arXiv subjects

Rachel Lawrence

Publications and source records attributed to Rachel Lawrence.

9 recordsLinked to original sources

arXiv2026

Subagents vs Agent Skills: Executing Reusable Knowledge for Long-Horizon Agentic Tasks

How can language model agents effectively leverage libraries of reusable knowledge to solve long-horizon tasks? Recent work has increasingly focused on agent skills: reusable capabilities represented as skill packages, i.e., multi-file bundles containing instructions, scripts, and other resources that help agents perform specific tasks. Agent skills are typically executed by loading their skill instructions into an agent's context and relying on the agent to follow them. As task horizons grow, however, this approach becomes increasingly brittle, because reasoning quality degrades as more information accumulates in the context window. We investigate an alternative approach in which skill packages are instead invoked as subagents. Rather than loading skill instructions into the main context, subagent execution spawns fresh context windows dedicated to solving individual subtasks. We show that subagent execution outperforms agent-skill execution when skill packages expose clear input-output contracts and their instructions encode the procedural knowledge needed to fulfill those contracts. The tradeoff is additional communication overhead, as extra tokens are required to coordinate between the main agent and its subagents. Our results show that the benefit of reusable knowledge depends not only on its content, but also on how it is organized and invoked.

cs.AI↗

arXiv2026

Position: Reasoning is a Learnable Rule-Based Process

Autonomous reasoning is among the most scientifically and economically motivating topics in AI today. Historically the purview of symbolic AI, recent advances have mainly emerged from deep probabilistic generative models. Despite immense interest and rapid progress, the generative AI community has not clearly converged on operational definitions for reasoning and often implicitly rejects the historical treatment of this topic in logic and verifiable automated reasoning. This position contends that definitional ambiguity leaves the construct validity of reasoning evaluation unverifiable, undermining quantifiable progress toward trustworthy autonomous reasoning. We also contend that this ambiguity is addressable. To that end, we provide (1) operational definitions based on a synthesis of the literature, positioning valid and sound reasoning as a learnable rule-based process; and (2) a checklist for best practices in the communication of AI reasoning research.

cs.AI↗

arXiv2026

Do Transformers Use their Depth Adaptively? Evidence from a Relational Reasoning Task

We investigate whether transformers use their depth adaptively across tasks of increasing difficulty. Using a controlled multi-hop relational reasoning task based on family stories, where difficulty is determined by the number of relationship hops that must be composed, we monitor (i) how predictions evolve across layers via early readouts (the logit lens) and (ii) how task-relevant information is integrated across tokens via causal patching. For pretrained models, we find some limited evidence for adaptive depth use: some larger models need fewer layers to arrive at plausible answers for easier tasks, and models generally use more layers to integrate information across tokens as chain length increases. For models finetuned on the task, we find clearer and more consistent evidence of adaptive depth use, with the effect being stronger for less constrained finetuning regimes that do not preserve general language modeling abilities.

cs.LG↗

arXiv2026

Better Think Thrice: Learning to Reason Causally with Double Counterfactual Consistency

Despite their strong performance on reasoning benchmarks, large language models (LLMs) have proven brittle when presented with counterfactual questions, suggesting weaknesses in their causal reasoning ability. While recent work has demonstrated that labeled counterfactual tasks can be useful benchmarks of LLMs' causal reasoning, producing such data at the scale required to cover the vast potential space of counterfactuals is limited. In this work, we introduce double counterfactual consistency (DCC), a lightweight inference-time method for measuring and guiding the ability of LLMs to reason causally. Without requiring labeled counterfactual data, DCC verifies a model's ability to execute two important elements of causal reasoning: causal intervention and counterfactual prediction. Using DCC, we evaluate the causal reasoning abilities of various leading LLMs across a range of reasoning tasks and interventions. Moreover, we demonstrate the effectiveness of DCC as a training-free test-time rejection sampling criterion and show that it can directly improve performance on reasoning tasks across multiple model families.

