arXiv subjects

C. Evans Hedges

Publications and source records attributed to C. Evans Hedges.

10 recordsLinked to original sources

arXiv2026

Finite Cores Exhaustion and the Failure of Strict Sequential-Pressure Approximation in Coded Shifts

Let $X=X(\mathcal{G})$ be a coded shift whose generating set uniquely represents its concatenation set. We prove that, for every continuous potential $φ$, the pressures of the finite-generator subshifts (the finite cores) converge to the sequential pressure $P_{\mathrm{seq}}(φ,\mathcal{G})$, the supremum of free energy over invariant measures giving full mass to the concatenation set. Thus full sequential pressure is the exact condition for the finite cores to recover global pressure. The proof is a refinement of the inducing argument of Burr, Das, Wolf, and Yang. Given an arbitrary enumeration of the generators and a length-ordered enumeration of the language, we obtain an algorithm which computes the global pressure of every computable potential with full sequential pressure. The set of equilibrium states is recursively compact, and a unique equilibrium state is computable from the same data. For the zero potential, $h_{\mathrm{con}}\geq h_{\mathrm{res}}$ therefore implies computability of topological entropy and of any unique measure of maximal entropy. We also construct a uniquely represented presentation of the full binary shift for which the zero potential has full sequential pressure but is not a uniform limit of potentials satisfying $P_{\mathrm{seq}}>P_{\mathrm{res}}$, disproving a conjecture of Burr, Das, Wolf, and Yang.

math.DS↗

arXiv2026

The Inference-Compute Frontier and a Latency-Efficient Architecture for Limit Order Book Prediction

We study whether a scaling-law-style inference-compute frontier appears in limit order book prediction. Using FI-2010 and a suite of models ranging from small decision trees to neural LOB architectures, we find that the realized empirical frontier of predictive loss versus structural forward work is well summarized by a power law. In particular, with MLPLOB held out as an architecture family, a power-law fit to the low- and mid-compute non-MLPLOB frontier extrapolates across multiple orders of magnitude and attains $R^2=0.941$ on the excluded high-compute MLPLOB target frontier. A similar exercise in latency space gives substantially weaker results, showing that latency is not merely noisy compute. We use this gap to motivate FastBiNLOB, a dense axis-separable LOB mixer built from hardware-friendly temporal and feature mixing operations. In a five-seed experiment, FastBiNLOB exceeds the published $y_{10}$ and $y_{100}$ macro-F1 targets at notably lower latency than existing published SOTA architectures.

cs.LG↗

arXiv2026

Which Phases Are Thermodynamically Realizable? A Local Entropy Criterion

In the variational approach to statistical mechanics, equilibrium states are the rigorous analogues of thermodynamic phases; the question of which invariant measures can arise as equilibrium states is therefore the question of which phases are thermodynamically realizable. We prove that for continuous actions of locally compact amenable groups on compact metrizable spaces with finite topological entropy, an ergodic measure $μ$ is an equilibrium state for some continuous potential if and only if the entropy map $h$ is upper semicontinuous at $μ$; equivalently, the unrealizable phases are exactly those hidden behind the convex envelope of the free energy. More generally, the same criterion applies whenever $(X, T)$ has bounded entropy and embeds as an invariant subsystem of a compact metrizable system. As a canonical case, one-point compactification yields a $C_0$-potential realization theorem for locally compact $σ$-compact systems, with applications to countable-state Markov shifts. We also show that the equilibrium-face realization stated by Jenkinson (2006) omits a necessary continuity hypothesis, exhibiting a counterexample on the full shift, and give the sharp corrected statement: a weak-$*$ closed set $\mathcal{E}$ of ergodic measures determines an equilibrium face if and only if $h|_{\mathcal{E}}$ is continuous and $h$ is upper semicontinuous at each point of $\mathcal{E}$.

math.DS↗

arXiv2026

Source-Optimal Training is Transfer-Suboptimal

We prove that training a source model optimally for its own task is generically suboptimal when the objective is downstream transfer. We study the source-side optimization problem in L2-SP ridge regression and show a fundamental mismatch between the source-optimal and transfer-optimal source regularization: outside of a measure-zero set, $τ_0^* \neq τ_S^*$. We characterize the transfer-optimal source penalty $τ_0^*$ as a function of task alignment and identify an alignment-dependent reversal: with imperfect alignment ($0<ρ<1$), transfer benefits from stronger source regularization, while in super-aligned regimes ($ρ>1$), transfer benefits from weaker regularization. Additionally, in isotropic settings, the decision of whether transfer helps is independent of the target sample size and noise, depending only on task alignment and source characteristics. We verify the linear predictions in a synthetic ridge regression experiment, and we present experiments on MNIST, CIFAR-10, and 20 Newsgroups as evidence that the source-optimal versus transfer-optimal mismatch persists in standard nonlinear transfer learning pipelines.

stat.ML↗

arXiv2025

$x$ Plays Pokemon, for Almost-Every $x$

This paper provides a brief write-up showing that for any finite state game, a disjunctive number $x$ will eventually win that game. The proof techniques here are well known and this result follows immediately from folklore results in graph theory and cellular automata. This short paper primarily serves as an expositional piece to collect this proof with the fun context of $π$ Plays Pokémon serving as motivation.

