The paper introduces MACCHIATO, a training algorithm that builds a ReLU‑MLP from partial truth‑table data while simultaneously constructing an explicit Boolean circuit over AND, OR, and XOR gates that certifies the network’s computation. The method iteratively projects residuals onto low‑dimensional Boolean classes, compiles the resulting circuit into a ReLU‑MLP, and uses logic minimization and influence‑based variable selection to achieve a six‑layer network with provable truth‑table error bounds. Experiments on synthetic random‑junta tasks show that these certified networks outperform Adam‑trained MLPs in data‑sparse or projection‑aligned regimes and complete faster than flat ESPRESSO in certain settings.
arXiv:2602.17493v2 Announce Type: replace-cross Abstract: We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly $\pm 1$, and the resulting mod...
arXiv:2605. 24033v2 Announce Type: replace Abstract: Mechanistic interpretability typically discovers circuits and then argues what they do from examples and ablations.
The paper presents a complete characterization of when two deep ReLU networks realize the same function, showing that this occurs iff one can be transformed into the other using a set of axioms from many‑valued logic. It introduces a symbolic calculus that maps networks to substitution graphs, proves a completeness theorem linking equivalent formulas, and provides an algorithm to reconstruct networks from these graphs. The framework yields a new compositional normal form for MV logic that preserves the algebraic structure of deep ReLU networks.
arXiv:2605.06240v2 Announce Type: replace-cross Abstract: Forward-Forward (FF) training lets each layer learn from a local goodness criterion. In cumulative-goodness variants, later layers can inheri...
arXiv:2602. 07400v2 Announce Type: replace Abstract: Gradient-based LUT- and logic-gate-based neural networks (LUTNet, LogicNets, DiffLogic, PolyLUT, NeuraLUT, WARP-LUT, DWN, LILogicNet, LightLUT) replace multiply-accumulate arithmetic with Boolean lookups.
arXiv:2608. 12655v1 Announce Type: new Abstract: A flat training curve does not reveal whether a neural network has reached a global optimum, is locally trapped, is representation-limited, or is mismatched to its trainer.
The paper introduces Kernelized Parameter Sensitivity Atlases (KPSA), a method that uses a block decomposition of the empirical neural tangent kernel to estimate input‑specific parameter sensitivities efficiently. KPSA embeds parameter groups in a query space and applies a lightweight kernel to predict sensitivities for unseen inputs, achieving a high fraction of the perturbation susceptibility of full back‑propagation while dramatically reducing computation and memory usage. Experiments across vision, forecasting, and protein‑modeling tasks show that KPSA identifies sparse, depth‑spanning sensitivity circuits and improves throughput and memory efficiency in activation‑attribution problems.
arXiv:2602. 03970v3 Announce Type: replace-cross Abstract: We study the statistical behavior of reasoning probes in a stylized model of iterative computation inspired by neural algorithmic reasoning.
arXiv:2607. 12266v1 Announce Type: new Abstract: Mixed-precision quantization must decide which parts of a model to keep at higher precision.
arXiv:2609.39768v1 Announce Type: cross Abstract: Certifying a deployed neural network raises decision problems that the verification literature has not classified: whether the model carries a backdo...
arXiv:2609.24942v1 Announce Type: new Abstract: A model generalizes outside its training distribution only when it computes a representation structurally equivalent to the generating mechanism, not a...
arXiv:2604. 11284v5 Announce Type: replace-cross Abstract: We present THEIA, a 2.