arXiv research

Unified approach to verify NN properties using ReLU's unique polytope structure.

We study smooth {\sf traversing} vector fields $v$ on compact manifolds $X$ with boundary. A traversing $v$ admits a Lyapunov function $f: X \to \Bbb R$ such that $df(v) > 0$. We show that the trajectory spaces $\mathcal T(v)$ of {\sf traversally generic} $v$-flows are {\sf Whitney stratified spaces}, and thus admit tr…

Euler's theorem extended to complex structures.

A novel multi-resolution Gaussian process model for efficient time traversal.

Many tasks in computer vision can be cast as a "label changing" problem, where the goal is to make a semantic change to the appearance of an image or some subject in an image in order to alter the class membership. Although successful task-specific methods have been developed for some label changing applications, to da…

We combine Gromov's amenable localization technique with the Poincaré duality to study the traversally generic vector flows on smooth compact manifolds $X$ with boundary. Such flows generate well-understood stratifications of $X$ by the trajectories that are tangent to the boundary in a particular canonical fashion. Sp…

Any traversally generic vector flow on a compact manifold $X$ with boundary leaves some residual structure on its boundary $\d X$. A part of this structure is the flow-generated causality map $C_v$, which takes a region of $\d X$ to the complementary region. By the Holography Theorem from \cite{K4}, the map $C_v$ allow…

Counterfactual regret minimization (CFR) is the most popular algorithm on solving two-player zero-sum extensive games with imperfect information and achieves state-of-the-art performance in practice. However, the performance of CFR is not fully understood, since empirical results on the regret are much better than the …

Predicts node sequences in graphs using multi-order network models.

Let $X$ be a compact smooth manifold with boundary. In this article, we study the spaces $\mathcal V^\dagger(X)$ and $\mathcal V^\ddagger(X)$ of so called boundary generic and traversally generic vector fields on $X$ and the place they occupy in the space $\mathcal V(X)$ of all fields (see Theorems \ref{th3.4} and Theo…

Attention-based encoder decoder network uses a left-to-right beam search algorithm in the inference step. The current beam search expands hypotheses and traverses the expanded hypotheses at the next time step. This traversal is implemented using a for-loop program in general, and it leads to speed down of the recogniti…

A colored graph is a directed graph in which nodes or edges have been assigned colors that are not necessarily unique. Observability problems in such graphs consider whether an agent observing the colors of edges or nodes traversed on a path in the graph can determine which node they are at currently or which nodes wer…

Method generates counterfactual explanations for graph classifiers.

SURF steers scalarization weights to uniformly traverse the Pareto front.

In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to extra combinatorial constraints, the only practical algorithms to date have been v…

Let $C_{k_1}^{k_2}$ denote the set of all closed curves of class $C^r$ on the sphere $S^2$ whose geodesic curvatures are restricted to lie in $(k_1,k_2)$, furnished with the $C^r$ topology (for some $r >= 2$ and possibly infinite $k_1 < k_2$). In 1970, J. Little proved that the space $C_0^{+\infty}$ of closed curves ha…

This paper is the third in a series that researches the Morse Theory, gradient flows, concavity and complexity on smooth compact manifolds with boundary. Employing the local analytic models from \cite{K2}, for \emph{traversally generic flows} on $(n+1)$-manifolds $X$, we embark on a detailed and somewhat tedious study …

We investigate the difficulties of training sparse neural networks and make new observations about optimization dynamics and the energy landscape within the sparse regime. Recent work of \citep{Gale2019, Liu2018} has shown that sparse ResNet-50 architectures trained on ImageNet-2012 dataset converge to solutions that a…

This paper proposes a novel type of random forests called a denoising random forests that are robust against noises contained in test samples. Such noise-corrupted samples cause serious damage to the estimation performances of random forests, since unexpected child nodes are often selected and the leaf nodes that the i…

Proposes a new method for completing swap cycles in decentralized exchanges.

