arXiv research

Quantum computers outperform classical methods in density modeling.

The study reveals the efficiency of sampling from tilted distributions.

Study shows SQ hardness for multiclass linear classification with random noise.

This paper strengthens the computational separation between multimodal and unimodal learning, showing unimodal learning is hard on typical instances.

In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth of size these sets of isospectral manifolds as a function of volume is super-pol…

Improved approximations for rough Heston model reduce errors.

We explain how to adapt a construction of M. Sageev's to construct a proper action on a CAT(0) cube complex starting from a proper action on a wall space, and use this to deduce that if G is a group containing an amenable subgroup H of super-polynomial growth and G acts properly on a space with walls then there are arb…

Lower bound shows super-polynomial gap for estimating truncated Gaussian means.

We prove that the colored HOMFLY polynomial of a link, colored by symmetric or exterior powers of the fundamental representation, is q-holonomic with respect to the color parameters. As a result, we obtain the existence of an (a,q) super-polynomial of all knots in 3-space. Our result has implications on the quantizatio…

We prove that the HOMFLYPT polynomial of a link, colored by partitions with a fixed number of rows is a $q$-holonomic function. Specializing to the case of knots colored by a partition with a single row, it proves the existence of an $(a,q)$ super-polynomial of knots in 3-space, as was conjectured by string theorists. …

In this work, we consider solutions of the Maxwell equations on the Schwarzschild-de Sitter family of black hole spacetimes. We prove that, in the static region bounded by black hole and cosmological horizons, solutions of the Maxwell equations decay to stationary Coulomb solutions at a super-polynomial rate, with deca…

Enhances quantum computing for symmetrical systems, proving a new class of problems.

We modify our previous construction of link homology in order to include a natural duality functor $\mathfrak{F}$. To a link $L$ we associate a triply-graded module $HXY(L)$ over the graded polynomial ring $R(L)=\mathbb{C}[x_1,y_1,\dots,x_\ell,y_\ell]$. The module has an involution $\mathfrak{F}$ that intertwines the F…

LLMs struggle with arithmetic tasks unless they use high numerical precision.

New algorithm learns ReLU networks efficiently using Schur polynomials.

We consider braids with repeating patterns inside arbitrary knots which provides a multi-parametric family of knots, depending on the "evolution" parameter, which controls the number of repetitions. The dependence of knot (super)polynomials on such evolution parameters is very easy to find. We apply this evolution meth…

WildCat efficiently compresses neural network attention mechanisms.

Study shows SQ lower bounds for learning ReLUs with Massart noise.

The paper proves barriers to approximating functions with small weights and depth in neural networks.

Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is increasingly often incomplete, rendering standard (full-data) methods inapplicable. …

In many estimation problems, e.g. linear and logistic regression, we wish to minimize an unknown objective given only unbiased samples of the objective function. Furthermore, we aim to achieve this using as few samples as possible. In the absence of computational constraints, the minimizer of a sample average of observ…

Quantum circuits are hard to learn on average.

New framework formalizes RLHF trilemma: improving safety, fairness, and robustness is computationally infeasible.

We provide a detailed study on the implicit bias of gradient descent when optimizing loss functions with strictly monotone tails, such as the logistic loss, over separable datasets. We look at two basic questions: (a) what are the conditions on the tail of the loss function under which gradient descent converges in the…

The paper explores how LLMs with CoT improve performance on complex tasks.

The paper tackles robust policy learning in multitask contextual bandits with adversarial users.

Algorithm learns near-optimal policies for reward-mixing MDPs with few latent contexts.

Quantum machine learning offers advantages for broader learning tasks.

This paper improves Q-learning bounds using reference-advantage decomposition.

Efficient algorithm for online learning with Massart noise achieves near-optimal mistake bound.

Polynomial-time algorithm learns high-dimensional halfspaces without labels.

New algorithm recovers sparse signals from linearly sparse dictionaries efficiently.

Machine learning predicts quantum advantage in noisy quantum walks.

This paper is concerned with jointly recovering $n$ node-variables $\left\{ x_{i}\right\}_{1\leq i\leq n}$ from a collection of pairwise difference measurements. Imagine we acquire a few observations taking the form of $x_{i}-x_{j}$; the observation pattern is represented by a measurement graph $\mathcal{G}$ with an ed…

DG improves policy gradients by weighting actions with a sigmoid of advantage and surprisal.

UCB-Advantage learns MDPs with $O(\sqrt{H^2SAT})$ regret.

New method learns time-varying home field advantage in football.

Study compares adaptive vs fixed query learning methods.

Near-optimal SQ hardness shows learning halfspaces with Massart noise is hard.

As the success of deep learning reaches more grounds, one would like to also envision the potential limits of deep learning. This paper gives a first set of results proving that certain deep learning algorithms fail at learning certain efficiently learnable functions. The results put forward a notion of cross-predictab…

This paper re-examines conformal e-prediction and its advantages over conformal prediction.

Two algorithms learn Gaussian graphical models from Glauber dynamics trajectories, achieving optimal performance.

Study on when RLVR can learn compositional problems.

This paper explores the limits of deep learning in poly-time.

Quantum advantage in derivative pricing requires 8k qubits and 54M T-depth.

Gradient descent benefits from tangent kernel advantages under specific conditions.

Algorithm learns means of spherical Gaussian mixtures efficiently in low dimensions.

Efficiently estimates Gaussian distributions privately and robustly.