Summary
It can be hard to understand how AI models make decisions as they get bigger and more complex. This paper introduces a new training method that builds neural networks designed to be easy to interpret, especially for problems where outputs depend on simple true/false rules. The authors create a way to link parts of the neural network to clear logical circuits using basic AND, OR, and XOR gates, providing a kind of explanation that also comes with mathematical guarantees about how well the network will work on unseen data. Their method performs well on synthetic tasks where the important inputs are limited and can do so more efficiently than some standard logical simplification tools.
What this means in practice
- •For machine learning engineers: Build neural networks for boolean tasks that produce interpretable logical explanations with guarantees on correctness.
- •For hardware verification teams: Use interpretable ReLU-MLPs with certified Boolean circuits to verify logical behavior in hardware design workflows efficiently.
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.