Related papers: The geometry of Tempotronlike problems

Automatic segmentation of neuronal topology is critical for handling large scale neuroimaging data, as it can greatly accelerate neuron annotation and analysis. However, the intricate morphology of neuronal branches and the occlusions among…

Two geometric spaces are in the same topological class if they are related by certain geometric deformations. We propose machine learning methods that automate learning of topological invariance and apply it in the context of knot theory,…

Temporal-difference learning (TD), coupled with neural networks, is among the most fundamental building blocks of deep reinforcement learning. However, due to the nonlinearity in value function approximation, such a coupling leads to…

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…

Deep learning methods have surpassed the performance of traditional techniques on a wide range of problems in computer vision, but nearly all of this work has studied consumer photos, where precisely correct output is often not critical. It…

The transversal hypergraph problem is the task of enumerating the minimal hitting sets of a hypergraph. It is a long-standing open question whether this can be done in output-polynomial time. For hypergraphs whose solutions have bounded…

We study the Steiner Tree problem on unit disk graphs. Given a $n$ vertex unit disk graph $G$, a subset $R\subseteq V(G)$ of $t$ vertices and a positive integer $k$, the objective is to decide if there exists a tree $T$ in $G$ that spans…

We study the complexity of counting (weighted) planar graph homomorphism problem $\tt{Pl\text{-}GH}(M)$ parametrized by an arbitrary symmetric non-negative real valued matrix $M$. For matrices with pairwise distinct diagonal values, we…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…

A computational problem exhibits a "gap property" when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the…

The brain can learn to solve a wide range of tasks with high temporal and energetic efficiency. However, most biological models are composed of simple single compartment neurons and cannot achieve the state-of-art performances of artificial…

Supervised learning in a binary perceptron is able to classify an extensive number of random patterns by a proper assignment of binary synaptic weights. However, to find such assignments in practice, is quite a nontrivial task. The relation…

A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical…

A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…

Complex systems can be effectively modeled via graphs that encode networked interactions, where relations between entities or nodes are often quantified by signed edge weights, e.g., promotion/inhibition in gene regulatory networks, or…

Deep Neural Networks miss a principled model of their operation. A novel framework for supervised learning based on Topological Quantum Field Theory that looks particularly well suited for implementation on quantum processors has been…

We consider the well-studied problem of learning a linear combination of $k$ ReLU activations with respect to a Gaussian distribution on inputs in $d$ dimensions. We give the first polynomial-time algorithm that succeeds whenever $k$ is a…

Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…