arXiv research

A new algorithm selects independent coordinates for complex manifolds.

Paper shows how to embed Möbius bands with many twists and small aspect ratios.

Improved bound for optimal Moebius band aspect ratio.

Gradient descent dynamics in nonconvex models explained with universality.

The study shows that inscribed rectangles in smooth curves cover at least one third of all possible aspect ratios.

New equivalences found between subsampling and ridge regularization methods.

Noise increases the Rashomon ratio, leading simpler models to perform similarly to complex ones.

The paper analyzes the benefit-cost ratio for feature selection in machine learning.

This paper uses GSNR to explain why neural networks generalize well.

Optimizes kernel density ratios for better predictions and information measures.

We present an elementary analysis of the dynamical aspects of the GDP / government surplus multiplier with relevance to the assessment of a country's debt repayment policy. We show the (at first) counter intuitive result that in order to reduce the Debt/GDP ratio, countries with high Debt to GDP should go into further …

Solves constant pre-factor problem for tt*-Toda equations using asymptotic data and symplectic structures.

Multicomponent bilayer structures arise as the ubiquitous plasma membrane in cellular biology and as blends of amphiphilic copolymers used in electrolyte membranes, drug delivery, and emulsion stabilization within the context of synthetic chemistry. We develop the multicomponent functionalized Cahn-Hilliard (mFCH) free…

Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the importance ratios have a heavy right tail. This routinely occurs when there are aspects of the target distribution that are not well captur…

New method resolves density ratio estimation saturation issues.

PolyModel theory and iTransformer improve hedge fund portfolio construction.

We present a reinforcement learning approach for detecting objects within an image. Our approach performs a step-wise deformation of a bounding box with the goal of tightly framing the object. It uses a hierarchical tree-like representation of predefined region candidates, which the agent can zoom in on. This reduces t…

Study optimal ridge regularization for out-of-distribution prediction.

Paper introduces lexical ratio to measure portfolio diversification.

The paper analyzes the Rashomon ratio for infinite classifier families and shows its importance for choosing good classifiers.

It had been believed in the conventional practice that the risk of a bank going bankrupt is lessened in a straightforward manner by transferring the risk of loan defaults. But the failure of American International Group in 2008 posed a more complex aspect of financial contagion. This study presents an extension of the …

We study two aspects of noisy computations during inference. The first aspect is how to mitigate their side effects for naturally trained deep learning systems. One of the motivations for looking into this problem is to reduce the high power cost of conventional computing of neural networks through the use of analog ne…

New algorithm for MDS with quasi-polynomial dependency on aspect ratio.

The systolic ratio of a contact form on a closed three-manifold is the quotient of the square of the shortest period of closed Reeb orbits by the contact volume. We show that every co-orientable contact structure on any closed three-manifold is defined by a contact form with arbitrarily large systolic ratio. This shows…

Online PCA phase transition depends on $n/d\log(d)$, not just $n/d$.

Direct Density Ratio Optimization aligns LLMs with human preferences without assuming specific models.

Aspect-level sentiment classification (ASC) aims at identifying sentiment polarities towards aspects in a sentence, where the aspect can behave as a general Aspect Category (AC) or a specific Aspect Term (AT). However, due to the especially expensive and labor-intensive labeling, existing public corpora in AT-level are…

Study ridge ensembles in proportional feature-to-sample size regime, proving risk equivalence and GCV consistency.

Let $(M,g)$ be a closed, oriented, Riemannian manifold of dimension $m$. We call a systole a shortest non-contractible loop in $(M,g)$ and denote by $sys(M,g)$ its length. Let $SR(M,g)=\frac{{sys(M,g)}^m}{vol(M,g)}$ be the systolic ratio of $(M,g)$. Denote by $SR(k)$ the supremum of $SR(S,g)$ among the surfaces of fixe…

GD with large init shows incremental learning in matrix factorization.

New binary loss functions improve density ratio estimation accuracy.

Framework mitigates risk non-monotonicity in high-dimensional predictions.

Proposes a method for ranking items across multiple aspects based on user feedback.

The book explains deep learning theory and how networks learn nontrivial representations.

Paper optimizes ES estimation under an $\ell_1$ constraint, reducing estimation errors.

Theory explains neural network scaling with dataset and model size.

Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.

The paper examines the unexpected losses and risk ratios for co-monotonic alternatives in large portfolios.

asp2vec learns dynamic node aspect distributions for better network embedding.

Adapts RKHS methods to estimate density ratios with optimal error.

This paper studies activation sparsity in large language models, finding key trends and implications.

Optimal reinsurance balances risk over surplus ratios for risk-adjusted surplus.

Large knots have very varied boundary slopes.

Aggregation defenses improve deep learning models' robustness against data poisoning attacks.

Study introduces new financial ratios for better predicting company performance.

This paper addresses privacy concerns in ratio statistics using differential privacy.

Adaptive multi-stage density ratio estimation improves learning of latent space EBM.

This paper introduces a simple and efficient density estimator that enables fast systematic search. To show its advantage over commonly used kernel density estimator, we apply it to outlying aspects mining. Outlying aspects mining discovers feature subsets (or subspaces) that describe how a query stand out from a given…