math.HO↗

arXiv2025

A Theoretical Framework Bridging Model Validation and Loss Ratio in Insurance

This paper establishes the first analytical relationship between predictive model performance and loss ratio in insurance pricing. We derive a closed-form formula connecting the Pearson correlation between predicted and actual losses to expected loss ratio. The framework proves that model improvements exhibit diminishing marginal returns, analytically confirming the actuarial intuition to prioritize poorly performing models. We introduce the Loss Ratio Error metric for quantifying business impact across frequency, severity, and pure premium models. Simulations show reliable predictions under stated assumptions, with graceful degradation under assumption violations. This framework transforms model investment decisions from qualitative intuition to quantitative cost-benefit analysis.

q-fin.RM↗

arXiv2025

OrthoGrad Improves Neural Calibration

We study $\perp$Grad, a geometry-aware modification to gradient-based optimization that constrains descent directions to address overconfidence, a key limitation of standard optimizers in uncertainty-critical applications. By enforcing orthogonality between gradient updates and weight vectors, $\perp$Grad alters optimization trajectories without architectural changes. On CIFAR-10 with 10% labeled data, $\perp$Grad matches SGD in accuracy while achieving statistically significant improvements in test loss ($p=0.05$), predictive entropy ($p=0.001$), and confidence measures. These effects show consistent trends across corruption levels and architectures. $\perp$Grad is optimizer-agnostic, incurs minimal overhead, and remains compatible with post-hoc calibration techniques. Theoretically, we characterize convergence and stationary points for a simplified $\perp$Grad variant, revealing that orthogonalization constrains loss reduction pathways to avoid confidence inflation and encourage decision-boundary improvements. Our findings suggest that geometric interventions in optimization can improve predictive uncertainty estimates at low computational cost.

cs.LG↗

arXiv2025

On the Equivalence of Equilibrium and Freezing States in Dynamical Systems

This paper is concerned with freezing phase transitions in general dynamical systems. A freezing phase transition is one in which, for a given potential $ϕ$, there exists some inverse temperature $β_0 > 0$ such that for all $α, β> β_0$, the collection of equilibrium states for $αϕ$ and $βϕ$ coincide. In this sense, below the temperature $1 / β_0$, the system "freezes" on a fixed collection of equilibrium states. We show that for a given invariant measure $μ$, it is no more restrictive that $μ$ is the freezing state for some potential than it is for $μ$ to be the equilibrium state for some potential. In fact, our main result applies to any collection of equilibrium states with the same entropy. In the case where the entropy map $h$ is upper semi-continuous, we show any ergodic measure $μ$ can be obtained as a freezing state for some potential. In this upper semi-continuous setting, we additionally show that the collection of potentials that freeze at a single state is dense in the space of all potentials. However, in the $\Z$ action setting where the dynamical system satisfies specification, the collection of potentials that do not freeze contains a dense $G_δ$.

math.DS↗

arXiv2024

Bounds for Equilibrium States on Amenable Group Subshifts

We prove a result on equilibrium measures for potentials with summable variation on arbitrary subshifts over a countable amenable group. For finite configurations $v$ and $w$, if $v$ is always replaceable by $w$, we obtain a bound on the measure of $v$ depending on the measure of $w$ and a cocycle induced by the potential. We then use this result to show that under this replaceability condition, we can obtain bounds on the Lebesgue-Radon-Nikodym derivative $d (μ_ϕ\circ ξ) / dμ_ϕ$ for certain holonomies $ξ$ that generate the homoclinic (Gibbs) relation. As corollaries, we obtain extensions of results by Meyerovitch and Garcia-Ramos and Pavlov to the countable amenable group subshift setting. Our methods rely on the exact tiling result for countable amenable groups by Downarowicz, Huczek, and Zhang and an adapted proof technique from Garcia-Ramos and Pavlov.

math.DS↗

arXiv2024

Computability of Pressure for Subshifts on Countable Amenable Groups

There are a variety of results in the literature proving forms of computability for topological entropy and pressure on subshifts. In this work, we prove two quite general results, showing that topological pressure is always computable from above given an enumeration for a forbidden list inducing the subshift, and that for strongly irreducible shifts of finite type, topological pressure is computable. Our results apply to subshifts on all finitely generated amenable groups with decidable word problem and generalize several previous results which applied only to $\mathbb{Z}^d$-subshifts. As corollaries, we obtain some results related to ground state energy and entropy, proving that the map sending $ϕ$ to $\sup_{μ\in M_σ(X)} \int ϕdμ$ is computable/computable from above when $P_X(ϕ)$ is, and that the map sending $ϕ$ to its ground state/residual entropy is computable from above when $P_X(ϕ)$ is computable. We conclude by giving explicit bounds on computation time of $P_X(ϕ)$ in the $\mathbb{Z}^d$ setting for SI SFTs and locally constant and rational valued $ϕ$, and show that in the special case $X = A^{\mathbb{Z}^2}$, this algorithm runs in singly exponential time.

math.DS↗