99% of papers use real-world data, but only 3% provide formal comparisons.
problem Lack of complete argumentative chains in demonstrating algorithmic effectiveness in machine learning papers.
method Systematic review of NeurIPS papers from 2017, assessing completeness of argumentative steps.
result Only 3% of papers provide formal comparisons, indicating incomplete argumentative chains.
Lean 4 formalizes Stokes' theorem for smooth singular cubes.
problem Formalizing Stokes' theorem for singular cubes in arbitrary dimensions.
method Using true differential-form pullback via Frechet derivative, bridging to mathlib4's extDeriv.
result d^2=0 for singular cubical chains, chain-level Stokes extended.
Paper formalizes multi-dimensional FSD using geometric methods.
problem Complex measure theory and calculus barriers to formalization in proof assistants.
method Geometric framework for first-order stochastic dominance in N dimensions.
result Geometric approach bypasses complex integration theory for direct comparison of survival probabilities.
The paper defines and studies the category of Z-graded manifolds, including their intrinsic structure and formal properties.
problem Understanding the categorical properties and intrinsic structure of Z-graded manifolds.
method Describing local models, explaining formality, and formulating analogues of theorems.
result Proper definitions of objects and morphisms in the category of Z-graded manifolds, and formulation of Batchelor's theorem.
Many objects in the real world are difficult to describe by a single numerical vector of a fixed length, whereas describing them by a set of vectors is more natural. Therefore, Multiple instance learning (MIL) techniques have been constantly gaining on importance throughout last years. MIL formalism represents each obj…
New comparison shows differences in how value is incorporated in AIF and CAI.
problem Clarifying the relationship between Active Inference and Control-as-Inference.
method Formal comparison of AIF and CAI frameworks.
result Primary difference is how value is incorporated into generative models.
We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices…
Modeling preference rankings with salient features to explain irrational choices.
problem Estimating rankings from noisy pairwise comparisons with irrational choices.
method Salient feature preference model with maximum likelihood estimation.
result Strong performance of maximum likelihood estimation on synthetic and real data.
New algorithm for identifying Condorcet team in noisy comparisons.
problem Online learning with noisy comparisons of teams.
method Formalized dueling teams problem, developed algorithms for stochastic and deterministic settings.
result Identifies Condorcet winning team with reduced number of duels.
The Schouten bracket (or antibracket) plays a central role in the Poisson formalism and the Batalin-Vilkovisky quantization of gauge systems. There are several (in)equivalent ways to realize this concept on jet spaces. In this paper, we compare the definitions, examining in what ways they agree or disagree and how they…
Systems of partial differential equations lie at the heart of physics. Despite this, the general theory of these systems has remained rather obscure in comparison to numerical approaches such as finite element models and various other discretisation schemes. There are, however, several theoretical approaches to systems…
Paper investigates monotonicity issues in AI preference learning.
problem AI models may violate monotonicity when learning preferences.
method Investigates root causes of non-monotonicity in comparison-based preference learning.
result Proves local pairwise monotonicity under mild assumptions.
The paper explores invariant subbundles in nonholonomic mechanics.
problem Determining invariant affine subbundles in nonholonomic and constrained variational mechanics.
method Using Spencer cohomology and iterative formulae, the paper formalizes the integrability of linear partial differential equations and determines the largest invariant affine subbundle.
result Iterative formulae for determining the largest invariant affine subbundle are provided.
Study homology manifolds using spectral sheaves and spectral six functor formalism.
problem Characterize and understand homology manifolds through spectral sheaves.
method Adapt six functor formalism to spectral sheaves on locally compact Hausdorff spaces.
result Prove that compact ANR homology manifolds are Poincaré duality complexes.
ModelDiff compares learning algorithms by identifying feature transformations.
problem Comparing models trained with different learning algorithms.
method ModelDiff uses datamodels framework to find distinguishing feature transformations.
result ModelDiff can compare models trained with/without data augmentation, pre-training, and different SGD hyperparameters.
