paper / typesfast / Jun 10
This paper proves that there exist function classes where compositional approximation (as used by neural networks) achieves strictly better approximation rates than superpositional approximation (linear combinations of dictionary elements). The authors construct explicit examples exhibiting an arbitrarily large gap between the two approaches, demonstrating that compositionality itself — not just parameter count — can drive superior approximation performance.
function-approximationneural-networkscompositional-methodssuperpositional-methodsapproximation-theorynumerical-analysis
“Many classically studied function classes are optimally approximated by superpositional methods (linear combination of dictionary elements), where optimality is defined by polynomial decay of uniform approximation error relative to parameter count.”
paper / typesfast / Jun 3 / failed
paper / typesfast / May 23
Global Fréchet regression extends linear regression to settings where responses are non-Euclidean random objects in metric spaces, but formal inference tools have been absent. This paper fills that gap by developing significance tests for predictor relevance — both global and partial effects — using random multipliers to construct non-degenerate null distributions and the Cauchy combination method to aggregate test statistics. The framework is theoretically grounded with consistency and convergence results under null and contiguous alternatives, and validated empirically on graph Laplacian network data, spherical data, NYC taxi transport networks, and U.S. energy compositional data.
frechet-regressionstatistical-inferencenon-euclidean-datametric-spaceshypothesis-testingstatistical-methodologyregression-analysis
“Statistical inference for Global Fréchet regression has been largely unexplored prior to this work, despite the regression model itself being established.”
paper / typesfast / May 23
Site-disordered materials — where crystal sites are occupied probabilistically by multiple elements or vacancies — are incompatible with standard first-principles simulation methods that assume perfect crystal order. Virp addresses this gap with a pipeline combining permutation-based virtual cell generation, a structured sampling regime, and thermodynamic post-processing, bypassing the system-specific overhead of quasirandom structures and cluster expansion approaches. The authors demonstrate that adequate sampling of the configurational space can be achieved with as few as 400 virtual cells, provided the supercell definition is sufficiently large — offering a practical, scalable alternative to large-scale Monte Carlo simulations.
neural-networksmaterials-sciencecomputational-materialscrystal-structuresfirst-principlesmachine-learningsite-disorder
“Standard first-principles simulation methods cannot directly handle site-disordered crystal structures because they assume perfect crystalline order.”
paper / typesfast / May 23
MaSC is a masked similarity metric designed to evaluate concept-driven text-to-image generation by separating foreground subject fidelity from background prompt adherence — a decomposition that global metrics like CLIP-I, DINO, and CLIP-T fail to make. It leverages frozen SigLIP2 SO400M-NaFlex features with masked max-cosine patch matching for concept preservation and background-only pooled embeddings for prompt following. On DreamBench++ human ratings, MaSC achieves Krippendorff α = 0.471 for concept preservation, surpassing all non-LLM baselines and even GPT-4V, while on the ORIDa identity-preservation benchmark it reaches AUC = 0.992. The results establish spatially decomposed aggregation as a principled and highly effective design strategy for personalization evaluation.
text-to-imagediffusion-modelsimage-generation-evaluationconcept-personalizationsimilarity-metricscomputer-visionai-evals
“Global image embedding metrics (CLIP-I, DINO, CLIP-T) correlate poorly with human perception for concept-driven generation evaluation because they do not separate the concept subject from the background.”
paper / typesfast / May 15 / failed