Fr\'echet
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Related Articles from SNS
Dynamical local Fr\'echet curve regression in manifolds
Announce Type: replace-cross Abstract: Under mild conditions, this paper derives a least-squares local linear Fr\'echet curve predictor for response and regressor evaluated in a separable Hilbert space. We obtain the conditions allowing the implementation of this local linear Fr\'echet functional predictor in the ambient L^{2}-space of vector functions, with values in the time-varying tangent space on a compact Riemannian manifold. An intrinsic local linear Fr\'echet curve predictor...
On Fr\'echet Traveling Salesmen Problems
arXiv:2606.01147v1 Announce Type: new Abstract: The Fr\'echet distance is a well-studied distance measure between two curves. In this work, we demonstrate that the merit of Fr\'echet distance extends beyond evaluating similarity, and introduce a new setting in which it proves useful. Consider a situation where two agents are required to visit a given set of sites, while staying close to each other throughout their traversal.
An Empirical Analysis of Task-Induced Encoder Bias in Fr\'echet Audio Distance
Announce Type: replace-cross Abstract: Fr\'echet Audio Distance (FAD) is the de facto standard for evaluating text-to-audio generation, yet its scores depend on the underlying encoder's embedding space. An encoder's training task dictates which acoustic features are preserved or discarded, causing FAD to inherit systematic task-induced biases. We decompose evaluation into Recall, Precision, and Alignment (split into semantic and structural dimensions), using log-scale normalization for fair...
Deep Single-Index Fr\'echet Regression
arXiv:2606.06957v1 Announce Type: cross Abstract: Predicting outputs that are located in non-Euclidean spaces, such as probability distributions, networks, and symmetric positive-definite matrices, is becoming increasingly important in modern data analysis, particularly when inputs are high-dimensional. We propose DeSI (Deep Single-Index Fr\'echet Regression), a semiparametric framework for regression with metric space-valued outputs and multivariate inputs that assumes a single-index...
Conditional Collapse in Sign Language Production: A Diagnostic and a Scaling Argument
arXiv:2606.01643v1 Announce Type: new Abstract: Sign Language Production (SLP) is the task of generating avatar sign language motion from natural language text. The quality of the generated motion is typically evaluated by a motion-space Fr\'echet distance (FID) and back-translation (BT) BLEU score on benchmarks such as How2Sign.
Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds
Announce Type: cross Abstract: Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps. In Euclidean space, barycentric projection converts a coupling into a map by taking conditional expectations, but on a Riemannian manifold curvature and cut loci make this operation nontrivial. We develop a framework for barycentric projections of transport couplings on Riemannian manifolds.
End-to-End Deep Learning for Predicting Metric Space-Valued Outputs
arXiv:2509.23544v2 Announce Type: replace-cross Abstract: Many modern applications involve predicting structured, non-Euclidean outputs such as probability distributions, networks, and symmetric positive-definite matrices. These outputs are naturally modeled as elements of general metric spaces, where classical regression techniques that rely on vector space structure no longer apply. We introduce E2M (End-to-End Metric regression), a deep learning framework for predicting metric...
Learning Coherent Representations: A Topological Approach to Interpretability
arXiv:2606.02841v1 Announce Type: new Abstract: Deep neural networks learn representations where individual features often lack interpretable meaning; a single neuron may activate for scattered, unrelated inputs. We introduce coherence, a geometric property inspired by neural coding in the brain, where neurons like grid cells and head direction cells respond to contiguous regions of state space. A non-negative matrix is coherent if each row (sample) attends to geometrically clustered columns...
Can LLMs understand LilyPond? A benchmark for symbolic music generation and understanding
Announce Type: new Abstract: Symbolic music evaluation for large language models remains fragmented across representations, datasets, and metrics. We introduce LilyBench, a LilyPond-based benchmark that jointly evaluates symbolic music generation and music understanding on the same family of open-weight LLMs. The benchmark includes a 200-prompt generation suite and ten understanding tasks adapted from ABC-Eval, covering syntax, metadata prediction, structural sequencing, and music recognition.
SPADE: Sketch-guided Path Planning Augmented with Diffusion Experts
arXiv:2606.03512v1 Announce Type: new Abstract: Path planning is essential for Autonomous Mobile Robots (AMRs). Conventional methods for incorporating human preferences into planning typically rely on either complex reward engineering or hardware-intensive solutions. Recent state-of-the-art frameworks leverage imitation learning to train behavior-specific path planning models from expert demonstrations.