Certifiably Interpretable Training of ReLU-MLPs for Boolean Tasks with Guaranteed Truth-Table Generalization

2026-09-11

AI Summary

该研究通过MACCHIATO算法训练ReLU-MLP模型解决布尔任务，保证真值表泛化，同时提供可解释性证书。

Abstract

As compute scales, models evolve, and training algorithms advance, our ability to explain the increasingly powerful AI systems they enable is eroding. To help safeguard interpretability, we introduce a specialized training algorithm (MACCHIATO) that jointly constructs (i) an explicitly structured $\operatorname{ReLU}$-MLP from partial truth-table observations and (ii) an explicit Boolean circuit over signed literals with $\{\operatorname{AND},\operatorname{OR},\operatorname{XOR}\}$ gates certifying what its subnetworks compute and how they compose. Intuitively, we iteratively project the residuals of a Boolean function onto low-dimensional $\{\operatorname{AND},\operatorname{OR},\operatorname{XOR}\}$-circuit classes and exactly compile the resulting circuit into a $\operatorname{ReLU}$-MLP; we combine $\operatorname{ReLU}$-MLP circuit compilation, ESPRESSO logic minimization, and influence-based variable selection. Roughly speaking, our interpretability certificate is complemented by a statistical guarantee: under the theorem's influence-recovery conditions, if each of the $m$ stage-wise residuals depends on at most $\log_2(B)$ bits, a sample-splitting variant of our algorithm trained on $T$ observations returns a six-layer $\operatorname{ReLU}$-MLP (counting the input layer) of width $\mathcal{O}(mB)$ with truth-table error $\mathcal{O}\bigl(\sqrt{m(B+\log(m/δ))/T}\bigr)$. On synthetic random-junta tasks, our networks outperform depth- and hidden-width-matched Adam-trained MLPs in several data-sparse or projection-aligned regimes, while the trained ReLU-MLPs are stronger in others. Moreover, in our explicit PyEDA truth-table implementation, the iterative procedure completes in regimes where flat ambient-dimensional ESPRESSO exceeds the three-hour computational budget.

Problem

• interpretability
• ReLU-MLP
• Boolean tasks
• truth-table generalization
• certifiably interpretable

Innovation

• MACCHIATO
• ReLU-MLP
• Boolean Circuit
• Truth-Table Generalization
• ESPRESSO