arXiv research

Graph neural networks fail to distinguish certain 3D atom configurations.

We construct a flat (and fake-flat) 2-connection in the configuration space of $n$ indistinguishable particles in the complex plane, which categorifies the $sl(2,C)$-Knizhnik-Zamolodchikov connection obtained from the adjoint representation of $sl(2,C)$. This will be done by considering the adjoint categorical represen…

New index principle shows indistinguishability of certain knot crossings.

The paper examines how to test if two learning algorithms produce similar outcomes.

The relationship between statistical dependency and causality lies at the heart of all statistical approaches to causal inference. Recent results in the ChaLearn cause-effect pair challenge have shown that causal directionality can be inferred with good accuracy also in Markov indistinguishable configurations thanks to…

Characterizes sample complexity for outcome indistinguishability in machine learning.

Framework uses human judgment to distinguish algorithmically indistinguishable cases.

Survey on calibration in machine learning, viewing it as indistinguishability.

A new metric evaluates classification algorithms at the point of indistinguishability.

Efficiently generates models resistant to falsification.

The paper formalizes robot environments using topological concepts.

LLMs show potential for predicting financial returns, contrary to common belief.

We investigate the possibility of statistical evaluation of the market completeness for discrete time stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper shows that market inc…

A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and Robbins is re-formulated in terms of certain locally flat vector bundles over n-parti…

New approach shows backdoor attacks are indistinguishable from natural data features.

Transformers approximate mean-field dynamics of indistinguishable particles.

The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one.…

ACFS optimizes spectral risk under decision-dependent uncertainty using adaptive forest sampling.

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish between different random graph models (corresponding to different class-conditional d…

Unsupervised learning models can be indistinguishable without identifiability, leading to unreliable representations.

Graphs indistinguishable by GNNs are fully characterized.

Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinate-independent language, in the tangent Minkowski space along the curve). For …

We show social events can be accurately predicted, but often undesirably.

Efficient algorithms for deleting data from machine learning models without significantly affecting performance.

We present a technique for efficiently synthesizing images of atmospheric clouds using a combination of Monte Carlo integration and neural networks. The intricacies of Lorenz-Mie scattering and the high albedo of cloud-forming aerosols make rendering of clouds---e.g. the characteristic silverlining and the "whiteness" …

Paper proposes a GAN-based method for better next event prediction in business processes.

Study on replicability in reinforcement learning algorithms.

Two knots in three-space are S-equivalent if they are indistinguishable by Seifert matrices. We show that S-equivalence is generated by the doubled-delta move on knot diagrams. It follows as a corollary that a knot has trivial Alexander polynomial if and only if it can be undone by doubled-delta moves.

Differential privacy has emerged as a gold standard in privacy-preserving data analysis. A popular variant is local differential privacy, where the data holder is the trusted curator. A major barrier, however, towards a wider adoption of this model is that it offers a poor privacy-utility tradeoff. In this work, we add…

We establish tools to facilitate the computation and application of the Chekanov-Eliashberg differential graded algebra (DGA), a Legendrian-isotopy invariant of Legendrian knots in standard contact three-space. More specifically, we reformulate the DGA in terms of front projection, and introduce the characteristic alge…

Paper distinguishes causal structures under latent confounding and selection bias.

Computes fundamental groups of restricted configuration spaces.

We resolve the open problem of optimal sample complexity for multicalibration and deterministic predictors.

This paper introduces a method to approximate Gaussian process regression by representing the problem as a stochastic differential equation and using variational inference to approximate solutions. The approximations are compared with full GP regression and generated paths are demonstrated to be indistinguishable from …

We study the configuration space of equilateral and equiangular spatial hexagons for any bond angle by giving explicit expressions of all the possible shapes. We show that the chair configuration is isolated, whereas the boat configuration allows one-dimensional deformations which form a circle in the configuration spa…

We inject undetectable backdoors into obfuscated neural networks and language models.

Study shows configuration spaces' homological dimension increases monotonically.

Researchers create a model for surface point configurations.

PathNNs improve graph neural networks by distinguishing non-isomorphic graphs.

Tripod configurations of plane curves, formed by certain triples of normal lines coinciding at a point, were introduced by Tabachnikov, who showed that $C^2$ closed convex curves possess at least two tripod configurations. Later, Kao and Wang established the existence of tripod configurations for $C^2$ closed locally c…

We study the Orchard relation for generic configurations of points in the plane (also called order types). We introduce infinitesimally-close points and analyse the relation of this notion with the Orchard relation. The second part of the paper deals with monochromatic configurations (for the Orchard relation). We give…

This paper extends homological stability results for configuration spaces of manifolds.

Quantum groups created from disk configuration space homologies.

We study configurations of immersed curves in surfaces and surfaces in 3-manifolds. Among other results, we show that primitive curves have only finitely many configurations which minimize the number of double points. We give examples of minimal configurations not realized by geodesics in any hyperbolic metric.

A machine learning configuration refers to a combination of preprocessor, learner, and hyperparameters. Given a set of configurations and a large dataset randomly split into training and testing set, we study how to efficiently select the best configuration with approximately the highest testing accuracy when trained f…

Study orders of canonical bundles over graph configuration spaces.

Solves Plateau-Douglas problem for singular configurations in general metric spaces.

Generative models create indistinguishable adversarial objects for object detection.