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Paper · 2303.05689 · ICCV · 2023

Inducing Neural Collapse to a Fixed Hierarchy-Aware Frame for Reducing Mistake Severity

Jim Davis, Tong Liang

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 7 functions out of this paper's own repositories and ran 7 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
ltong1130ztr/haframe — 7 of 7
FunctionStatusWhere it lives
DistanceDict Ran ltong1130ztr/haframe/HAFrame/solve_HAF.py
pointer only (licence: NONE) · get_code("b2ebddc977309207")
cls_weights_matrix_factorization_solver Ran ltong1130ztr/haframe/HAFrame/solve_HAF.py
pointer only (licence: NONE) · get_code("35485c4530562fe0")
find_max_separation_matrix_factorization_solver Ran ltong1130ztr/haframe/HAFrame/solve_HAF.py
pointer only (licence: NONE) · get_code("88560c243b8f8496")
fixed_haf_cls_weights Ran ltong1130ztr/haframe/HAFrame/solve_HAF.py
pointer only (licence: NONE) · get_code("480ca9eff5a52152")
load_distance_matrix Ran ltong1130ztr/haframe/HAFrame/solve_HAF.py
pointer only (licence: NONE) · get_code("449bc1c4ca4fa6bb")
load_distances Ran ltong1130ztr/haframe/HAFrame/solve_HAF.py
pointer only (licence: NONE) · get_code("4da9d5c7c6c3c9ce")
map_hdistance_to_cosine_similarity_exponential_decay Ran ltong1130ztr/haframe/HAFrame/solve_HAF.py
pointer only (licence: NONE) · get_code("22db6d272cd3127f")

Repositories linked to this paper

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Abstract

There is a recently discovered and intriguing phenomenon called Neural Collapse: at the terminal phase of training a deep neural network for classification, the within-class penultimate feature means and the associated classifier vectors of all flat classes collapse to the vertices of a simplex Equiangular Tight Frame (ETF). Recent work has tried to exploit this phenomenon by fixing the related classifier weights to a pre-computed ETF to induce neural collapse and maximize the separation of the learned features when training with imbalanced data. In this work, we propose to fix the linear classifier of a deep neural network to a Hierarchy-Aware Frame (HAFrame), instead of an ETF, and use a cosine similarity-based auxiliary loss to learn hierarchy-aware penultimate features that collapse to the HAFrame. We demonstrate that our approach reduces the mistake severity of the model's predictions while maintaining its top-1 accuracy on several datasets of varying scales with hierarchies of heights ranging from 3 to 12.

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