Simplex
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Related Articles from SNS
Reed-Muller type codes over a combinatorial simplex: an algebraic description
arXiv:2606.02819v1 Announce Type: new Abstract: Given an ordered set $B$ of a finite field, a combinatorial simplex over $B$ is defined as the set of vectors such that the positions of the entries, with respect to $B$, sum up to a fixed integer. CAP codes are Reed-Muller type codes defined over a combinatorial simplex.
Beyond the Simplex: Balanced Prototype Geometry for Scorer-Agnostic Open-Set Recognition
arXiv:2606.01883v1 Announce Type: new Abstract: Open-set recognition (OSR) requires a classifier to reject inputs from unseen classes which is essential in safety-critical settings such as medical imaging. Simplex based methods, which fix class prototypes at the vertices of a regular simplex and then reject via a distance-ratio score, perform well empirically but lack theoretical justification, and existing analysis applies only when the embedding dimension d is at least C-1, which is the...
Log-Ratio Propagation on the Simplex: A Theory of Cellwise Contamination for Compositional Data
Announce Type: cross Abstract: Compositional data must be analysed through log-ratios: scale invariance, the defining axiom of the field, leaves no alternative. The centred log-ratio divides by the geometric mean of every part, so a single contaminated component shifts every centred-log-ratio coordinate at once, displacing the log-ratio vector by a fixed amount that no choice of coordinates can reduce. We develop a theory of cellwise contamination on the simplex around this observation.
Explaining a probabilistic prediction on the simplex with Shapley compositions
arXiv:2408.01382v3 Announce Type: replace Abstract: Originating in game theory, Shapley values are widely used for explaining a machine learning model's prediction by quantifying the contribution of each feature's value to the prediction. This requires a scalar prediction as in binary classification, whereas a multiclass probabilistic prediction is a discrete probability distribution, living on a multidimensional simplex. In such a multiclass setting the Shapley values are typically computed...
Distributed Triangle and Simplex Enumeration in Hypergraphs
Announce Type: replace Abstract: In the last decade, subgraph detection and enumeration have emerged as central problems in distributed graph algorithms. This is largely due to the problems' theoretical challenges and practical applications. In this paper, we initiate the systematic study of distributed sub-hypergraph enumeration in hypergraphs.
Toward Operationalizing Rasmussen: Drift Observability on the Simplex for Evolving Systems
arXiv:2602.05483v2 Announce Type: replace Abstract: Software operations increasingly rely on SLOs, traces, deployment specifications, and change events, yet dashboards and thresholding practices often expose share-like operational signals as separate scalar panels or baseline distances. This can create false alarms under benign redistribution and miss movement toward policy boundaries. Rasmussen's dynamic safety model motivates drift under competing pressures, but operationalizing it for...
Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic
arXiv:2606.08985v1 Announce Type: new Abstract: While neural collapse (NC) predicts that a $K$-class-balanced classifier should organize terminal representations as a $(K-1)$-dimensional simplex equiangular tight frame (ETF), modular addition consistently enters a different regime: networks compress to a two-dimensional cyclic geometry in which both classifier weights and token embeddings lie on circles. We refine the explanation of this phenomenon in three directions. First, we formalize a...
Neural Collapse Dynamics: Depth, Activation, Regularisation, and Feature Norm Threshold
arXiv:2604.00230v2 Announce Type: replace Abstract: Neural collapse (NC) -- the convergence of penultimate-layer features to a simplex equiangular tight frame -- is well understood at equilibrium, but the dynamics governing its onset remain poorly characterised. We identify a simple and predictive regularity: NC occurs when the mean feature norm reaches a model-dataset-specific critical value, fn*, that is largely invariant to training conditions. This value concentrates tightly within each...
Spherical Flows for Sampling Categorical Data
arXiv:2605.05629v3 Announce Type: replace-cross Abstract: We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere $\mathbb S^{d-1}$. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable.
Bernard Roizman, Virologist Who Demystified Herpes, Dies at 96
He mapped the herpes simplex virus genome, revealing how it invades cells. His work also helped lay the groundwork for potential vaccines and gene therapies.