arXiv research

We address noisy Euclidean distances in high dimensions, estimating noise levels and correcting distances.

SCoreBO improves Bayesian optimization by learning hyperparameters and self-correcting.

Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are LDPC codes with linear rate and distance $n^ε$. Their rate is evaluated via Euler characteristic arguments and their distance using $\mathbb{Z}_2$-systolic geometry. This construction answers …

GICDM corrects hubness in embedding spaces for better generative model evaluation.

Corrects local error estimates for UBU integrator in SDEs, improving complexity guarantees.

This paper corrects the proof of the Theorem 2 from the Gower's paper \cite[page 5]{Gower:1982} as well as corrects the Theorem 7 from Gower's paper \cite{Gower:1986}. The first correction is needed in order to establish the existence of the kernel function used commonly in the kernel trick e.g. for $k$-means clusterin…

Khovanov homology helps create quantum error-correcting codes.

Though deep learning has been applied successfully in many scenarios, malicious inputs with human-imperceptible perturbations can make it vulnerable in real applications. This paper proposes an error-correcting neural network (ECNN) that combines a set of binary classifiers to combat adversarial examples in the multi-c…

Author corrects an error in a paper about certain knot surgeries.

New optimization method corrects data-driven optimizer's curse.

We propose and analyze an alternate approach to off-policy multi-step temporal difference learning, in which off-policy returns are corrected with the current Q-function in terms of rewards, rather than with the target policy in terms of transition probabilities. We prove that such approximate corrections are sufficien…

We present a case-study demonstrating the usefulness of Bayesian hierarchical mixture modelling for investigating cognitive processes. In sentence comprehension, it is widely assumed that the distance between linguistic co-dependents affects the latency of dependency resolution: the longer the distance, the longer the …

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering pr…

Partial soft-matching distance improves neural representation comparison by allowing some neurons to remain unmatched.

In this paper we discuss a class of AutoEncoder based generative models based on one dimensional sliced approach. The idea is based on the reduction of the discrimination between samples to one-dimensional case. Our experiments show that methods can be divided into two groups. First consists of methods which are a modi…

In my masters thesis I prove a square root bound on the distance of homological codes that come from two dimensional surfaces, as a result of the systolic inequality. I also give a detailed version of M.H. Freedman's proof that due to systolic freedom, this bound does not hold in higher dimensions.

Bayesian neural networks improve uncertainty calibration with DAP priors.

Distance-based hierarchical clustering (HC) methods are widely used in unsupervised data analysis but few authors take account of uncertainty in the distance data. We incorporate a statistical model of the uncertainty through corruption or noise in the pairwise distances and investigate the problem of estimating the HC…

This paper is on the normal approximation of singular subspaces when the noise matrix has i.i.d. entries. Our contributions are three-fold. First, we derive an explicit representation formula of the empirical spectral projectors. The formula is neat and holds for deterministic matrix perturbations. Second, we calculate…

Quantum codes on hyperbolic lattices outperform Euclidean ones with higher rates and lower overhead.

Improved MALA method for neural networks uncertainty quantification.

Efficient algorithm approximates discrete random variables with minimal Kolmogorov distance.

We introduce a notion of geodesic curvature $k_ζ$ for a smooth horizontal curve $ζ$ in a three-dimensional contact sub-Riemannian manifold, measuring how much a horizontal curve is far from being a geodesic. We show that the geodesic curvature appears as the first corrective term in the Taylor expansion of the sub-Riem…

New method improves sampling from score-based models by correcting bias.

Study shows effective resistance distance yields more accurate network barycenter than Hamming distance.

Paper proposes a chi-square test for distance correlation.

In this paper we study the notion of geodesic curvature of smooth horizontal curves parametrized by arc lenght in the Heisenberg group, that is the simplest sub-Riemannian structure. Our goal is to give a metric interpretation of this notion of geodesic curvature as the first corrective term in the Taylor expansion of …

LOT Wassmap speeds up Wasserstein space manifold learning.

We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups $G$ of H-type. Specifically, we show that there exist positive constants $C_1$, $C_2$ and a polynomial correction function $Q_t$ on $G$ such that $C_1 Q_t e^{-\frac{d^2}{4t}} \le p_t \le C_2 Q_t e^{-\frac{d^2}{4t}}$ wh…

The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown support leads to the polynomial correction to the standard maximum likelihood est…

End-to-end deep metric learning tackles multi-label image classification.

Tests if vertices in graphs have the same latent positions.

The paper constructs Gromov-Hausdorff metrics for Lorentzian spaces and calculates dimensions.

Algorithm learns affine transformations robustly from corrupted samples.

We consider sequences of metrics, $g_j$, on a Riemannian manifold, $M$, which converge smoothly on compact sets away from a singular set $S\subset M$, to a metric, $g_\infty$, on $M\setminus S$. We prove theorems which describe when $M_j=(M, g_j)$ converge in the Gromov-Hausdorff sense to the metric completion, $(M_\in…

Paper proposes a new method for estimating treatment effects using interpretable deep learning models.

A corrective neural network approach improves memorization and learning efficiency.

The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties are derived. Theoretical results to guarantee the correctness of the identificatio…

Two log-linear approximations speed up optimal transport for deep learning applications.

Finding efficient decoders for quantum error correcting codes adapted to realistic experimental noise in fault-tolerant devices represents a significant challenge. In this paper we introduce several decoding algorithms complemented by deep neural decoders and apply them to analyze several fault-tolerant error correctio…

In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain theoretical guaranties for a few emblematic methods based on pairwise distances: a si…

A new method corrects bias in causal inference by balancing covariate distributions.

xAI-GAN improves GANs by providing richer feedback, enhancing image quality.

This work introduces a protocol to automatically select the correct range of scales for meaningful Intrinsic Dimension estimation.

Deep reinforcement learning has made significant progress in the field of continuous control, such as physical control and autonomous driving. However, it is challenging for a reinforcement model to learn a policy for each task sequentially due to catastrophic forgetting. Specifically, the model would forget knowledge …

Chatbot uses BERT to handle financial investment questions, improving accuracy and decision-making.

The Lasso method is analyzed for high-dimensional regression with Gaussian designs, leading to new insights on its performance.

Paper corrects Max-Margin loss for multi-label tasks.