arXiv research

Study learning and refutation in non-interactive LDP, showing sample complexity equivalence.

Study tests five popular trading signal families and finds four refuted, one inconclusive, and one not refuted.

Proposes bounds on bias from low-dimensional representations in CATE estimation.

New formula refutes random CSPs with fewer constraints.

We discuss the mathematician George Bruce Halsted's accusations against Carl Friedrich Gauss, as well as refutations both by the latter's American grandson Robert Gauss in a letter to Felix Klein, and by the historian of mathematics Florian Cajori.

The paper challenges the notion that asset return doesn't affect Black-Scholes-Merton model.

Note refutes examples of Landsberg surfaces with vanishing flag curvature.

Example shows learnable distributions not privately learnable.

Audit shows risk claims from distributional reinforcement learning agents are often false.

The generalization of Frobenius' theorem to foliations with singularities is usually attributed to Stefan and Sussmann, for their simultaneous discovery around 1973. However, their result is often referred to without caring much on the precise statement, as some sort of magic spell. This may be explained by the fact th…

The paper proves a conjecture about spacetimes and singularities.

Investigates principles of generalization in list learning, refutes sample compression conjecture.

Paper refutes conjecture on tensor power iteration convergence in overcomplete models.

We characterize the three-dimensional spaces admitting at least six or at least seven equidistant points. In particular, we show the existence of $C^\infty$ norms on $\R^3$ admitting six equidistant points, which refutes a conjecture of Lawlor and Morgan (1994, Pacific J. Math \textbf{166}, 55--83), and gives the exist…

Examples are given of prime Legendrian knots in the standard contact 3-space that have arbitrarily many distinct Chekanov polynomials, refuting a conjecture of Lenny Ng. These are constructed using a new `Legendrian tangle replacement' technique. This technique is then used to show that the phenomenon of multiple Cheka…

This paper addresses a gap in the classifcation of Codazzi tensors with exactly two eigenfunctions on a Riemannian manifold of dimension three or higher. Derdzinski proved that if the trace of such a tensor is constant and the dimension of one of the the eigenspaces is $n-1$, then the metric is a warped product where t…

Study mapping class group actions on cohomology of configuration spaces.

Boosting algorithms produce a classifier by iteratively combining base hypotheses. It has been observed experimentally that the generalization error keeps improving even after achieving zero training error. One popular explanation attributes this to improvements in margins. A common goal in a long line of research, is …

This paper uses neural networks to predict stock prices more accurately.

We construct a financial "Turing test" to determine whether human subjects can differentiate between actual vs. randomized financial returns. The experiment consists of an online video-game (http://arora.ccs.neu.edu) where players are challenged to distinguish actual financial market returns from random temporal permut…

Study on mapping class groups of non-orientable surfaces, proving some conjectures and refuting others.

New evidence refutes old conjectures about knot homology ranks, suggesting new congruences.

Time-aware fact-checking improves veracity predictions for time-sensitive claims.

New mass-type invariants for cosmological space-times.

There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error accumulation, a notion made precise in d'Aspremont 2008 and Devolder, Glineur, …

In this paper we characterise the propensity of big capital investments to systematically deliver poor outcomes as "fragility," a notion suggested by Nassim Taleb. A thing or system that is easily harmed by randomness is fragile. We argue that, contrary to their appearance, big capital investments break easily - i.e. d…

Adaptive optimization algorithms such as Adam are widely used in deep learning. The stability of such algorithms is often improved with a warmup schedule for the learning rate. Motivated by the difficulty of choosing and tuning warmup schedules, recent work proposes automatic variance rectification of Adam's adaptive l…

Gathering the most information by picking the least amount of data is a common task in experimental design or when exploring an unknown environment in reinforcement learning and robotics. A widely used measure for quantifying the information contained in some distribution of interest is its entropy. Greedily minimizing…

Flat minimal tori counterexamples refute Lu's second-gap conjecture.

Study disproves conjecture about low-degree polynomials in hypothesis testing.

Paper develops robust SVM classifiers for uncertain data.

A stable smooth map $f:N\to M$ is called "$k$-realizable" if its composition with the inclusion $M\subset M\times\Bbb R^k$ is $C^0$-approximable by smooth embeddings; and a "$k$-prem" if the same composition is $C^\infty$-approximable by smooth embeddings, or equivalently if $f$ lifts vertically to a smooth embedding $…

We find stationary distributions in a financial model with trends and mean-reversion.

Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics, machine learning, and complexity theory. Many high dimensional estimation problems ca…

SAM minimizes loss sharpness, improving adversarial transferability.

Gradient flow with infinitesimal initialization converges to Greedy Low-Rank Learning for matrix factorization.

Optimizes algorithms for non-concave bandit problems.

Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.

Injectivity of ReLU networks studied using statistical physics.

Transformers for binary decisions are sensitive to evidence order, leading to unreliable outcomes.

This thesis focuses on gaining linguistic insights into textual discussions on a word level. It was of special interest to distinguish messages that constructively contribute to a discussion from those that are detrimental to them. Thereby, we wanted to determine whether "I"- and "You"-messages are indicators for eithe…

Paper refutes EM convergence theory and introduces a new EM algorithm.

The paper refutes the manifold hypothesis for image data and proposes the union of manifolds hypothesis.

For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime. Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by statistical physics and related algorithms such as belief propagation and AMP (ap…

New algorithm reduces constraint violation to $O(T^{1/3})$ while maintaining $O(\sqrt{T})$ regret.

In the noisy tensor completion problem we observe $m$ entries (whose location is chosen uniformly at random) from an unknown $n_1 \times n_2 \times n_3$ tensor $T$. We assume that $T$ is entry-wise close to being rank $r$. Our goal is to fill in its missing entries using as few observations as possible. Let $n = \max(n…

New analysis shows how attention masks and LayerNorm prevent rank collapse in transformers.

Long horizon reinforcement learning is as hard as short horizon learning.