Mathematical Modeling seminars

This webinar addressed computational perspectives on how animals and humans make decisions, spanning normative, descriptive, and mechanistic models. Sam Gershman (Harvard) presented a capacity-limited reinforcement learning framework in which policies are compressed under an information bottleneck constraint. This approach predicts pervasive perseveration, stimulus‐independent “default” actions, and trade-offs between complexity and reward. Such policy compression reconciles observed action stochasticity and response time patterns with an optimal balance between learning capacity and performance. Jonathan Pillow (Princeton) discussed flexible descriptive models for tracking time-varying policies in animals. He introduced dynamic Generalized Linear Models (Sidetrack) and hidden Markov models (GLM-HMMs) that capture day-to-day and trial-to-trial fluctuations in choice behavior, including abrupt switches between “engaged” and “disengaged” states. These models provide new insights into how animals’ strategies evolve under learning. Finally, Kenji Doya (OIST) highlighted the importance of unifying reinforcement learning with Bayesian inference, exploring how cortical-basal ganglia networks might implement model-based and model-free strategies. He also described Japan’s Brain/MINDS 2.0 and Digital Brain initiatives, aiming to integrate multimodal data and computational principles into cohesive “digital brains.”

In this talk, I will explore how social affective biases arise even in the absence of motivational factors as an emergent outcome of the basic structure of social learning. In several studies, we found that initial negative interactions with some members of a group can cause subsequent avoidance of the entire group, and that this avoidance perpetuates stereotypes. Additional cognitive modeling discovered that approach and avoidance behavior based on biased beliefs not only influences the evaluative (positive or negative) impressions of group members, but also shapes the depth of the cognitive representations available to learn about individuals. In other words, people have richer cognitive representations of members of groups that are not avoided, akin to individualized vs group level categories. I will end presenting a series of multi-agent reinforcement learning simulations that demonstrate the emergence of these social-structural feedback loops in the development and maintenance of affective biases.

Cognitive maps confer animals with flexible intelligence by representing spatial, temporal, and abstract relationships that can be used to shape thought, planning, and behavior. Cognitive maps have been observed in the hippocampus, but their algorithmic form and the processes by which they are learned remain obscure. Here, we employed large-scale, longitudinal two-photon calcium imaging to record activity from thousands of neurons in the CA1 region of the hippocampus while mice learned to efficiently collect rewards from two subtly different versions of linear tracks in virtual reality. The results provide a detailed view of the formation of a cognitive map in the hippocampus. Throughout learning, both the animal behavior and hippocampal neural activity progressed through multiple intermediate stages, gradually revealing improved task representation that mirrored improved behavioral efficiency. The learning process led to progressive decorrelations in initially similar hippocampal neural activity within and across tracks, ultimately resulting in orthogonalized representations resembling a state machine capturing the inherent struture of the task. We show that a Hidden Markov Model (HMM) and a biologically plausible recurrent neural network trained using Hebbian learning can both capture core aspects of the learning dynamics and the orthogonalized representational structure in neural activity. In contrast, we show that gradient-based learning of sequence models such as Long Short-Term Memory networks (LSTMs) and Transformers do not naturally produce such orthogonalized representations. We further demonstrate that mice exhibited adaptive behavior in novel task settings, with neural activity reflecting flexible deployment of the state machine. These findings shed light on the mathematical form of cognitive maps, the learning rules that sculpt them, and the algorithms that promote adaptive behavior in animals. The work thus charts a course toward a deeper understanding of biological intelligence and offers insights toward developing more robust learning algorithms in artificial intelligence.

Humans and animals are not always rational. They not only rationally exploit rewards but also explore an environment owing to their curiosity. However, the mechanism of such curiosity-driven irrational behavior is largely unknown. Here, we developed a decision-making model for a two-choice task based on the free energy principle, which is a theory integrating recognition and action selection. The model describes irrational behaviors depending on the curiosity level. We also proposed a machine learning method to decode temporal curiosity from behavioral data. By applying it to rat behavioral data, we found that the rat had negative curiosity, reflecting conservative selection sticking to more certain options and that the level of curiosity was upregulated by the expected future information obtained from an uncertain environment. Our decoding approach can be a fundamental tool for identifying the neural basis for reward–curiosity conflicts. Furthermore, it could be effective in diagnosing mental disorders.

When interacting with complex environments, humans can rapidly adapt their behavior to changes in task or context. To facilitate this adaptation, we often spend substantial periods of time contemplating possible futures before acting. For such planning to be rational, the benefits of planning to future behavior must at least compensate for the time spent thinking. Here we capture these features of human behavior by developing a neural network model where not only actions, but also planning, are controlled by prefrontal cortex. This model consists of a meta-reinforcement learning agent augmented with the ability to plan by sampling imagined action sequences drawn from its own policy, which we refer to as 'rollouts'. Our results demonstrate that this agent learns to plan when planning is beneficial, explaining the empirical variability in human thinking times. Additionally, the patterns of policy rollouts employed by the artificial agent closely resemble patterns of rodent hippocampal replays recently recorded in a spatial navigation task, in terms of both their spatial statistics and their relationship to subsequent behavior. Our work provides a new theory of how the brain could implement planning through prefrontal-hippocampal interactions, where hippocampal replays are triggered by - and in turn adaptively affect - prefrontal dynamics.

