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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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48 results for Abstract domains

We study the problem of formally verifying the robustness to adversarial examples of support vector machines (SVMs), a major machine learning model for classification and regression tasks. Following a recent stream of works on formal robustness verification of (deep) neural networks, our approach relies on a sound abst…

2019-04-26abs ↗pdf ↗

Deep neural network learns discrete state abstractions for efficient planning.

problem Efficient sequential decision making in large state spaces.
method Information bottleneck method for learning approximate bisimulations using deep neural encoders and action-conditioned HMM.
result Trained method efficiently plans for unseen goals in multi-goal reinforcement learning.

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…

2019-03-29abs ↗pdf ↗

The paper introduces a method to learn Markov state abstractions for reinforcement learning.

problem Learning Markov state representations in complex environments.
method The paper introduces a novel set of conditions and a training procedure combining inverse model estimation and temporal contrastive learning.
result The approach learns representations that capture the underlying structure of the domain and improve sample efficiency.

Survey examines challenges and solutions in sim-to-real transfer for robotics.

problem Challenges in transferring robotic systems from simulation to real-world environments.
method Leveraging techniques like domain randomization, real-to-sim transfer, state and action abstractions, and sim-real co-training.
result Promising results in closing the reality gap across various robotic domains.

Biomedical research papers use significantly different language and jargon when compared to typical English text, which reduces the utility of pre-trained NLP models in this domain. Meanwhile Medline, a database of biomedical abstracts, introduces nearly a million new documents per-year. Applications that could benefit…

2020-02-13abs ↗pdf ↗

VQShape learns interpretable time-series representations and achieves comparable performance to specialist models.

problem Lack of interpretability in existing time-series models.
method Vector quantization of time-series data into abstracted shapes.
result VQShape achieves comparable performance to specialist models in classification tasks.

TASID learns policies in high-dimensional settings with abstract simulator knowledge.

problem RL in high-dimensional settings with limited observation knowledge.
method TASID algorithm for transfer RL from abstract simulator with bounded perturbations.
result Sample complexity polynomial in horizon, independent of number of states.

Though reinforcement learning has greatly benefited from the incorporation of neural networks, the inability to verify the correctness of such systems limits their use. Current work in explainable deep learning focuses on explaining only a single decision in terms of input features, making it unsuitable for explaining …

2019-05-28abs ↗pdf ↗

Abstract framework for two meromorphic forms on punctured surfaces.

problem Developing a framework for two meromorphic forms on punctured Riemann surfaces.
method Abstract framework with Teichmüller regularity, degeneration detection, and pushability.
result Existence of a surface carrying two meromorphic differentials realizing any prescribed restricted pair.

Paper proves neural networks can be approximated using interval bounds.

problem Verifying safety and robustness of neural networks.
method Introduces interval universal approximation (IUA) theorem for neural networks.
result Neural networks can be approximated using interval bounds for any continuous function and squashable activation functions.

Improves neural network verification by merging abstract domains and Lagrangian methods.

problem Prove provable bounds for neural network outputs given input ranges.
method Uses zonotopes within a Lagrangian decomposition to verify deep neural networks.
result Yields bounds that improve upon existing techniques in both time and tightness.

Enhances BO with expert preferences about abstract properties.

problem Lack of expert knowledge in BO for black-box experimental design.
method Human-AI collaboration to incorporate expert preferences into surrogate modeling.
result Superior performance compared to baselines in synthetic and real-world datasets.

MXGNet tackles visual reasoning tasks using graph neural networks.

problem Abstract reasoning, especially in the visual domain, is challenging for AI.
method Combines object-level representations, graph neural networks, and multiplex graphs.
result Achieves state-of-the-art accuracy on Euler Diagram Syllogisms and outperforms state-of-the-art models on RPM datasets.

Novel framework for uncertainty quantification in neurosymbolic programs.

problem Lack of correctness guarantees in neurosymbolic programs due to machine learning model fallibility.
method Adapting conformal prediction to neurosymbolic programs using abstract interpretation.
result Framework provides probabilistic guarantees for correctness, compositionality, and structured values.

This work abstracts deep neural networks into concept graphs for better interpretability in medical tasks.

problem Lack of interpretability in deep learning models, especially in medical domains.
method Developed a graphical representation of medical image processing models to understand concept-based reasoning.
result Extracted a concept-level graph that reveals the decision-making process of deep learning models.

The abstract discusses transversality for infinite dimensional manifolds.

problem Transversality for infinite dimensional Fréchet manifolds.
method Constructing degree of nonlinear Fredholm mappings using transversality results.
result Proof of rank theorem, invariance of domain theorem, and Bursuk-Ulam type theorem.

A new layer learns abstract relations from graph structure using finite-state automata.

problem Learning abstract relations from graph structure for program analysis.
method Relaxing the problem into learning finite-state automata policies on a graph-based POMDP and training these policies using implicit differentiation.
result GFSA layer finds shortcuts in grid-world graphs and reproduces simple static analyses on Python programs.

Our goal is to better understand the relationship between the polyhedron and the group associated with a fundamental domain in H^3. In this paper, we will study torsion-free groups and determine a formula for how many edge classes a given abstract polyhedron must have. We will use that result to classify all fundamenta…

2019-10-08abs ↗pdf ↗

Automatic summarization of natural language is a current topic in computer science research and industry, studied for decades because of its usefulness across multiple domains. For example, summarization is necessary to create reviews such as this one. Research and applications have achieved some success in extractive …

2018-12-18abs ↗pdf ↗

In this paper we study a sharp Hardy-Littlewood-Sobolev (HLS) type inequality with Riesz potential on bounded smooth domains. We obtain the inequality for a general bounded domain ΩΩ and show that if the extension constant for ΩΩ is strictly larger than the extension constant for the unit ball B1B_1 then extremal fun…

2017-09-12abs ↗pdf ↗

Abstract: Shows nonexistence of Courant-type nodal domain bounds for eigenfunctions of Dirichlet-to-Neumann operator.

problem Courant-type nodal domain bounds for eigenfunctions of Dirichlet-to-Neumann operator.
method Constructs a metric on a compact manifold to demonstrate the nonexistence of Courant-type bounds.
result Provides a negative answer to the existence of Courant-type nodal domain bounds.

Abstract: Mapping 3-manifold bordisms to topological orders and domain walls.

problem Mapping spin 3-manifolds to topological orders and their domain walls.
method Defining topological orders from torsion elements in H1(N)H_1(N), linking form, and quadratic refinement. Extending to spin bordisms and domain walls.
result Constructing domain walls between topological orders from spin bordisms.

The paper analyzes the stability of an observer error in a vibrating string system.

problem Stability analysis of observer error in a vibrating string system.
method Abstract Cauchy problem reformulation and application of LaSalle's invariance principle for infinite-dimensional systems.
result The observer error is asymptotically stable.

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

problem Challenging to learn accurate MDPs for high-dimensional states.
method Learn an abstract MDP over low-dimensional coarse states, using an abstraction function.
result Achieves superhuman performance on Pitfall! and higher reward with fewer samples.

Unified model learns concepts across domains like left and right.

problem Limited generalization of language concepts in inference-only models.
method Logic-Enhanced Foundation Model (LEFT) with a differentiable, domain-independent program executor.
result LEFT flexibly learns and reasons with concepts across 2D images, 3D scenes, human motions, and robotic manipulation.