A Python library to calculate Neural Collapse (NC) related metrics.
So far, the metrics as described in "Robert Wu and Vardan Papyan. Linguistic Collapse: Neural Collapse in (Large) Language Models, 2024" are implemented.
pip install 'nc-toolbox @ git+https://github.com/felixsh/nc-toolbox'
N: number of samples
Nc: number of samples in class c
D: feature dimensionality
C: number of classes
W: weight matrix of linear classifier (C, D)
H: feature matrix (N, D)
L: label vector (N,)
mu_c: matrix of class embedding means (C, D)
mu_g: vector of global embedding mean (D,)
import nc_toolbox as nctb
import numpy as np
# Setup
N = 1000
C = 10
D = 100
W = np.random.rand(C, D)
H = np.random.rand(N, D)
L = np.random.randint(0, C, N)
H_test = np.random.rand(N // 2, D)
# Statistics
mu_c = nctb.class_embedding_means(H, L)
var_c = nctb.class_embedding_variances(H, L, mu_c)
mu_g = nctb.global_embedding_mean(H)
# Metrics
print(f'nc1_cdnv: {nctb.nc1_cdnv(mu_c, var_c)}')
print(f'nc2_equinormness: {nctb.nc2_equinormness(mu_c, mu_g)}')
print(f'nc2_equiangularity: {nctb.nc2_equiangularity(mu_c, mu_g)}')
print(f'gnc2_hypershperical_uniformity: {nctb.gnc2_hypershperical_uniformity(mu_c, mu_g)}')
print(f'nc3_self_duality: {nctb.nc3_self_duality(W, mu_c, mu_g)}')
print(f'unc3_uniform_duality: {nctb.unc3_uniform_duality(W, mu_c, mu_g)}')
print(f'nc4_classifier_agreement: {nctb.nc4_classifier_agreement(H_test, W, mu_c)}')