Previous work has found a gap between the scale of neural networks that reliably learn Conway’s Game of Life, and minimal networks capable of representing the classic cellular automaton with hard-coded parameter values. Viewing neural network learning as a search process suggests a dependence on networks large enough to contain sub-networks with lucky initializations (sometimes known as ‘winning tickets’) that actually learn the task. In this work, we reorient our perspective from discovering Life rules as a search […]

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What does a world of total user-aligned AI actually look like?

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arXiv:2603.22294v1 Announce Type: new Abstract: Synthetic Data Generation (SDG), leveraging Large Language Models (LLMs), has recently been recognized and broadly adopted as an effective approach to improve the performance of smaller but more resource and compute efficient LLMs through fine-tuning. A key challenge in SDG is ensuring the quality and diversity of the generated data. In this paper, we analyze the diversity and distribution of generated data in the embedding space, and demonstrate a strong correlation between the […]

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arXiv:2603.17085v1 Announce Type: new Abstract: We present a simple greedy procedure to compute an $(alpha,beta)$-spanner for a graph $G$. We then show that this procedure is useful for building fault-tolerant spanners, as well as spanners for weighted graphs. Our first main result is an algorithm that, given a multigraph $G$, outputs an $f$ edge fault-tolerant $(k,k-1)$-spanner $H$ of size $O(fn^{1+frac1k})$ which is tight. To our knowledge, this is the first tight result concerning the price of fault tolerance […]

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Anomaly detection is often formulated under the assumption that abnormality is an intrinsic property of an observation, independent of context. This assumption breaks down in many real-world settings, where the same object or action may be normal or anomalous depending on latent contextual factors (e.g., running on a track versus on a highway). We revisit emph{contextual anomaly detection}, classically defined as context-dependent abnormality, and operationalize it in the visual domain, where anomaly labels depend on subject–context compatibility rather […]

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arXiv:2603.28971v1 Announce Type: new Abstract: Model-based reinforcement learning (MBRL) improves sample efficiency by leveraging learned dynamics models for policy optimization. However, the effectiveness of methods such as actor-critic is often limited by compounding model errors, which degrade long-horizon value estimation. Existing approaches, such as Model-Based Value Expansion (MVE), partially mitigate this issue through multi-step rollouts, but remain sensitive to rollout horizon selection and residual model bias. Motivated by the Pontryagin Maximum Principle (PMP), we propose Hamiltonian Actor-Critic (HAC), […]

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Reaction-diffusion (RD) equations underpin pattern formation across chemistry, biology, and physics, yet learning stable operators that forecast their long-term dynamics from data remains challenging. Neural-operator surrogates provide resolution-robust prediction, but autoregressive rollouts can drift due to the accumulation of error, and out-of-distribution (OOD) initial conditions often degrade accuracy. Physics-based numerical residual objectives can regularize operator learning, although they introduce additional assumptions, sensitivity to discretization and loss design, and higher training cost. Here we develop a purely data-driven operator […]

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arXiv:2601.09864v1 Announce Type: new Abstract: We study the input-entropy-constrained Gaussian channel capacity problem in the asymptotic high signal-to-noise ratio (SNR) regime. We show that the capacity-achieving distribution as SNR goes to infinity is given by a discrete Gaussian distribution supported on a scaled integer lattice. Further, we show that the gap between the input entropy and the capacity decreases to zero exponentially in SNR, and characterize this exponent.

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arXiv:2604.07406v1 Announce Type: new Abstract: The definition of NP requires, for each member language~$L$, a polynomial-time checking relation~$R$ and a constant~$k$ such that $w in L iff exists y,(|y| leq |w|^k wedge R(w,y))$. We show that this biconditional instantiates, for each member language, Hilbert’s triple: a sound, complete, decidable proof system in which truth-in-$L$ and bounded provability coincide by fiat. We show further that the polynomial-time restriction on~$R$ does not exclude G”odel’s proof-checking relation, which is itself polynomial-time […]

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