arXiv subjects

Allen G Hart

Publications and source records attributed to Allen G Hart.

8 recordsLinked to original sources

arXiv2026

Harbor Adapters and Harbor-Index: Infrastructure and a Curated Meta-Dataset for Large-Scale Agentic Evaluation

Evaluating agents on the growing number of agentic benchmarks is challenging because they often require complex environments and agent integrations. We introduce Harbor Adapters, a unified evaluation infrastructure for agentic benchmarks. Our work makes three contributions. First, we develop benchmark adapters that port more than 80 benchmarks to evaluate arbitrary agents, and validate them through rigorous code review and parity experiments. Second, we conduct a large-scale evaluation of 8 models spanning capability tiers across 54 benchmarks; every model is run with Terminus-2 and with one of 3 native harnesses. This enables a broader analysis of agent capabilities and failure modes than was previously possible. Third, we introduce Harbor-Index, a curated set of 82 difficult, diverse, and high-quality tasks spanning 29 benchmarks, refined from the adapted suite through difficulty filtering, AI and human audit, and an audit-and-fix loop. Harbor-Index preserves the challenge and breadth of large-scale agentic evaluations while being affordable to run; no evaluated model-harness configuration exceeds 30% pass rate, and the strongest (GPT-5.5 with Codex) reaches 28.0%. We release the adapters, evaluation results, in-depth analysis, and Harbor-Index as open-source artifacts to support more reliable and comprehensive evaluation of language-model agents.

cs.AI↗

arXiv2025

Can LLMs Write Mathematics Papers? A Case Study in Reservoir Computing

As AI capabilities continue to grow exponentially on economically relevant human expert tasks, with task completion horizons doubling every 7 months according to the Model Evaluation and Threat Research (METR), we are interested in how this applies to the task of mathematics research. To explore this, we evaluated the capability of four frontier large language models (LLMs), ChatGPT 5, Claude 4.1 Opus, Gemini 2.5 Pro, and Grok 4, at the task of creating a mini-paper on reservoir computing. All models produced engaging papers with some apparent understanding of various techniques, but were sometimes lead to mistakes by surface level understanding of key ideas. That said, the capabilities on LLMs on this task was likely as good or greater than that predicted by METR.

math.DS↗

arXiv2025

Generic and Isometric Embeddings in Reservoir Computers

We prove that a generic reservoir system admits a generalized synchronization that is a topological embedding of the input system's attractor. We also prove that for sufficiently high reservoir dimension (given by Nash's embedding theorem) there exists an isometric embedding generalized synchronization. The isometric embedding can be constructed explicitly when the reservoir system and source dynamics are linear.

math.DS↗

arXiv2023

Generalised Synchronisations, Embeddings, and Approximations for Continuous Time Reservoir Computers

We establish conditions under which a continuous time reservoir computer, such as a leaky integrator echo state network, admits a generalised synchronisation $f$ between between the source dynamics and reservoir dynamics. We show that multiple generalised synchronisations can exist simultaneously, and connect this to the multi-Echo-State-Property (multi-ESP). In the special case of a linear reservoir computer, we derive a closed form expression for the generalised synchronisation $f$. Furthermore, we establish conditions under which $f$ is of class $C^1$, and conditions under which $f$ is a topological embedding on the fixed points of the source system. This embedding result is closely related to Takens' embedding Theorem. We also prove that the embedding of fixed points occurs almost surely for randomly generated linear reservoir systems. With an embedding achieved, we discuss how the universal approximation theorem makes it possible to forecast the future dynamics of the source system and replicate its topological properties. We illustrate the theory by embedding a fixed point of the Lorenz-63 system into the reservoir space using numerical methods. Finally, we show that if the observations are perturbed by white noise, the GS is preserved up to a perturbation by an Ornstein-Uhlenbeck process.