We propose a topic modeling approach to the prediction of preferences in pairwise comparisons. We develop a new generative model for pairwise comparisons that accounts for multiple shared latent rankings that are prevalent in a population of users. This new model also captures inconsistent user behavior in a natural wa…
Understanding the flow of information in Deep Neural Networks (DNNs) is a challenging problem that has gain increasing attention over the last few years. While several methods have been proposed to explain network predictions, there have been only a few attempts to compare them from a theoretical perspective. What is m…
In this paper we show strategies to easily identify fake samples generated with the Generative Adversarial Network framework. One strategy is based on the statistical analysis and comparison of raw pixel values and features extracted from them. The other strategy learns formal specifications from the real data and show…
Interdisciplinary comparison of sequence modeling methods for next-element prediction.
problem Comparing sequence modeling methods across different fields.
method Experimental evaluation of four real-life sequence datasets using machine learning, process mining, and grammar inference techniques.
result Machine learning techniques outperform interpretability-focused methods in next-element prediction accuracy.
The paper examines A/B tests in recommendation systems to detect biased algorithm comparisons due to shared data.
problem Bias in comparing recommendation algorithms due to shared data.
method Formalized as a multi-armed bandit problem, analyzed the sign of difference-in-means estimator vs true GTE.
result Data sharing can lead to biased comparisons of recommendation algorithms, and a detection procedure is proposed.
Unified view on random walk and Weisfeiler-Leman kernels, improving accuracy.
problem Improving graph kernel methods for better classification accuracy.
method Define and analyze walk-based node refinement methods, relate to Weisfeiler-Leman test, and introduce new walk-based kernels.
result Walk-based kernels are as expressive as Weisfeiler-Leman subtree kernel but support non-strict neighborhood comparison.
For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to a distance based on Pearson Correlation. This has profound impact on many distanc…
Paper improves safe policy improvement with estimated baseline policy.
problem Unreliable batch Reinforcement Learning algorithms in real-world applications.
method Apply SPIBB algorithms with an estimated baseline policy.
result Safe policy improvement guarantees over true baseline without direct access.
It is shown that the characteristic classes of foliations that were defined by Losik and that take values in the de~Rham cohomology of the space of infinite order frames over the leaf space may be mapped to the characteristic classes with values in the Čech-de~Rham cohomology of the leaf space studied in details by Cra…
Extends metrics for SPD matrices to infinite dimensions.
problem Lack of generalized forms for Riemannian metrics.
method Unitized Hilbert-Schmidt operators and extended Mahalanobis norm.
result Improved performance in high-dimensional comparisons.
Given a binary prediction problem, which performance metric should the classifier optimize? We address this question by formalizing the problem of Metric Elicitation. The goal of metric elicitation is to discover the performance metric of a practitioner, which reflects her innate rewards (costs) for correct (incorrect)…
Survey of three geometric frameworks for action-dependent field theories.
problem Understanding action-dependent field theories through geometric structures.
method Introduction and analysis of three geometric frameworks: k-contact, k-cocontact, and multicontact.
result Analysis of relationships among these geometric structures and comparison with other definitions.
We study the geometry of jets of submanifolds with special interest in the relationship with the calculus of variations. We give a new proof of the fact that higher order jets of submanifolds are affine bundles; as a by-product we obtain a new expression for the associated vector bundles. We use Green-Vinogradov formul…
Proposes a new hierarchical clustering method combining DP and DBSCAN strengths.
problem Combining strengths of DP and DBSCAN for arbitrary shape clusters.
method DC-HDP: Combines Density Peak and Density-Connectivity approaches.
result Produces best clustering results on 14 datasets.
Bitcoin price prediction models fail to outperform a simple 'today's price' baseline, especially at longer horizons.
problem Lack of robust models that consistently outperform a naive price predictor at various horizons.
method Surveyed peer-reviewed papers, categorized by evaluation methodology, contrasted with social media discourse, and proposed methodological standards.
result No peer-reviewed study has shown robust superiority over the naive baseline across multiple market regimes at short-to-medium horizons.
We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph cluste…
Study finds companies react negatively to material cybersecurity incident disclosures.
problem Understanding market reactions to cybersecurity incidents.
method Examined daily stock price movements of companies disclosing material cybersecurity incidents.
result Companies tend to experience negative price reactions after disclosing material cybersecurity incidents.
