arXiv:2602.02530v1 Announce Type: new Abstract: Reinforcement learning (RL) has the potential to transform real-world decision-making systems by enabling autonomous agents to learn from experience. Deploying RL in real-world settings, especially in the context of human-robot interaction, requires defining state representations and reward functions, which are critical for learning efficiency and policy performance. Traditional RL approaches often rely on domain expertise and trial-and-error, necessitating extensive human involvement as well as direct interaction with the environment, which can be costly […]

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I’ve written a couple times about Fibonacci numbers and certificates. Here the certificate is auxiliary data that makes it faster to confirm that the original calculation was correct. This post puts some timing numbers to this. I calculated the 10 millionth Fibonacci number using code from this post. n = 10_000_000 F = fib_mpmath(n) This took 150.3 seconds. As I’ve discussed before, a number f is a Fibonacci number if and only if 5f² ± 4 is a […]

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arXiv:2602.23573v1 Announce Type: new Abstract: For every real number $c geq 1$ and for all $varepsilon > 0$, there is a fitness function $f : {0,1}^n to mathbb{R}$ for which the optimal mutation rate for the $(1+1)$ evolutionary algorithm on $f$, denoted $p_n$, satisfies $p_n approx c/n$ in that $|np_n – c| < varepsilon$. In other words, the set of all $c geq 1$ for which the mutation rate $c/n$ is optimal for the $(1+1)$ EA is dense […]

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arXiv:2602.03863v1 Announce Type: new Abstract: Computational reproducibility, the possibility for independent researchers to exactly reproduce published empirical results, is fundamental to science. Despite its importance, the proportion of research articles aiming for reproducibility remains low and uneven across disciplines. Barriers include a perceived lack of incentives for researchers and journals, practical challenges in preparing reproducible materials, and the absence of harmonised standards of reproducibility processes and requirements by journals. Existing guidance is often highly technical, reaching mainly those […]

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arXiv:2601.18909v1 Announce Type: new Abstract: Knowledge distillation transfers behavior from a teacher to a student model, but the process is inherently stochastic: teacher outputs, student training, and student inference can all be random. Collapsing these uncertainties to a single point estimate can distort what is learned. We systematically study how uncertainty propagates through knowledge distillation across three representative model classes–linear regression, feed-forward neural networks, and large language models (LLMs)–and propose simple corrections. We distinguish inter-student uncertainty (variance across […]

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arXiv:2511.11666v3 Announce Type: replace-cross Abstract: Bayesian neural networks (BNNs) require scalable sampling algorithms to approximate posterior distributions over parameters. Existing stochastic gradient Markov Chain Monte Carlo (SGMCMC) methods are highly sensitive to the choice of stepsize and adaptive variants such as pSGLD typically fail to sample the correct invariant measure without addition of a costly divergence correction term. In this work, we build on the recently proposed `SamAdams’ framework for timestep adaptation (Leimkuhler, Lohmann, and Whalley 2025), introducing […]

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arXiv:2603.20284v1 Announce Type: new Abstract: Online 3D reconstruction from streaming inputs requires both long-term temporal consistency and efficient memory usage. Although causal VGGT transformers address this challenge through a key-value (KV) cache mechanism, the cache grows linearly with the stream length, creating a major memory bottleneck. Under limited memory budgets, early cache eviction significantly degrades reconstruction quality and temporal consistency. In this work, we observe that attention in causal transformers for 3D reconstruction exhibits intrinsic spatio-temporal sparsity. Based […]

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arXiv:2601.23236v2 Announce Type: replace-cross Abstract: We propose a variational framework that interprets transformer layers as iterations of an optimization algorithm acting on token embeddings. In this view, self-attention implements a gradient step of an interaction energy, while MLP layers correspond to gradient updates of a potential energy. Standard GPT-style transformers emerge as vanilla gradient descent on the resulting composite objective, implemented via Lie–Trotter splitting between these two energy functionals. This perspective enables principled architectural design using classical optimization […]

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