math.DS↗

arXiv2021

(Thesis) Reservoir Computing With Dynamical Systems

A reservoir computer is a special type of neural network, where most of the weights are randomly fixed and only a subset are trained. In this thesis we prove results about reservoir computers trained on deterministic dynamical systems, and stochastic processes. We focus mostly on a special type of reservoir computer called an Echo State Network (ESN). In the deterministic case, we prove (under some assumptions) that if a reservoir computer has the Echo State Property (ESP), then there is a C1 generalised synchronisation between the input dynamical system and the dynamics in the reservoir space. Furthermore, we prove that a reservoir computer with the local ESP in several disjoint subsets of the reservoir space will admit several distinct generalised synchronisations. In the special case that the reservoir map is linear, and has the ESP, we prove that the generalised synchronisation is generically an embedding. This result admits Takens' embedding Theorem as a special case. We go to show that ESNs trained on scalar observations of an ergodic dynamical system can approximate an arbitrary target function, including the next step map used in time series forecasting. This universal approximation property holds despite the training process being entirely linear. We prove analogous results for ESNs trained on observations of a stochastic process, which are not be Markovian in general. We use these results to develop supervised learning, and reinforcement learning algorithms supported by an ESN. In the penultimate chapter of this thesis, we use a reservoir computer to numerically solve linear PDEs. In the final chapter, we conclude and discuss directions for future work.

math.DS↗

arXiv2021

Echo State Networks trained by Tikhonov least squares are L2(μ) approximators of ergodic dynamical systems

Echo State Networks (ESNs) are a class of single-layer recurrent neural networks with randomly generated internal weights, and a single layer of tuneable outer weights, which are usually trained by regularised linear least squares regression. Remarkably, ESNs still enjoy the universal approximation property despite the training procedure being entirely linear. In this paper, we prove that an ESN trained on a sequence of observations from an ergodic dynamical system (with invariant measure $μ$) using Tikhonov least squares regression against a set of targets, will approximate the target function in the $L^2(μ)$ norm. In the special case that the targets are future observations, the ESN is learning the next step map, which allows time series forecasting. We demonstrate the theory numerically by training an ESN using Tikhonov least squares on a sequence of scalar observations of the Lorenz system.

cs.LG↗

arXiv2021

A Markov theoretic description of stacking disordered aperiodic crystals including ice and opaline silica

We review the Markov theoretic description of 1D aperiodic crystals, describing the stacking-faulted crystal polytype as a special case of an aperiodic crystal. Under this description we generalise the centrosymmetric unit cell underlying a topologically centrosymmetric crystal to a reversible Markov chain underlying a reversible aperiodic crystal. We show that for the close-packed structure, almost all stackings are irreversible when the interaction reichweite is greater than 4. Moreover, we present an analytic expression of the scattering cross section of a large class of stacking disordered aperiodic crystals, lacking translational symmetry of their layers, including ice and opaline silica (opal CT). We then relate the observed stackings and their underlying reichweite to the physics of various nucleation and growth processes of disordered ice.

physics.chem-ph↗

arXiv2020

Embedding and Approximation Theorems for Echo State Networks

Echo State Networks (ESNs) are a class of single layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces a C1 map from the dynamical system's phase space to the ESN's reservoir space. We call this the Echo State Map. We then prove that the Echo State Map is generically an embedding with positive probability. Under additional mild assumptions, we further conjecture that the Echo State Map is almost surely an embedding. For sufficiently large, and specially structured, but still randomly generated ESNs, we prove that there exists a linear readout layer that allows the ESN to predict the next observation of a dynamical system arbitrarily well. Consequently, if the dynamical system under observation is structurally stable then the trained ESN will exhibit dynamics that are topologically conjugate to the future behaviour of the observed dynamical system. Our theoretical results connect the theory of ESNs to the delay-embedding literature for dynamical systems, and are supported by numerical evidence from simulations of the traditional Lorenz equations. The simulations confirm that, from a one dimensional observation function, an ESN can accurately infer a range of geometric and topological features of the dynamics such as the eigenvalues of equilibrium points, Lyapunov exponents and homology groups.

nlin.CD↗