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Related Articles from SNS
A Goal-Set Characterization of Task Composition in the Boolean Task Algebra
arXiv:2606.04053v1 Announce Type: new Abstract: The Boolean Task Algebra (BTA) provides a principled framework for zero-shot task composition in reinforcement learning by equipping goal-reaching tasks with Boolean operations. We revisit its structural assumptions and formalize a collapse in the space of optimal extended Q-value functions: in deterministic MDPs, every such function is fully determined by the universal and empty tasks. This makes the logarithmic set of base tasks proposed in...
Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits
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. The underlying computation is given by a looped Boolean circuit whose graph is a perfect $\nu$-ary tree ($\nu\ge 2$), with outputs recursively fed back as inputs across computation rounds. A probe observes a sampled subset of internal nodes and seeks to infer the latent operation at each node,...
Layerwise Terminal Discrepancy in Chen's Reverse-Heat Coupling on the Boolean Cube
arXiv:2606.04573v1 Announce Type: cross Abstract: We isolate a layerwise refinement of the terminal testing-discrepancy step in Chen's perturbed reverse-heat approach~\cite{Chen2026} to Talagrand's convolution conjecture on the Boolean cube. Built on the joint-filtration martingale formulation of Chen's coupling, and on Chen's approximate monotonicity and conditional squared-score estimates being available in the joint-filtration form stated below, we prove the localized testing estimate \[...
Graphical and algebraic methods for Boolean factoring
arXiv:2606.04038v1 Announce Type: cross Abstract: The problem of factoring Boolean polynomials has significant applications in both classical and quantum computing technology. In this paper we have developed novel algorithms for factoring both ESOP and SOP expressions. Our aim is to optimize the AND-count.
Accelerated Fourier SAT (AFSAT): Fully Realising a GPU-based Symmetric Pseudo-Boolean SAT Solver
Announce Type: new Abstract: We present Accelerated Fourier SAT (AFSAT), a GPU-accelerated solver for pseudo-Boolean satisfiability based on continuous local search (CLS). AFSAT realises the proof-of-concept approach, FastFourierSAT, into a fully-engineered solver supporting any heterogeneous mixture of symmetric constraint types and lengths within a single problem instance. Using the JAX compiler, AFSAT leverages pure function composition, automatic vectorisation, automatic differentiation,...
Understanding the Parameter Space Geometry of Transformers Encoding Boolean Functions
arXiv:2606.08768v1 Announce Type: new Abstract: Transformers consistently fail to learn certain simple functions that are provably expressible with specific parameter settings. This gap between learnability and expressivity is particularly prominent for sensitive functions -- functions whose output is likely to change if a single bit of the input is flipped -- for example, PARITY. While prior work has established that transformers exhibit a bias toward functions with low average sensitivity,...
Further evidence towards the Fourier Entropy-Influence conjecture
arXiv:2606.00246v1 Announce Type: cross Abstract: The Fourier Entropy-Influence (FEI) conjecture states that the Fourier entropy of Boolean functions is uniformly bounded by their total influence. It has been verified for canonical examples such as disjoint tribes and for some classes of Boolean functions such as symmetric functions and read-$k$ decision trees (with a constant that depends linearly on $k$). In this note we present new classes of Boolean functions that verify the FEI conjecture.
A Study of Parallel Continuous Local Search
arXiv:2606.06656v2 Announce Type: replace Abstract: We study parallel Continuous Local Search (CLS) as a solution approach for Boolean satisfiability problems with symmetric pseudo-Boolean (PB) constraints. Here, the $n$-variable PB-satisfiability problem is relaxed to a continuous optimisation problem with a differentiable objective function on an $n$-dimensional hypercube. For satisfiable instances, the global minimisers of this optimisation problem correspond to satisfying assignments of...
Finite-n Estimate of Dedekind Numbers by Layer-Ratio Monte Carlo
Announce Type: cross Abstract: Dedekind's problem counts monotone Boolean functions, equivalently downsets of a Boolean lattice. We recast this enumeration as a finite layer-ratio reconstruction problem for the Whitney numbers of the ranked ideal lattice. An exact adjacent-layer double count expresses each layer ratio through local averages of the number of addable elements and the number of removable elements.
A Study of Parallel Continuous Local Search
Announce Type: new Abstract: We study parallel Continuous Local Search (CLS) as a solution approach for Boolean satisfiability problems with symmetric pseudo-Boolean (PB) constraints. Here, the $n$-variable PB-satisfiability problem is relaxed to a continuous optimisation problem with a differentiable objective function on an $n$-dimensional hypercube. For satisfiable instances, the global minimisers of this optimisation problem correspond to satisfying assignments of the SAT problem at hand.