--sparse tokenized representations of the present--in continuous time. The goal is to record pairwise temporal relationships between symbols over a wide range of time scales. We assume that the brain has access to a temporal memory in the form of the real Laplace transform. Hebbian associations with a diversity of synaptic time scales are formed between the past timeline and the present symbol. The associative memory stores the convolution between the past and the present. Knowing the temporal relationship between the past and the present allows one to infer relationships between the present and the future. With appropriate normalization, this Hebbian associative matrix can store a Laplace successor representation and a Laplace predecessor representation from which measures of temporal contingency can be evaluated. The diversity of synaptic time constants allows for learning of non-stationary statistics as well as joint statistics between triplets of symbols. This framework synthesizes a number of recent neuroscientific findings including results from dopamine neurons in the mesolimbic forebrain.

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arXiv2024

Continuous Attractor Networks for Laplace Neural Manifolds

Many cognitive models, including those for predicting the time of future events, can be mapped onto a particular form of neural representation in which activity across a population of neurons is restricted to manifolds that specify the Laplace transform of functions of continuous variables. These populations coding Laplace transform are associated with another population that inverts the transform, approximating the original function. This paper presents a neural circuit that uses continuous attractor dynamics to represent the Laplace transform of a delta function evolving in time. One population places an edge at any location along a 1-D array of neurons; another population places a bump at a location corresponding to the edge. Together these two populations can estimate a Laplace transform of delta functions in time along with an approximate inverse transform. Building the circuit so the edge moves at an appropriate speed enables the network to represent events as a function of log time. Choosing the connections appropriately within the edge network make the network states map onto Laplace transform with exponential change as a function of time. In this paper we model a learned temporal association in which one stimulus predicts another at some fixed delay $T$. Shortly after $t=0$ the first stimulus recedes into the past. The Laplace Neural Manifold representing the past maintains the Laplace transform $\exp(-st)$. Another Laplace Neural Manifold represents the predicted future. At $t=0$, the second stimulus is represented a time $T$ in the future. At each moment between 0 and $T$, firing over the Laplace transform predicting the future changes as $\exp[-s(T-t)]$. Despite exponential growth in firing, the circuit is robust to noise, making it a practical means to implement Laplace Neural Manifolds in populations of neurons for a variety of cognitive models.

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arXiv2022

A deep convolutional neural network that is invariant to time rescaling

Human learners can readily understand speech, or a melody, when it is presented slower or faster than usual. Although deep convolutional neural networks (CNNs) are extremely powerful in extracting information from time series, they require explicit training to generalize to different time scales. This paper presents a deep CNN that incorporates a temporal representation inspired by recent findings from neuroscience. In the mammalian brain, time is represented by populations of neurons with temporal receptive fields. Critically, the peaks of the receptive fields form a geometric series, such that the population codes a set of temporal basis functions over log time. Because memory for the recent past is a function of log time, rescaling the input results in translation of the memory. The Scale-Invariant Temporal History Convolution network (SITHCon) builds a convolutional layer over this logarithmically-distributed temporal memory. A max-pool operation results in a network that is invariant to rescalings of time modulo edge effects. We compare performance of SITHCon to a Temporal Convolution Network (TCN). Although both networks can learn classification and regression problems on both univariate and multivariate time series f(t), only SITHCon generalizes to rescalings f(at). This property, inspired by findings from contemporary neuroscience and consistent with findings from cognitive psychology, may enable networks that learn with fewer training examples, fewer weights and that generalize more robustly to out of sample data.

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arXiv2022

Formal models of memory based on temporally-varying representations

The idea that memory behavior relies on a gradually-changing internal state has a long history in mathematical psychology. This chapter traces this line of thought from statistical learning theory in the 1950s, through distributed memory models in the latter part of the 20th century and early part of the 21st century through to modern models based on a scale-invariant temporal history. We discuss the neural phenomena consistent with this form of representation and sketch the kinds of cognitive models that can be constructed using it and connections with formal models of various memory tasks.