cs.LG↗

arXiv2025

Configurations of 10 points and their incidence varieties

Incidence varieties are spaces of $n$-tuples of points in the projective plane that satisfy a given set of collinearity conditions. We classify the components of incidence varieties and realization moduli spaces associated to configurations of up to 10 points, up to birational equivalence. We show that each realization space component is birational to a projective space, a genus 1 curve, or a K3 surface. To do this, we reduce the problem to a study of 163 special arrangements called superfigurations. Then we use computer algebra to describe the realization space of each superfiguration.

math.AG↗

arXiv2025

RE-IMAGINE: Symbolic Benchmark Synthesis for Reasoning Evaluation

Recent Large Language Models (LLMs) have reported high accuracy on reasoning benchmarks. However, it is still unclear whether the observed results arise from true reasoning or from statistical recall of the training set. Inspired by the ladder of causation (Pearl, 2009) and its three levels (associations, interventions and counterfactuals), this paper introduces RE-IMAGINE, a framework to characterize a hierarchy of reasoning ability in LLMs, alongside an automated pipeline to generate problem variations at different levels of the hierarchy. By altering problems in an intermediate symbolic representation, RE-IMAGINE generates arbitrarily many problems that are not solvable using memorization alone. Moreover, the framework is general and can work across reasoning domains, including math, code, and logic. We demonstrate our framework on four widely-used benchmarks to evaluate several families of LLMs, and observe reductions in performance when the models are queried with problem variations. These assessments indicate a degree of reliance on statistical recall for past performance, and open the door to further research targeting skills across the reasoning hierarchy.

cs.CL↗

arXiv2025

A Fourier Space Perspective on Diffusion Models

Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the standard Denoising Diffusion Probabilistic Models (DDPM) forward process of additive white noise, this property results in high-frequency components being corrupted faster and earlier in terms of their Signal-to-Noise Ratio (SNR) than low-frequency ones. The reverse process then generates low-frequency information before high-frequency details. In this work, we study the inductive bias of the forward process of diffusion models in Fourier space. We theoretically analyse and empirically demonstrate that the faster noising of high-frequency components in DDPM results in violations of the normality assumption in the reverse process. Our experiments show that this leads to degraded generation quality of high-frequency components. We then study an alternate forward process in Fourier space which corrupts all frequencies at the same rate, removing the typical frequency hierarchy during generation, and demonstrate marked performance improvements on datasets where high frequencies are primary, while performing on par with DDPM on standard imaging benchmarks.

stat.ML↗

arXiv2022

Zero Forcing with Random Sets

Given a graph $G$ and a real number $0\le p\le 1$, we define the random set $B_p(G)\subset V(G)$ by including each vertex independently and with probability $p$. We investigate the probability that the random set $B_p(G)$ is a zero forcing set of $G$. In particular, we prove that for large $n$, this probability for trees is upper bounded by the corresponding probability for a path graph. Given a minimum degree condition, we also prove a conjecture of Boyer et.\ al.\ regarding the number of zero forcing sets of a given size that a graph can have.

math.CO↗

arXiv2016

Counting Arcs in Projective Planes via Glynn's Algorithm

An $n$-arc in a projective plane is a collection of $n$ distinct points in the plane, no three of which lie on a line. Formulas counting the number of $n$-arcs in any finite projective plane of order $q$ are known for $n \le 8$. In 1995, Iampolskaia, Skorobogatov, and Sorokin counted $9$-arcs in the projective plane over a finite field of order $q$ and showed that this count is a quasipolynomial function of $q$. We present a formula for the number of $9$-arcs in any projective plane of order $q$, even those that are non-Desarguesian, deriving Iampolskaia, Skorobogatov, and Sorokin's formula as a special case. We obtain our formula from a new implementation of an algorithm due to Glynn; we give details of our implementation and discuss its consequences for larger arcs.

math.CO↗