Paper constructs unfaithful probability distributions in binary causal graphs.
problem Unfaithful probability distributions in binary causal graphs.
method Constructs unfaithful probability distributions in binary causal graphs.
result Examples of unfaithful probability distributions in binary causal graphs.
This classification is found by analyzing the action of a normal subgroup of B3 as hyperbolic isometries. This paper gives an example of an unfaithful specialization of the Burau representation on B4 that is faithful when restricted to B3, as well as examples of unfaithful specializations of B3.
dcFCI discovers causal relationships robustly under latent confounding and mixed data.
problem Causal discovery under latent confounding and unfaithfulness.
method dcFCI integrates a new score to assess PAG compatibility, guided by FCI search.
result Significantly outperforms state-of-the-art methods in small and heterogeneous datasets.
Simulation-based inference methods can produce unreliable posterior approximations.
problem Reliability of simulation-based inference methods for scientific use cases.
method Benchmarked algorithms including Neural Posterior Estimation, Neural Ratio Estimation, Sequential Neural Likelihood, and Approximate Bayesian Computation.
result Ensembling posterior surrogates provides more reliable approximations.
SCARY dataset generates complex causal scenarios for causality research.
problem Lack of complexity in existing causal datasets.
method Synthetic dataset with 40 scenarios, three seeds, and two data generation mechanisms.
result Provides a valuable resource for realistic causal discovery.
Anderson and Canary have shown that if the algebraic limit of a sequence of discrete, faithful representations of a finitely generated group into PSL(2,C) does not contain parabolics, then it is also the sequence's geometric limit. We construct examples that demonstrate the failure of this theorem for certain sequences…
Method trains deep models to explain predictions with fewer examples.
problem Difficulty in humans understanding deep model predictions.
method Simultaneously trains prediction and explanation models with sparse regularization.
result Improves faithfulness of explanations with fewer examples while maintaining predictive performance.
Measures faithfulness of LLM explanations to reveal hidden biases and misleading claims.
problem LLM explanations can misrepresent the model's reasoning process, leading to over-trust and misuse.
method Defines faithfulness in terms of concept influence and uses counterfactuals and Bayesian models to estimate it.
result Can quantify and discover interpretable patterns of unfaithfulness in LLM explanations.
New research shows Manturov-Nikonov map fails for large k values.
problem Proving Manturov-Nikonov map is unfaithful for k ≥ 6.
method Analyzing composite maps and Burau kernel properties.
result Burau kernel is a subgroup of M-N kernel, leading to map unfaithfulness.
We study the kernel of the evaluated Burau representation through the braid element σiσi+1σi. The element is significant as a part of the standard braid relation. We establish the form of this element's image raised to the nth power. Interestingly, the cyclotomic polynomials arise and can be used to defin…
We consider spaces of plane curves in the setting of algebraic geometry and of singularity theory. On one hand there are the complete linear systems, on the other we consider unfolding spaces of bivariate polynomials of Brieskorn-Pham type. For suitable open subspaces we can define the bifurcation braid monodromy takin…
A long-standing open problem is to determine for which values of n the Burau representation Psi_n of the braid group B_n is faithful. Following work of Moody, Long-Paton, and Bigelow, the remaining open case is n = 4. One criterion states that Psi_n is unfaithful if and only if there exists a pair of arcs in the n-punc…
Existing dimensionality reduction methods are adept at revealing hidden underlying manifolds arising from high-dimensional data and thereby producing a low-dimensional representation. However, the smoothness of the manifolds produced by classic techniques over sparse and noisy data is not guaranteed. In fact, the embed…
YAHPO Gym introduces a new benchmark for evaluating hyperparameter optimization methods.
problem Evaluating and comparing hyperparameter optimization methods on well-curated benchmark suites.
method Surrogate-based benchmark collection of 14 scenarios, each with multi-fidelity and multi-objective hyperparameter optimization problems.
result Surrogate-based benchmarks produce more faithful results than tabular benchmarks.
Cost-effective method detects language model hallucinations.
problem Detecting unreliable outputs from LLMs.
method Pipeline including confidence score, input attributes calibration, and thresholding.
result Multi-scoring framework outperforms individual methods and reduces computational cost.
New groups and subgroups classified with representations and properties.
problem Classifying representations of new groups and subgroups.
method Introduced new groups and subgroups, classified representations into GL_n(C), investigated properties.
result Classified homogeneous 2-local representations of M_kVT_n into eight distinct types.
MambaLRP enhances Mamba models' explainability and performance.
problem Lack of transparency in Mamba models for real-world applications.
method Layer-wise Relevance Propagation (LRP) with relevance conservation axioms.
result MambaLRP provides stable and reliable explanations for Mamba models.
New findings on Jones polynomial for 4-strand braids.
problem Whether there are non-trivial knots with trivial Jones polynomial.
method Study of 4-strand braids, exploration of various properties of hypothetical HOMFLY-PT polynomials.
result Existence of a 1-parameter family of 2-variable polynomials that can be HOMFLY-PT polynomials of some knots.
Paper introduces SDM for detecting LLM hallucinations, improving on entropy tests.
problem Challenges of Large Language Models (LLMs) with non-factual, nonsensical responses.
method Joint clustering on sentence embeddings to measure semantic divergence between prompts and responses.
result SDM framework detects deeper form of arbitrariness in LLM responses.
Bayesian networks are typically faithful, with implications for causal inference.
problem Determining the typicality of faithfulness in Bayesian networks.
method Analysis of Bayesian networks over a given DAG, parametrized by conditional exponential families, and nonparametric conditional densities.
result The faithful Bayesian networks are dense and open with respect to the total variation metric, extending existing results for specific classes of Bayesian networks.