Understanding sensory processing involves relating the stimulus space, its neural representation, and perceptual quality. In olfaction, the difficulty in establishing these links lies partly in the complexity of the underlying odor input space and perceptual responses. Based on the recently proposed primacy model for concentration invariant odor identity representation and a few assumptions, we have developed a theoretical framework for mapping the odor input space to the response properties of olfactory receptors. We analyze a geometrical structure containing odor representations in a multidimensional space of receptor affinities and describe its low-dimensional implementation, the primacy hull. We propose the implications of the primacy hull for the structure of feedforward connectivity in early olfactory networks. We test the predictions of our theory by comparing the existing receptor-ligand affinity and connectivity data obtained in the fruit fly olfactory system. We find that the Kenyon cells of the insect mushroom body integrate inputs from the high-affinity (primacy) sets of olfactory receptors in agreement with the primacy theory.

Representational drift refers to over-time changes in neural activation accompanied by a stable task performance. Despite being observed in the brain and in artificial networks, the mechanisms of drift and its implications are not fully understood. Motivated by recent experimental findings of stimulus-dependent drift in the piriform cortex, we use theory and simulations to study this phenomenon in a two-layer linear feedforward network. Specifically, in a continual online learning scenario, we study the drift induced by the noise inherent in the Stochastic Gradient Descent (SGD). By decomposing the learning dynamics into the normal and tangent spaces of the minimum-loss manifold, we show the former corresponds to a finite variance fluctuation, while the latter could be considered as an effective diffusion process on the manifold. We analytically compute the fluctuation and the diffusion coefficients for the stimuli representations in the hidden layer as functions of network parameters and input distribution. Further, consistent with experiments, we show that the drift rate is slower for a more frequently presented stimulus. Overall, our analysis yields a theoretical framework for better understanding of the drift phenomenon in biological and artificial neural networks.

Social conflict is a survival mechanism yielding both normal and pathological behaviors. To understand its underlying principles, we collected behavioral and whole-brain neural data from mice advancing through stages of social conflict. We modeled the animals’ interactions as a normal-form game using Bayesian inference to account for the partial observability of animals’ strengths. We find that our behavioral and neural data are consistent with the first-level Theory of Mind (1-ToM) model where mice form “primary” beliefs about the strengths of all mice involved and “secondary” beliefs that estimate the beliefs of their opponents. Our model identifies the brain regions that carry the information about these beliefs and offers a framework for studies of social behaviors in partially observable settings.

In real-world settings, we repeatedly decide whether to pursue better conditions or to keep things unchanged. Examples include time investment, employment, entertainment preferences etc. How do we make such decisions? To address this question, the field of behavioral ecology has developed foraging paradigms – the model settings in which human and non-human subjects decided when to leave depleting food resources. Foraging theory, represented by the marginal value theorem (MVT), provided accurate average-case stay-or-leave rules consistent with behaviors of subjects towards depleting resources. Yet, the algorithms underlying individual choices and ways to learn such algorithms remained unclear. In this work, we build interpretable deep actor-critic models to show that R-learning – a reinforcement learning (RL) approach balancing short-term and long-term rewards – is consistent with the way real-life agents may learn making stay-or-leave decisions. Specifically we show that deep R-learning predicts choice patterns consistent with behavior of mice in foraging tasks; its TD error, the training signal in our model, correlates with dopamine activity of ventral tegmental area (VTA) neurons in the brain. Our theoretical and experimental results show that deep R-learning agents leave depleting reward resources when reward intake rates fall below their exponential averages over past trials. This individual-case decision rule, learned within RL and matching the MVT on average, bridges the gap between these major approaches to sequential decision-making. We further argue that our proposed decision rule, resulting from R-learning and consistent with animals’ behavior, is Bayes optimal in dynamic real-world environments. Overall, our work links available sequential decision-making theories including the MVT, RL, and Bayesian approaches to propose the learning mechanism and an optimal decision rule for sequential stay-or-leave choices in natural environments.

The olfactory system employs an ensemble of odorant receptors (ORs) to sense odorants and to derive olfactory percepts. We trained artificial neural networks to represent the chemical space of odorants and used this representation to predict human olfactory percepts. We hypothesized that ORs may be considered 3D convolutional filters that extract molecular features and, as such, can be trained using machine learning methods. First, we trained a convolutional autoencoder, called DeepNose, to deduce a low-dimensional representation of odorant molecules which were represented by their 3D spatial structure. Next, we tested the ability of DeepNose features in predicting physical properties and odorant percepts based on 3D molecular structure alone. We found that, despite the lack of human expertise, DeepNose features often outperformed molecular descriptors used in computational chemistry in predicting both physical properties and human perceptions. We propose that DeepNose network can extract de novo chemical features predictive of various bioactivities and can help understand the factors influencing the composition of ORs ensemble.

In the olfactory system, odor percepts retain their identity despite substantial variations in concentration, timing, and background. We study a novel strategy for encoding intensity-invariant stimulus identity that is based on representing relative rather than absolute values of stimulus features. For example, in what is known as the primacy coding model, odorant identities are represented by the conditions that some odorant receptors are activated more strongly than others. Because, in this scheme, odorant identity depends only on the relative amplitudes of olfactory receptor responses, identity is invariant to changes in both intensity and monotonic nonlinear transformations of its neuronal responses. Here we show that sparse vectors representing odorant mixtures can be recovered in a compressed sensing framework via elastic net loss minimization. In the primacy model, this minimization is performed under the constraint that some receptors respond to a given odorant more strongly than others. Using duality transformation, we show that this constrained optimization problem can be solved by a neural network whose Lyapunov function represents the dual Lagrangian and whose neural responses represent the Lagrange coefficients of primacy and other constraints. The connectivity in such a dual network resembles known features of connectivity in olfactory circuits. We thus propose that networks in the piriform cortex implement dual computations to compute odorant identity with the sparse activities of individual neurons representing Lagrange coefficients. More generally, we propose that sparse neuronal firing rates may represent Lagrange multipliers, which we call the dual brain hypothesis. We show such a formulation is well suited to solve problems with multiple interacting relative constraints.

We investigated a model for the neural integrator based on hysteretic units connected by positive feedback. Hysteresis is assumed to emerge from the intrinsic properties of the cells. We consider the recurrent networks containing either bistable or multistable neurons. We apply our analysis to the oculomotor velocity-to-position neural integrator that calculates eye positions using the inputs that carry information about eye angular velocity. By analyzing this system in the parameter space, we show the following. The direction of hysteresis in the neuronal response may be reversed for the system with recurrent connections compared to the case of unconnected neurons. Thus, for the NMDA receptor-based bistability, the firing rates after ON saccades may be higher than after OFF saccades for the same eye position. The reversal of hysteresis occurs in this model only when the size of hysteresis differs from neuron to neuron. We also relate the macroscopic leak time constant of the integrator to the rate of microscopic spontaneous noise-driven transitions in the hysteretic units. Finally, we investigate the conditions under which the hysteretic integrator may have no threshold for integration.