arXiv research

The paper explores higher property T in lattices and its connections to geometric phenomena.

A new concept of causality for abstract phenomena.

Introduces a new bracket for multicontact geometry and applies it to field theories.

Survey on quasi-isometries of group pairs and their invariants.

The abstract discusses special Lagrangians and their flow, proving conjectures and observing related phenomena.

Abstract: Study of surface transitions and IDE inflections via contact geometry.

As modern deep networks become more complex, and get closer to human-like capabilities in certain domains, the question arises of how the representations and decision rules they learn compare to the ones in humans. In this work, we study representations of sentences in one such artificial system for natural language pr…

Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…

Develops SCMs for latent selection to simplify causal analysis.

DisCoPyro combines category theory with machine learning for program learning.

Abstraction is a fundamental part when learning behavioral models of systems. Usually the process of abstraction is manually defined by domain experts. This paper presents a method to perform automatic abstraction for network protocols. In particular a weakly supervised clustering algorithm is used to build an abstract…

The (relativistic) center of mass of an asymptotically flat Riemannian manifold is often defined by certain surface integral expressions evaluated along a foliation of the manifold near infinity, e. g. by Arnowitt, Deser, and Misner (ADM). There are also what we call 'abstract' definitions of the center of mass in term…

The paper aims to mathematically define and learn abstractions from data.

Unified framework for causal models at different levels of abstraction.

Abstract MDPs enable strategic exploration and fast reward transfer in complex environments.

The paper argues against the inefficiency of explaining deep learning phenomena.

Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical approaches that do consider both phenomena simulta…

In this paper, we consider a concentration of measure problem on Riemannian manifolds with boundary. We study concentration phenomena of non-negative $1$-Lipschitz functions with Dirichlet boundary condition around zero, which is called boundary concentration phenomena. We first examine relation between boundary concen…

New approach to abstract neural network representations using renormalization group.

Study investigates how simple speech sounds can form abstract categories.

Abstract Neural Networks (ANNs) improve DNN verification efficiency.

A distinctive property of human and animal intelligence is the ability to form abstractions by neglecting irrelevant information which allows to separate structure from noise. From an information theoretic point of view abstractions are desirable because they allow for very efficient information processing. In artifici…

Algorithm finds latent structure in value functions for improved reinforcement learning.

Abstraction plays a key role in concept learning and knowledge discovery; this paper is concerned with computational abstraction. In particular, we study the nature of abstraction through a group-theoretic approach, formalizing it as symmetry-driven---as opposed to data-driven---hierarchical clustering. Thus, the resul…

A collection of the accepted abstracts for the Machine Learning for Health (ML4H) workshop at NeurIPS 2019. This index is not complete, as some accepted abstracts chose to opt-out of inclusion.

The paper proposes a principle for dynamically adjusting the granularity of reinforcement learning abstractions.

We present PubMed 200k RCT, a new dataset based on PubMed for sequential sentence classification. The dataset consists of approximately 200,000 abstracts of randomized controlled trials, totaling 2.3 million sentences. Each sentence of each abstract is labeled with their role in the abstract using one of the following …

Develops MgCSL for discovering causal structures in high-dimensional data.

Sharp changes in time series representing market dynamics are studied by means of the self--similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous to critical phenomena in physics. A simple classification of the market crisis p…

An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: what are the theoretical principles governing the ability of neural networks to acquire, or…

We prove a definable version of the Whitney embedding theorem for abstract-definable $\mathcal{C}^p$ manifolds with $1\leq p<\infty$, namely: every abstract-definable $\mathcal{C}^p$ manifold is abstract-definable $C^p$ embedded into $R^N$, for some positive integer $N$. As a consequence, we show that every abstract-de…

Study on Lane-Emden equation on curved spaces, revealing new existence and non-existence phenomena.

This paper simplifies OPE in large state spaces using state abstractions.

We introduce an algorithm for model-based hierarchical reinforcement learning to acquire self-contained transition and reward models suitable for probabilistic planning at multiple levels of abstraction. We call this framework Planning with Abstract Learned Models (PALM). By representing subtasks symbolically using a n…

CIB compresses variables causally, preserving key causal interactions.

Constellation learns group-level visual relationships for abstract reasoning.

Abstract discusses different corks.

Can simple algorithms with a good representation solve challenging reinforcement learning problems? In this work, we answer this question in the affirmative, where we take "simple learning algorithm" to be tabular Q-Learning, the "good representations" to be a learned state abstraction, and "challenging problems" to be…

We present a training system, which can provably defend significantly larger neural networks than previously possible, including ResNet-34 and DenseNet-100. Our approach is based on differentiable abstract interpretation and introduces two novel concepts: (i) abstract layers for fine-tuning the precision and scalabilit…

Paper connects Stokes phenomena to quantum groups and Poisson-Lie groups.

In this paper we observe that 2-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of 2-dimensional 0-surgery with the observed dynamics. To d…

Deep neural network learns discrete state abstractions for efficient planning.

moment maps arise as a generalization of genuine moment maps on symplectic manifolds when the symplectic structure is discarded, but the relation between the mapping and the action is kept. Particular examples of abstract moment maps had been used in Hamiltonian mechanics for some time, but the abstract notion originat…

Abstraction of Markov Decision Processes is a useful tool for solving complex problems, as it can ignore unimportant aspects of an environment, simplifying the process of learning an optimal policy. In this paper, we propose a new algorithm for finding abstract MDPs in environments with continuous state spaces. It is b…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

Paper investigates rigidity phenomena for weighted Ricci curvature bounds with Laplacian comparison theorem.

In this paper, we develop a framework to obtain graph abstractions for decision-making by an agent where the abstractions emerge as a function of the agent's limited computational resources. We discuss the connection of the proposed approach with information-theoretic signal compression, and formulate a novel optimizat…

Defines a generalized string concept for abstract root systems.