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Thanks to the power of representation learning, neural contextual bandit algorithms demonstrate remarkable performance improvement against their classical counterparts. But because their exploration has to be performed in the entire neural…
Understanding how stimuli and synaptic connectivity in uence the statistics of spike patterns in neural networks is a central question in computational neuroscience. Maximum Entropy approach has been successfully used to characterize the…
Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on…
Recent years have witnessed a growing number of attack vectors against increasingly interconnected traffic networks. Informational attacks have emerged as the prominent ones that aim to poison traffic data, misguide users, and manipulate…
A central question in computational neuroscience is how structure determines function in neural networks. The emerging high-quality large-scale connectomic datasets raise the question of what general functional principles can be gleaned…
The response time of physical computational elements is finite, and neurons are no exception. In hierarchical models of cortical networks each layer thus introduces a response lag. This inherent property of physical dynamical systems…
We define a neural network as a septuple consisting of (1) a state vector, (2) an input projection, (3) an output projection, (4) a weight matrix, (5) a bias vector, (6) an activation map and (7) a loss function. We argue that the loss…
We investigate optimal order execution problems in discrete time with instantaneous price impact and stochastic resilience. First, in the setting of linear transient price impact we derive a closed-form recursion for the optimal strategy,…
In this paper, we investigate stability of a class of analytic neural networks with the synaptic feedback via event-triggered rules. This model is general and include Hopfield neural network as a special case. These event-trigger rules can…
We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial distribution shifts, where the labels can be arbitrary, and the goal is to find a ``best-fit'' function. More precisely, given…
We develop a general theory of synaptic neural balance and how it can emerge or be enforced in neural networks. For a given regularizer, a neuron is said to be in balance if the total cost of its input weights is equal to the total cost of…
Characterizing the relation between weight structure and input/output statistics is fundamental for understanding the computational capabilities of neural circuits. In this work, I study the problem of storing associations between analog…
A recent breakthrough in biologically-plausible normative frameworks for dimensionality reduction is based upon the similarity matching cost function and the low-rank matrix approximation problem. Despite clear biological interpretation,…
Neural Networks (NNs) are vulnerable to adversarial examples. Such inputs differ only slightly from their benign counterparts yet provoke misclassifications of the attacked NNs. The required perturbations to craft the examples are often…
Price of anarchy quantifies the degradation of social welfare in games due to the lack of a centralized authority that can enforce the optimal outcome. At its antipodes, mechanism design studies how to ameliorate these effects by…
To understand cognitive reasoning in the brain, it has been proposed that symbols and compositions of symbols are represented by activity patterns (vectors) in a large population of neurons. Formal models implementing this idea [Plate…
When a neuron fires and the resulting action potential travels down its axon toward other neurons' dendrites, the effect on each of those neurons is mediated by the weight of the synapse that separates it from the firing neuron. This…
Synaptic plasticity is widely accepted to be the mechanism behind learning in the brain's neural networks. A central question is how synapses, with access to only local information about the network, can still organize collectively and…
In recurrent networks of leaky integrate-and-fire (LIF) neurons, mean-field theory has proven successful in describing various statistical properties of neuronal activity at equilibrium, such as firing rate distributions. Mean-field theory…
In computational neuroscience, fixed points of recurrent neural networks are commonly used to model neural responses to static or slowly changing stimuli. These applications raise the question of how to train the weights in a recurrent…