Visual processing starts in the outer retina where photoreceptors transform light into electrochemical signals. These signals are modulated by inhibition from horizontal cells and sent to the inner retina via excitatory bipolar cells. The outer retina is thought to play an important role in contrast invariant coding of visual information, but how the different cell types implement this computation together remains incompletely understood. To understand the role of each cell type, we developed a fully-differentiable biophysical model of a circular patch of mouse outer retina. The model includes 200 cone photoreceptors with a realistic phototransduction cascade and ribbon synapses as well as horizontal and bipolar cells, all with celltype specific ion channels. Going beyond decades of work constraining biophysical models of neurons only by experimental data, we used a dual approach, constraining some parameters of the model with available measurements and others by a visual task: (1) We fit the parameters of the cone models to whole cell patch-clamp measurements of photocurrents and two-photon glutamate imaging measurements of synaptic release.

We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supported on a fixed polyhedral simplicial fan. We investigate the expressivity of these function classes and describe the combinatorial and geometric structure of the loss landscape, most prominently the sublevel sets, for two loss-functions: the 0/1-loss (discrete loss) and a log-likelihood loss function. In particular, we give explicit bounds on the VC dimension of this model, and concretely describe the sublevel sets of the discrete loss as chambers in a hyperplane arrangement. For the log-likelihood loss, we give sufficient conditions for the optimum to be unique, and describe the geometry of the optimum when varying the rate parameter of the underlying exponential probability distribution.

Preference-based Pure Exploration (PrePEx) aims to identify with a given confidence level the set of Pareto optimal arms in a vector-valued (aka multi-objective) bandit, where the reward vectors are ordered via a (given) preference cone C. Though PrePEx and its variants are well-studied, there does not exist a computationally efficient algorithm that can optimally track the existing lower bound (Shukla and Basu, 2024) for arbitrary preference cones. We successfully fill this gap by efficiently solving the minimisation and maximisation problems in the lower bound. First, we derive three structural properties of the lower bound that yield a computationally tractable reduction of the minimisation problem. Then, we deploy a Frank-Wolfe optimiser to accelerate the maximisation problem in the lower bound. Together, these techniques solve the maxmin optimisation problem in O(KL2) time for a bandit instance with K arms and L dimensional reward, which is a significant acceleration over the literature. We further prove that our proposed PrePEx algorithm, FraPPE, asymptotically achieves the optimal sample complexity. Finally, we perform numerical experiments across synthetic and real datasets demonstrating that FraPPE achieves the lowest sample complexities to identify the exact Pareto set among the existing algorithms.

High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and rotated sparse vectors, etc. In this paper, we consider general superposition models which allow sum of any number of component parameters, and each component structure can be characterized by any norm. We present a simple estimator for such models, give a geometric condition under which the components can be accurately estimated, characterize sample complexity of the estimator, and give high probability nonasymptotic bounds on the componentwise estimation error. We use tools from empirical processes and generic chaining for the statistical analysis, and our results, which substantially generalize prior work on superposition models, are in terms of Gaussian widths of suitable sets.

We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex hull of vertices representing the latent topics. Our algorithms are shown in practice to have accuracy comparable to a Gibbs sampler in terms of topic estimation, which requires the number of topics be given. Moreover, they are one of the fastest among several state of the art parametric techniques.1 Statistical consistency of our estimator is established under some conditions.

In topic modeling, many algorithms that guarantee identifiability of the topics have been developed under the premise that there exist anchor words - i.e., words that only appear (with positive probability) in one topic. Follow-up work has resorted to three or higher-order statistics of the data corpus to relax the anchor word assumption. Reliable estimates of higher-order statistics are hard to obtain, however, and the identification of topics under those models hinges on uncorrelatedness of the topics, which can be unrealistic. This paper revisits topic modeling based on second-order moments, and proposes an anchor-free topic mining framework. The proposed approach guarantees the identification of the topics under a much milder condition compared to the anchor-word assumption, thereby exhibiting much better robustness in practice. The associated algorithm only involves one eigendecomposition and a few small linear programs. This makes it easy to implement and scale up to very large problem instances. Experiments using the TDT2 and Reuters-21578 corpus demonstrate that the proposed anchor-free approach exhibits very favorable performance (measured using coherence, similarity count, and clustering accuracy metrics) compared to the prior art.

In this paper, we focus on solving Extensive-F orm Games (EFGs).

Reasoning over TKGs has two challenges: 1.