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arXiv2021

DeepSITH: Efficient Learning via Decomposition of What and When Across Time Scales

Extracting temporal relationships over a range of scales is a hallmark of human perception and cognition -- and thus it is a critical feature of machine learning applied to real-world problems. Neural networks are either plagued by the exploding/vanishing gradient problem in recurrent neural networks (RNNs) or must adjust their parameters to learn the relevant time scales (e.g., in LSTMs). This paper introduces DeepSITH, a network comprising biologically-inspired Scale-Invariant Temporal History (SITH) modules in series with dense connections between layers. SITH modules respond to their inputs with a geometrically-spaced set of time constants, enabling the DeepSITH network to learn problems along a continuum of time-scales. We compare DeepSITH to LSTMs and other recent RNNs on several time series prediction and decoding tasks. DeepSITH achieves state-of-the-art performance on these problems.

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arXiv2021

Predicting the future with a scale-invariant temporal memory for the past

In recent years it has become clear that the brain maintains a temporal memory of recent events stretching far into the past. This paper presents a neurally-inspired algorithm to use a scale-invariant temporal representation of the past to predict a scale-invariant future. The result is a scale-invariant estimate of future events as a function of the time at which they are expected to occur. The algorithm is time-local, with credit assigned to the present event by observing how it affects the prediction of the future. To illustrate the potential utility of this approach, we test the model on simultaneous renewal processes with different time scales. The algorithm scales well on these problems despite the fact that the number of states needed to describe them as a Markov process grows exponentially.

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arXiv2020

Cognitive computation using neural representations of time and space in the Laplace domain

Memory for the past makes use of a record of what happened when---a function over past time. Time cells in the hippocampus and temporal context cells in the entorhinal cortex both code for events as a function of past time, but with very different receptive fields. Time cells in the hippocampus can be understood as a compressed estimate of events as a function of the past. Temporal context cells in the entorhinal cortex can be understood as the Laplace transform of that function, respectively. Other functional cell types in the hippocampus and related regions, including border cells, place cells, trajectory coding, splitter cells, can be understood as coding for functions over space or past movements or their Laplace transforms. More abstract quantities, like distance in an abstract conceptual space or numerosity could also be mapped onto populations of neurons coding for the Laplace transform of functions over those variables. Quantitative cognitive models of memory and evidence accumulation can also be specified in this framework allowing constraints from both behavior and neurophysiology. More generally, the computational power of the Laplace domain could be important for efficiently implementing data-independent operators, which could serve as a basis for neural models of a very broad range of cognitive computations.

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arXiv2018

Scale-invariant temporal history (SITH): optimal slicing of the past in an uncertain world

In both the human brain and any general artificial intelligence (AI), a representation of the past is necessary to predict the future. However, perfect storage of all experiences is not feasible. One approach utilized in many applications, including reward prediction in reinforcement learning, is to retain recently active features of experience in a buffer. Despite its prior successes, we show that the fixed length buffer renders Deep Q-learning Networks (DQNs) fragile to changes in the scale over which information can be learned. To enable learning when the relevant temporal scales in the environment are not known *a priori*, recent advances in psychology and neuroscience suggest that the brain maintains a compressed representation of the past. Here we introduce a neurally-plausible, scale-free memory representation we call Scale-Invariant Temporal History (SITH) for use with artificial agents. This representation covers an exponentially large period of time by sacrificing temporal accuracy for events further in the past. We demonstrate the utility of this representation by comparing the performance of agents given SITH, buffer, and exponential decay representations in learning to play video games at different levels of complexity. In these environments, SITH exhibits better learning performance by storing information for longer timescales than a fixed-size buffer, and representing this information more clearly than a set of exponentially decayed features. Finally, we discuss how the application of SITH, along with other human-inspired models of cognition, could improve reinforcement and machine learning algorithms in general.

cs.AI↗

arXiv2018

Estimating scale-invariant future in continuous time

Natural learners must compute an estimate of future outcomes that follow from a stimulus in continuous time. Widely used reinforcement learning algorithms discretize continuous time and estimate either transition functions from one step to the next (model-based algorithms) or a scalar value of exponentially-discounted future reward using the Bellman equation (model-free algorithms). An important drawback of model-based algorithms is that computational cost grows linearly with the amount of time to be simulated. On the other hand, an important drawback of model-free algorithms is the need to select a time-scale required for exponential discounting. We present a computational mechanism, developed based on work in psychology and neuroscience, for computing a scale-invariant timeline of future outcomes. This mechanism efficiently computes an estimate of inputs as a function of future time on a logarithmically-compressed scale, and can be used to generate a scale-invariant power-law-discounted estimate of expected future reward. The representation of future time retains information about what will happen when. The entire timeline can be constructed in a single parallel operation which generates concrete behavioral and neural predictions. This computational mechanism could be incorporated into future reinforcement learning algorithms.

