质疑CC模型的叠加假设
论文研究Braun等人2025年提出的压缩计算（CC）玩具模型。该模型用50个神经元计算100个ReLU函数，但作者发现性能提升来自输入混合而非叠加计算。训练目标分为ReLU项和混合项，增益随混合矩阵幅度增大而消失。学习到的神经元方向集中在混合矩阵前50个特征值对应的子空间。基于混合矩阵的SNMF基线能复现损失轮廓，但未完全匹配训练模型。
Compressed Computation is (probably) not Computation in Superposition
We study whether the Compressed Computation (CC) toy model (Braun et al., 2025) is an instance of computation in superposition. The CC model appears to compute 100 ReLU functions with just 50 neurons, achieving a better loss than expected from only representing 50 ReLU functions. We show that the model mixes inputs via its noisy residual stream, corresponding to an unintended mixing matrix in the labels. Splitting the training objective into the ReLU term and the mixing term, we find that performance gains scale with the magnitude of the mixing matrix and vanish when the matrix is removed. The learned neuron directions concentrate in the subspace associated with the top 50 eigenvalues of the mixing matrix, suggesting that the mixing term governs the solution. Finally, a semi-non-negative matrix factorization (SNMF) baseline derived solely from the mixing matrix reproduces the qualitative loss profile and improves on prior baselines, though it does not match the trained model. These results suggest CC is not a suitable toy model of computation in superposition.