Wide Neural Networks as a Baseline for the Computational No-Coincidence Conjecture
This work addresses a foundational issue in AI interpretability by providing a theoretical baseline for measuring limits, but it is incremental as it builds on existing conjectures without broad empirical validation.
The paper tackles the problem of understanding when neural networks produce independent outputs, showing that randomly initialized wide networks with zero-mean activation functions (e.g., shifted ReLU or tanh) yield nearly independent outputs, which supports the computational no-coincidence conjecture for AI interpretability.
We establish that randomly initialized neural networks, with large width and a natural choice of hyperparameters, have nearly independent outputs exactly when their activation function is nonlinear with zero mean under the Gaussian measure: $\mathbb{E}_{z \sim \mathcal{N}(0,1)}[σ(z)]=0$. For example, this includes ReLU and GeLU with an additive shift, as well as tanh, but not ReLU or GeLU by themselves. Because of their nearly independent outputs, we propose neural networks with zero-mean activation functions as a promising candidate for the Alignment Research Center's computational no-coincidence conjecture -- a conjecture that aims to measure the limits of AI interpretability.