In many real-world scenarios, an autonomous agent often encounters various tasks within a single complex environment. We propose to build a graph abstraction over the environment structure to accelerate the learning of these tasks. Here, nodes are important points of interest (pivotal states) and edges represent feasib…

As has been observed by Morse \cite{Mo}, any generic vector field $v$ on a compact smooth manifold $X$ with boundary gives rise to a stratification of the boundary $\d X$ by compact submanifolds $\{\d_j^\pm X(v)\}_{1 \leq j \leq \dim(X)}$, where $\textup{codim}(\d_j^\pm X(v))= j$. Our main observation is that this stra…

This paper proposes an active learning system for sound event detection (SED). It aims at maximizing the accuracy of a learned SED model with limited annotation effort. The proposed system analyzes an initially unlabeled audio dataset, from which it selects sound segments for manual annotation. The candidate segments a…

In this paper, we present our general results about traversing flows on manifolds with boundary in the context of the flows on surfaces with boundary. We take advantage of the relative simplicity of $2D$-worlds to explain and popularize our approach to the Morse theory on smooth manifolds with boundary, in which the bo…

Music Inpainting is the task of filling in missing or lost information in a piece of music. We investigate this task from an interactive music creation perspective. To this end, a novel deep learning-based approach for musical score inpainting is proposed. The designed model takes both past and future musical context i…

This paper describes a mechanism by which a traversally generic flow $v$ on a smooth connected manifold $X$ with boundary produces a compact $CW$-complex $\mathcal T(v)$, which is homotopy equivalent to $X$ and such that $X$ embeds in $\mathcal T(v)\times \mathbf R$. The $CW$-complex $\mathcal T(v)$ captures some resid…

The study explores vector flows on manifolds, focusing on polynomial constraints and equivalence relations.

CCVAE captures label characteristics in VAEs for better representation learning.

The paper studies curves in surfaces using flow-spines and apparent contours.

Computational chemists typically assay drug candidates by virtually screening compounds against crystal structures of a protein despite the fact that some targets, like the $μ$ Opioid Receptor and other members of the GPCR family, traverse many non-crystallographic states. We discover new conformational states of $μOR$…

Automates optimizer design for diverse tasks efficiently.

Director learns hierarchical behaviors from pixels, outperforming exploration methods.

Let $M$ be a compact smooth Riemannian $n$-manifold with boundary. We combine Gromov's amenable localization technique with the Poincaré duality to study the {\sf traversally generic} geodesic flows on $SM$, the space of the spherical tangent bundle. Such flows generate stratifications of $SM$, governed by rich univers…

Suppose that $M$ is a $2$-dimensional oriented Riemannian manifold, and let $γ$ be a simple closed curve on $M$. Let $m γ$ denote the curve formed by tracing $γ$ $m$ times. We prove that if $m γ$ is contractible through curves of length less than $L$, then $γ$ is contractible through curves of length less than $L$. In …

A simple DQN-based multi-agent RL system for binary actions.

CTM improves diffusion model sampling quality with efficient ODE traversal.

For a non-vanishing gradient-like vector field on a compact manifold $X^{n+1}$ with boundary, a discrete set of trajectories may be tangent to the boundary with reduced multiplicity $n$, which is the maximum possible. (Among them are trajectories that are tangent to $\partial X$ exactly $n$ times.) We prove a lower bou…

The paper uses Bayesian Surprise to identify unexpected structures in indoor environments.

Characterizes sequences from two-component link diagrams.

Developing effective and efficient recommendation methods is very challenging for modern e-commerce platforms. Generally speaking, two essential modules named "Click-Through Rate Prediction" (\textit{CTR}) and "Conversion Rate Prediction" (\textit{CVR}) are included, where \textit{CVR} module is a crucial factor that a…

Classifier-based AI safety gates fail in self-improvement, even with advanced verification methods.

FIVES generates high-order interactive features efficiently and effectively.

New privacy bounds for DP-SGD's last iterate, even with cyclic sampling.

This study provides an explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.

This paper employs a formal connection of machine learning with thermodynamics to characterize the quality of learnt representations for transfer learning. We discuss how information-theoretic functional such as rate, distortion and classification loss of a model lie on a convex, so-called equilibrium surface.We prescr…

We compute the transition probability between two learning tasks, and show that it decomposes into two factors. The first depends on the geometry of the loss landscape of a model trained on each task, independent of any particular model used. This is related to an information theoretic distance function, but is insuffi…

Decision Machines embeds decision trees into vector spaces for improved optimization.

The paper examines how neural network topology affects adversarial robustness.