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

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.Comment: Revised for CB

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.First author draf

Human episodic memory retrieval is accompanied by a neural contiguity effect

Cognitive psychologists have long hypothesized that experiences are encoded in a temporal context that changes gradually over time. When an episodic memory is retrieved, the state of context is recovered—a jump back in time. We recorded from single units in the MTL of epilepsy patients performing an item recognition task. The population vector changed gradually over minutes during presentation of the list. When a probe from the list was remembered with high confidence, the population vector reinstated the temporal context of the original presentation of that probe during study—a neural contiguity effect that provides a possible mechanism for behavioral contiguity effects. This pattern was only observed for well-remembered probes; old probes that were not well-remembered showed an anti-contiguity effect. These results constitute the first direct evidence that recovery of an episodic memory in humans is associated with retrieval of a gradually-changing state of temporal context—a neural “jump-back-in-time” that parallels the act of remembering

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.Accepted manuscrip

Is working memory stored along a logarithmic timeline? Converging evidence from neuroscience, behavior and models

A growing body of evidence suggests that short-term memory does not only store the identity of recently experienced stimuli, but also information about when they were presented. This representation of 'what' happened 'when' constitutes a neural timeline of recent past. Behavioral results suggest that people can sequentially access memories for the recent past, as if they were stored along a timeline to which attention is sequentially directed. In the short-term judgment of recency (JOR) task, the time to choose between two probe items depends on the recency of the more recent probe but not on the recency of the more remote probe. This pattern of results suggests a backward self-terminating search model. We review recent neural evidence from the macaque lateral prefrontal cortex (lPFC) (Tiganj, Cromer, Roy, Miller, & Howard, in press) and behavioral evidence from human JOR task (Singh & Howard, 2017) bearing on this question. Notably, both lines of evidence suggest that the timeline is logarithmically compressed as predicted by Weber-Fechner scaling. Taken together, these findings provide an integrative perspective on temporal organization and neural underpinnings of short-term memory.R01 EB022864 - NIBIB NIH HHS; R01 MH112169 - NIMH NIH HHSAccepted manuscrip