Humans and animals learn and plan with flexibility and efficiency well beyond that of modern Machine Learning methods. This is hypothesized to owe in part to the ability of animals to build structured representations of their environments, and modulate these representations to rapidly adapt to new settings. In the first part of this talk, I will discuss theoretical work describing how learned representations in hippocampus enable rapid adaptation to new goals by learning predictive representations, while entorhinal cortex compresses these predictive representations with spectral methods that support smooth generalization among related states. I will also cover recent work extending this account, in which we show how the predictive model can be adapted to the probabilistic setting to describe a broader array of generalization results in humans and animals, and how entorhinal representations can be modulated to support sample generation optimized for different behavioral states. In the second part of the talk, I will overview some of the ways in which we have combined many of the same mathematical concepts with state-of-the-art deep learning methods to improve efficiency and performance in machine learning applications like physical simulation, relational reasoning, and design.

Understanding Human ability to learn novel concepts from just a few sensory experiences is a fundamental problem in cognitive neuroscience. I will describe a recent work with Ben Sorcher and Surya Ganguli (PNAS, October 2022) in which we propose a simple, biologically plausible, and mathematically tractable neural mechanism for few-shot learning of naturalistic concepts. We posit that the concepts that can be learned from few examples are defined by tightly circumscribed manifolds in the neural firing-rate space of higher-order sensory areas. Discrimination between novel concepts is performed by downstream neurons implementing ‘prototype’ decision rule, in which a test example is classified according to the nearest prototype constructed from the few training examples. We show that prototype few-shot learning achieves high few-shot learning accuracy on natural visual concepts using both macaque inferotemporal cortex representations and deep neural network (DNN) models of these representations. We develop a mathematical theory that links few-shot learning to the geometric properties of the neural concept manifolds and demonstrate its agreement with our numerical simulations across different DNNs as well as different layers. Intriguingly, we observe striking mismatches between the geometry of manifolds in intermediate stages of the primate visual pathway and in trained DNNs. Finally, we show that linguistic descriptors of visual concepts can be used to discriminate images belonging to novel concepts, without any prior visual experience of these concepts (a task known as ‘zero-shot’ learning), indicated a remarkable alignment of manifold representations of concepts in visual and language modalities. I will discuss ongoing effort to extend this work to other high level cognitive tasks.

Artificial neural networks can be useful for studying brain functions. In cognitive neuroscience, recurrent neural networks are often used to model cognitive functions. I will first offer my opinion on what is missing in the classical use of recurrent neural networks. Then I will discuss two lines of ongoing efforts in our group to move beyond the classical recurrent neural networks by studying multi-system neural networks (the talk will focus on two-system networks). These are networks that combine modules for several neural systems, such as vision, audition, prefrontal, hippocampal systems. I will showcase how multi-system networks can potentially be constrained by experimental data in fundamental ways and at scale.

Neural representations of time are central to our understanding of the world around us. I review cognitive, neurophysiological and theoretical work that converges on three simple ideas. First, the time of past events is remembered via populations of neurons with a continuum of functional time constants. Second, these time constants evenly tile the log time axis. This results in a neural Weber-Fechner scale for time which can support behavioral Weber-Fechner laws and characteristic behavioral effects in memory experiments. Third, these populations appear as dual pairs---one type of population contains cells that change firing rate monotonically over time and a second type of population that has circumscribed temporal receptive fields. These ideas can be used to build artificial neural networks that have novel properties. Of particular interest, a convolutional neural network built using these principles can generalize to arbitrary rescaling of its inputs. That is, after learning to perform a classification task on a time series presented at one speed, it successfully classifies stimuli presented slowed down or sped up. This result illustrates the point that this confluence of ideas originating in cognitive psychology and measured in the mammalian brain could have wide-reaching impacts on AI research.

Every thought is associated with a unique pattern of brain activity. Thus, in principle, it should be possible to use these activity patterns as "brain fingerprints" for different thoughts and to read out what a person is thinking based on their brain activity alone. Indeed, using machine learning considerable progress has been made in such "brainreading" in recent years. It is now possible to decode which image a person is viewing, which film sequence they are watching, which emotional state they are in or which intentions they hold in mind. This talk will provide an overview of the current state of the art in brain reading. It will also highlight the main challenges and limitations of this research field. For example, mathematical models are needed to cope with the high dimensionality of potential mental states. Furthermore, the ethical concerns raised by (often premature) commercial applications of brain reading will also be discussed.

Behavioural measurements are often overlooked by computational neuroscientists, who prefer to focus on electrophysiological recordings or neuroimaging data. This attitude is largely due to perceived lack of depth/richness in relation to behavioural datasets. I will show how contemporary psychophysics can deliver extremely rich and highly constraining datasets that naturally interface with computational modelling. More specifically, I will demonstrate how psychophysics can be used to guide/constrain/refine computational models, and how models can be exploited to design/motivate/interpret psychophysical experiments. Examples will span a wide range of topics (from feature detection to natural scene understanding) and methodologies (from cascade models to deep learning architectures).