Pith. sign in

REVIEW 2 cited by

Neural Collapse with Cross-Entropy Loss

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2012.08465 v2 pith:HQYLRA5M submitted 2020-12-15 cs.LG math.CA

classification cs.LGmath.CA
keywords collapsecross-entropyframehyperspherelossneuralprovebehavior
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We consider the variational problem of cross-entropy loss with $n$ feature vectors on a unit hypersphere in $\mathbb{R}^d$. We prove that when $d \geq n - 1$, the global minimum is given by the simplex equiangular tight frame, which justifies the neural collapse behavior. We also prove that as $n \rightarrow \infty$ with fixed $d$, the minimizing points will distribute uniformly on the hypersphere and show a connection with the frame potential of Benedetto & Fickus.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 12 citations worldwide. Full citation record

  1. Imitate Optimal Policy: Prevail and Induce Action Collapse in Policy Gradient

    cs.LG 2025-09 reject novelty 6.0 of 10

    Action Collapse Policy Gradient (ACPG) fixes the action-selection layer to a simplex ETF and claims improved discrete-action RL performance, with a theory that only covers a weighted optimal-action imitation objective.

  2. Memory-efficient Continual Learning with Neural Collapse Contrastive

    cs.CV 2024-12 conditional novelty 5.0 of 10

    A continual learning method that combines focal contrastive learning with fixed neural-collapse prototypes and a distillation loss achieves state-of-the-art accuracy in memory-free class- and task-incremental learning.

Pith tools