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arXiv2018

Evidence accumulation in a Laplace domain decision space

Evidence accumulation models of simple decision-making have long assumed that the brain estimates a scalar decision variable corresponding to the log-likelihood ratio of the two alternatives. Typical neural implementations of this algorithmic cognitive model assume that large numbers of neurons are each noisy exemplars of the scalar decision variable. Here we propose a neural implementation of the diffusion model in which many neurons construct and maintain the Laplace transform of the distance to each of the decision bounds. As in classic findings from brain regions including LIP, the firing rate of neurons coding for the Laplace transform of net accumulated evidence grows to a bound during random dot motion tasks. However, rather than noisy exemplars of a single mean value, this approach makes the novel prediction that firing rates grow to the bound exponentially, across neurons there should be a distribution of different rates. A second set of neurons records an approximate inversion of the Laplace transform, these neurons directly estimate net accumulated evidence. In analogy to time cells and place cells observed in the hippocampus and other brain regions, the neurons in this second set have receptive fields along a "decision axis." This finding is consistent with recent findings from rodent recordings. This theoretical approach places simple evidence accumulation models in the same mathematical language as recent proposals for representing time and space in cognitive models for memory.

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arXiv2017

Neural scaling laws for an uncertain world

Autonomous neural systems must efficiently process information in a wide range of novel environments, which may have very different statistical properties. We consider the problem of how to optimally distribute receptors along a one-dimensional continuum consistent with the following design principles. First, neural representations of the world should obey a neural uncertainty principle---making as few assumptions as possible about the statistical structure of the world. Second, neural representations should convey, as much as possible, equivalent information about environments with different statistics. The results of these arguments resemble the structure of the visual system and provide a natural explanation of the behavioral Weber-Fechner law, a foundational result in psychology. Because the derivation is extremely general, this suggests that similar scaling relationships should be observed not only in sensory continua, but also in neural representations of ``cognitive' one-dimensional quantities such as time or numerosity.

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arXiv2015

Neural mechanism to simulate a scale-invariant future timeline

Predicting future events, and their order, is important for efficient planning. We propose a neural mechanism to non-destructively translate the current state of memory into the future, so as to construct an ordered set of future predictions. This framework applies equally well to translations in time or in one-dimensional position. In a two-layer memory network that encodes the Laplace transform of the external input in real time, translation can be accomplished by modulating the weights between the layers. We propose that within each cycle of hippocampal theta oscillations, the memory state is swept through a range of translations to yield an ordered set of future predictions. We operationalize several neurobiological findings into phenomenological equations constraining translation. Combined with constraints based on physical principles requiring scale-invariance and coherence in translation across memory nodes, the proposition results in Weber-Fechner spacing for the representation of both past (memory) and future (prediction) timelines. The resulting expressions are consistent with findings from phase precession experiments in different regions of the hippocampus and reward systems in the ventral striatum. The model makes several experimental predictions that can be tested with existing technology.

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arXiv2013

Optimally fuzzy temporal memory

Any learner with the ability to predict the future of a structured time-varying signal must maintain a memory of the recent past. If the signal has a characteristic timescale relevant to future prediction, the memory can be a simple shift register---a moving window extending into the past, requiring storage resources that linearly grows with the timescale to be represented. However, an independent general purpose learner cannot a priori know the characteristic prediction-relevant timescale of the signal. Moreover, many naturally occurring signals show scale-free long range correlations implying that the natural prediction-relevant timescale is essentially unbounded. Hence the learner should maintain information from the longest possible timescale allowed by resource availability. Here we construct a fuzzy memory system that optimally sacrifices the temporal accuracy of information in a scale-free fashion in order to represent prediction-relevant information from exponentially long timescales. Using several illustrative examples, we demonstrate the advantage of the fuzzy memory system over a shift register in time series forecasting of natural signals. When the available storage resources are limited, we suggest that a general purpose learner would be better off committing to such a fuzzy memory system.

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