arXiv research

Paper explores statistical and computational limits of estimating low-rank Gaussian mixtures.

Study on reproducibility in optimization with bounds on limits.

Develops a framework for decision-making abstractions under computational limitations.

Researchers compute limits of Kähler-Einstein forms on degenerating manifolds.

Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz constant may indeed enable adversarially robust neural networks. However, the m…

The paper classifies and computes limits of equivariant compactifications of groups.

We give a complete description of the closure of the space of one-generator closed subgroups of PSL2(R) for the Chabauty topology, by computing explicitly the matrices associated with elements of Aut(D) = PSL2(R), and finding quantities parametrizing the limit cases. Along the way, we investigate under what conditions …

Autoregressive models struggle with hard-to-compute distributions, alternatives like energy-based and latent-variable models solve this.

Paper explores limits of high-order clustering with planted structures.

Study on functions computed by deep-layered machines finds same distribution in neural networks and Boolean circuits.

New insights on stability in reservoir computing for better performance.

Computational method approximates homology groups of compact metric spaces.

Eta invariant computed for circle bundles over Fano manifolds.

New phases identified in neural scaling laws with compute limits.

New CR representations are found and shown to be redundant.

We study the limit of quasilocal mass defined in [4] and [5] for a family of spacelike 2-surfaces in spacetime. In particular, we show the limit coincides with the ADM mass at spatial infinity. The limit for coordinate spheres of a boosted slice of the Schwarzchild solution is computed explicitly and shown to give the …

New framework limits testing algorithmic stability under computational constraints.

We study the problem of identifying a probability distribution for some given randomly sampled data in the limit, in the context of algorithmic learning theory as proposed recently by Vinanyi and Chater. We show that there exists a computable partial learner for the computable probability measures, while by Bienvenu, M…

Machine learning models are vulnerable to adversarial examples: small changes to images can cause computer vision models to make mistakes such as identifying a school bus as an ostrich. However, it is still an open question whether humans are prone to similar mistakes. Here, we address this question by leveraging recen…

This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning where objective functions are estimated from available data. We show that these alg…

Study wSAA for contextual decisions, improving uncertainty quantification under computational constraints.

A power-law fit to the empirical inference-compute frontier in LOB prediction suggests a scaling-law-style frontier.

Study calculates Kulkarni limit sets for quaternionic projective groups.

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…

Efficiently scales continuous kernels with sparse Fourier domain learning.

New methods improve Reservoir Computing for chaotic time series prediction.

In this paper, we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems, we also derive a Kastler-Kalau-Walze type theorem for the noncommutative residue in the case of foliations.

We present a new proof, as well as a ${\bf C/Q}$ extension, of the Riemann-Roch-Grothendieck theorem of Bismut-Lott for flat vector bundles. The main techniques used are the computations of the adiabatic limits of $η$-invariants associated to the so-called sub-signature operators. We further show that the Bismut-Lott a…

We compute the cohomology of a Fuchsian group of the second kind with coefficients in the hyperfunction vectors of the principal series representations of $SL(2,R)$ supported on the limit set.

Ambitwistor string matches superstring chiral integrands at zero tension.

Time-limited metaheuristics find near-optimal solutions for constrained portfolio optimisation.

In this paper, we consider the streaming memory-limited matrix completion problem when the observed entries are noisy versions of a small random fraction of the original entries. We are interested in scenarios where the matrix size is very large so the matrix is very hard to store and manipulate. Here, columns of the o…

We analyze computational limits of modern Hopfield models based on pattern norms.

Training of large-scale deep neural networks is often constrained by the available computational resources. We study the effect of limited precision data representation and computation on neural network training. Within the context of low-precision fixed-point computations, we observe the rounding scheme to play a cruc…

Paper derives CLT for Bayesian neural networks trained with variational inference.

One of the big restrictions in brain computer interface field is the very limited training samples, it is difficult to build a reliable and usable system with such limited data. Inspired by generative adversarial networks, we propose a conditional Deep Convolutional Generative Adversarial (cDCGAN) Networks method to ge…

Method for computing Khovanov homology of tangles.

Researchers approximate partition functions on Riemannian spaces in the large N limit.

This paper contains a thorough investigation of invariant distributions supported on limit sets of discrete groups acting convex cocompactly on symmetric spaces of negative curvature. It can be considered as a continuation of math.DG/9810146. Based on this investigation we provide proofs of the Hodge theoretic results …

This paper improves computational efficiency in kernel ridge regression under covariate shift.

Efficiently computes quasiconcave envelope with limited data.

Developing active inference agents for edge devices with limited resources.

Researchers compute invariants for knots and links in lens spaces using large N and k limits.

New method models PDEs from noisy, limited data.

Restricted Boltzmann machines (RBMs) are powerful machine learning models, but learning and some kinds of inference in the model require sampling-based approximations, which, in classical digital computers, are implemented using expensive MCMC. Physical computation offers the opportunity to reduce the cost of sampling …

Study reveals limits of detecting local geometry in random graphs.

This work characterizes the fundamental limit of network pruning using statistical dimension and convex geometry.

Coded computation techniques provide robustness against straggling servers in distributed computing, with the following limitations: First, they increase decoding complexity. Second, they ignore computations carried out by straggling servers; and they are typically designed to recover the full gradient, and thus, canno…