A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as i.i.d. random variables. The dependence was found by analysis of empirical histogram…
New approach for learning with unknown utilities without explicit specification.
problem Learning with unknown and context-dependent utility functions.
method Agnostic learning with unknown utilities, using k-comparison oracle.
result Learning a decision function with small excess risk using sampled data and k-comparison oracle.
Robust method estimates state, input, and parameters of linear systems online.
problem Joint estimation of state, input, and parameters in noisy or outlier-prone measurements.
method Combines recursive, alternating, and iteratively-reweighted least squares into a single algorithm.
result Good performance in presence of outliers and compared to state-of-the-art methods.
Operationalizes engagement as human behavior, linking theory and data.
problem Fuzziness of engagement concept.
method Formal framework, Melchoir Model, model comparison, theory-driven hypothesis.
result Engagement can be shaped and interpreted using data-driven methods.
This paper improves DQN agents' robustness to adversarial perturbations.
problem Improving DQN agents' robustness to adversarial perturbations.
method Adversarial training and a novel AGE mechanism based on ε-greedy and Boltzmann exploration. result AGE mechanism enhances DQN agents' robustness to adversarial perturbations.
Establishes Poincaré's lemma for formal manifolds.
problem Developing smooth relative Lie algebra homologies and cohomologies.
method Theory of formal manifolds and formal Lie groups.
result Poincaré's lemma for de Rham complexes with formal functions and generalized functions.
Smooth Z2n-supermanifolds have been introduced and studied recently. The corresponding sign rule is given by the "scalar product" of the involved Z2n-degrees. It exhibits interesting changes in comparison with the sign rule using the parity of the total degree. With the new rule, nonzero degre…
Foundations laid for formal manifolds in differential geometry.
problem No specific problem stated; focuses on formal manifolds.
method Introducing formal manifolds, developing their theory, and proving finite products.
result Established a fully faithful contravariant functor and finite products in the category of formal manifolds.
We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on several approximate variations of the Policy Iteration algorithm: Approximate Policy Iteration, Conservative Policy Iteration (CPI), a natural adaptation of the Policy Search by Dynamic Programming a…
Explores local structure of morphisms and formal submanifolds in formal manifolds theory.
problem Understanding the local structure of morphisms and formal submanifolds in formal manifolds.
method Study of formal manifolds, including local structure of constant rank morphisms and formal submanifolds.
result Developed the local structure of constant rank morphisms and formal submanifolds.
Study non-formal pseudo-differential operators over formal ones.
problem Understanding structure of non-formal pseudo-differential operators.
method Diffeological principal bundles, smoothing connections.
result Structure of diffeological bundle of non-formal pseudo-differential operators over formal ones.
Greedy algorithm performs well in online matching despite non-i.i.d. connections.
problem Online matching in sparse random graphs with fixed degree distributions.
method Approximating stochastic processes with partial differential equations.
result GREEDY algorithm can outperform RANKING in certain configurations.
The isotropy action on certain symmetric spaces is shown to be equivariantly formal.
problem Understanding the equivariant formality of isotropy actions on symmetric spaces.
method Developed a new approach to prove equivariant formality for (Z2⊕Z2)-symmetric spaces. result Symmetric spaces with (Z2⊕Z2)-symmetry are equivariantly formal and formal in the Sullivan sense. A new anomaly detection method using partial identification.
problem Detecting anomalies in large datasets.
method Partial Identification framework and PIDScore geometric anomaly measure.
result PIDForest outperforms other methods in anomaly detection.
Strong formal properties for toric and homogeneous Kähler manifolds.
problem Understanding formal properties of Kähler manifolds.
method Analyzing rationally and strongly formal properties of toric and homogeneous Kähler manifolds.
result Toric and homogeneous Kähler manifolds are both rationally and strongly formal.
Develops a framework to analyze financial structures.
problem Difficulty in systematic analysis, comparison, and verification of financial structures.
method Formalizes financial structures as structured allocation systems with explicit allocation operators.
result Specifies inputs, structural requirements, and feasibility restrictions for financial structures.