{"slug": "certifiably-interpretable-training-of-relu-mlps-for-boolean-tasks-with-truth", "title": "Certifiably Interpretable Training of ReLU-MLPs for Boolean Tasks with Guaranteed Truth-Table Generalization", "summary": "Researchers introduced MACCHIATO, a specialized training algorithm that jointly constructs an explicitly structured ReLU-MLP from partial truth-table observations and an explicit Boolean circuit over signed literals with AND, OR, and XOR gates certifying what its subnetworks compute. Under the theorem's influence-recovery conditions, if each of the m stage-wise residuals depends on at most log2(B) bits, a sample-splitting variant trained on T observations returns a six-layer ReLU-MLP of width O(mB) with truth-table error O(sqrt(m(B+log(m/delta))/T)). On synthetic random-junta tasks, the networks outperform depth- and hidden-width-matched Adam-trained MLPs in several data-sparse or projection-aligned regimes, and the iterative procedure completes in regimes where flat ambient-dimensional ESPRESSO exceeds a three-hour computational budget.", "body_md": "arXiv:2609.13439v1 Announce Type: new \nAbstract: 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.\n  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 $\\mathcal{O}\\bigl(\\sqrt{m(B+\\log(m/\\delta))/T}\\bigr)$.\n  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.", "url": "https://wpnews.pro/news/certifiably-interpretable-training-of-relu-mlps-for-boolean-tasks-with-truth", "canonical_source": "https://arxiv.org/abs/2609.13439", "published_at": "2026-09-15 04:00:00+00:00", "updated_at": "2026-09-15 04:30:32.360010+00:00", "lang": "en", "topics": ["machine-learning", "neural-networks", "ai-research", "ai-safety"], "entities": ["MACCHIATO", "ReLU-MLP", "ESPRESSO", "PyEDA"], "alternates": {"html": "https://wpnews.pro/news/certifiably-interpretable-training-of-relu-mlps-for-boolean-tasks-with-truth", "markdown": "https://wpnews.pro/news/certifiably-interpretable-training-of-relu-mlps-for-boolean-tasks-with-truth.md", "text": "https://wpnews.pro/news/certifiably-interpretable-training-of-relu-mlps-for-boolean-tasks-with-truth.txt", "jsonld": "https://wpnews.pro/news/certifiably-interpretable-training-of-relu-mlps-for-boolean-tasks-with-truth.jsonld"}}