A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New method breaks symmetry in neural networks, improving sample efficiency.
This work relaxes GNN symmetries to approximate automorphisms, improving model performance.
Paper relaxes symmetry conditions for universal feature selection in noisy data.
We consider clustering problems where the goal is to determine an optimal partition of a given point set in Euclidean space in terms of a collection of affine subspaces. While there is vast literature on heuristics for this kind of problem, such approaches are known to be susceptible to poor initializations and getting…
New framework uses symmetry-based matrices for efficient, flexible NNs.
Published in 1999, Christodoulou proved that the naked singularities of a self-gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical sym…
New method selects equivariant models using uncertainty metrics.
The paper extends gradient flow and relaxation studies to non-flat Riemannian manifolds.
The paper studies how adding a 'Gauge Mass' term breaks gauge symmetry in Yang-Mills-Higgs systems and analyzes the resulting behavior.
We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a -component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the -means clustering method achieves such sharp threshol…
New classification of conformal structures with maximal symmetry.
Unified framework for enforcing, discovering, and promoting symmetry in machine learning.
Identity testing for reversible Markov chains without symmetry assumption.
Proves positive Euler characteristic for certain manifolds with positive second intermediate Ricci curvature.
DeepPhaseCut uses neural networks to improve Fourier phase retrieval.
The study finds regular null hypersurfaces in a perturbed Schwarzschild black hole exterior.
A 3-dimensional vector field is said to be Beltrami vector field (force free-magnetic vector field in physics), if . Motivated by our investigations on projective an polynomial superflows, and as an important side result, in the first paper on this topic we constructed two unique Beltrami…
New operators generalize Michelsohn's on almost Hermitian manifolds.
C-SymmPI provides near-conditional coverage for structured data with group symmetries.
The backpropagation (BP) algorithm is often thought to be biologically implausible in the brain. One of the main reasons is that BP requires symmetric weight matrices in the feedforward and feedback pathways. To address this "weight transport problem" (Grossberg, 1987), two more biologically plausible algorithms, propo…
In the analysis of machine learning models, it is often convenient to assume that the parameters are IID. This assumption is not satisfied when the parameters are updated through training processes such as SGD. A relaxation of the IID condition is a probabilistic symmetry known as exchangeability. We show the sense in …
New distributions allow greedy arm selection in sparse bandit problems.
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group provides a precise mathematical framework for lifted inference in the general expone…
This work relaxes energy constraints in self-attention layers for a more general analysis.
Improves convergence speed in compressive sensing with a new probabilistic approach.
In the NeurIPS 2018 Artificial Intelligence for Prosthetics challenge, participants were tasked with building a controller for a musculoskeletal model with a goal of matching a given time-varying velocity vector. Top participants were invited to describe their algorithms. In this work, we describe the challenge and pre…
Unconstrained MLIPs outperform constrained ones in accuracy and speed.
In the NIPS 2017 Learning to Run challenge, participants were tasked with building a controller for a musculoskeletal model to make it run as fast as possible through an obstacle course. Top participants were invited to describe their algorithms. In this work, we present eight solutions that used deep reinforcement lea…
Dense Associative Memories outperform classical networks in robustness and signal processing.
ShotgunCSP predicts crystal structures using machine learning, achieving high accuracy with minimal computation.
As first noted in Korevaar, Kusner and Solomon ("KKS"), constant mean curvature implies a homological conservation law for hypersurfaces in ambient spaces with Killing fields.In Theorem 3.5 here, we generalize that law by relaxing the topological restrictions assumed in [KKS] and by allowing a weighted mean curvature f…
Axioms of Lie algebroid are discussed in order to review some known aspects for non-experts. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the Functions(M)-module F of sections of a vector bundle E over a manifold M which satisfies [X,fY]=f[X,Y]+A(X,f)Y for all X,Y from F, all f from…
Tractor Calculus is a powerful tool for analyzing Weyl invariance; although fundamentally linked to the Cartan connection, it may also be arrived at geometrically by viewing a conformal manifold as the space of null rays in a Lorentzian ambient space. For dimension d conformally flat manifolds we show that the (d+2)-di…
New method improves neural network verification by considering multivariate input space of ReLU neurons.
New regularizers tighten convex relaxation bounds for neural networks.
Improved neural network robustness certification through tighter convex relaxations.
In this note we compare two recently proposed semidefinite relaxations for the sparse linear regression problem by Pilanci, Wainwright and El Ghaoui (Sparse learning via boolean relaxations, 2015) and Dong, Chen and Linderoth (Relaxation vs. Regularization A conic optimization perspective of statistical variable select…
Despite their impressive performance on diverse tasks, neural networks fail catastrophically in the presence of adversarial inputs---imperceptibly but adversarially perturbed versions of natural inputs. We have witnessed an arms race between defenders who attempt to train robust networks and attackers who try to constr…
We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the glob…
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this paper, we study the statistical limits of convex relaxations. Particularly, we con…
A new framework describes dissipation using a metriplectic 4-bracket.
The biological plausibility of the backpropagation algorithm has long been doubted by neuroscientists. Two major reasons are that neurons would need to send two different types of signal in the forward and backward phases, and that pairs of neurons would need to communicate through symmetric bidirectional connections. …
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they lift the original -dimensional variable to an -d…
New method finds Lie group representations without explicit groups, enabling new neural network architectures.
Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction time of SIR methods hinders their use in X-ray CT in practice. To accelerate st…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a third observed multinomial distribution. We study the entire relaxation path for thi…
Bayesian learning is often hampered by large computational expense. As a powerful generalization of popular belief propagation, expectation propagation (EP) efficiently approximates the exact Bayesian computation. Nevertheless, EP can be sensitive to outliers and suffer from divergence for difficult cases. To address t…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a quadratic optimization problem with an l0-norm penalty. Exactly enforcing the l0-no…