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Scott Taylor

Publications and source records attributed to Scott Taylor.

8 recordsLinked to original sources
arXiv2026

Learning on the Job: Continual Learning from Deployment Feedback for Frozen-Weights Agents

AI agents encounter learning opportunities in every episode they run, and discard nearly all of them: the underlying models are frozen at deployment, so an agent that resolves a difficult request today starts from zero when it recurs tomorrow. Yet ordinary operation already produces feedback, in the form of outcome verdicts and after-the-fact corrections. We show that this feedback is a sufficient signal for continual learning when the frozen model is paired with an external memory that distils each episode into retrievable natural-language rules. On the banking domain of $\tau$-bench, against a static-RAG control retrieving over the complete policy corpus, learning from the one-bit outcome verdict lifts single-trial success to 1.6$\times$ the baseline, and learning from corrections to 2.6$\times$, converting 22 of the 84 tasks the baseline never solves. The result spans the deployment spectrum, measured on Mistral Large, an open-weights model that organisations with data sovereignty requirements can self-host, and replicated on a frontier model, Claude Sonnet 5. The accumulated memory also transfers: each model, reading the store built by the other, rises above its own no-memory baseline. The harness, protocol, and data are released.

cs.AI↗
arXiv2025

Smarter Together: Creating Agentic Communities of Practice through Shared Experiential Learning

The transition from human-centric to agent-centric software development practices is disrupting existing knowledge sharing environments for software developers. Traditional peer-to-peer repositories and developer communities for shared technical knowledge and best practice have witnessed dramatic drops in participation in a short period of time. At the same time, agentic functional equivalents are yet to emerge leaving AI agents, which already generate a significant proportion of all new software code produced, without access to repositories of valuable shared learning. In this paper, we introduce Spark, a novel shared agentic memory architecture which is designed to emulate the collective intelligence and know-how of human developer communities. Spark enables AI coding agents to both contribute to and draw from a persistent and continuously evolving experiential memory. Agents operating in the same general problem space use the Spark shared memory as a repository of new knowledge to achieve collective continual learning. We evaluate Spark as a coach for AI coding agents performing software development tasks. We demonstrate that recommendations made by Spark improve the quality of code generated by generic code generation models at varying sizes and capability tiers. Boosted by Spark, a small open-weights model with 30 billion parameters was able to match the code quality afforded by a much larger state-of-the-art model. Separately, we measure the intrinsic quality of recommendations generated by Spark against a wide range of criteria inspired by software development best practice, and achieve helpfulness levels of up to 98.2% in the top two (out of five) qualitative helpfulness bands.

cs.AI↗
arXiv2024

Signature, slicing foams, and crossing changes of Klein graphs

A totally oriented Klein graph is a trivalent spatial graph in the 3-sphere with a 3-coloring of its edges and an orientation on each bicolored link. A totally oriented Klein foam is a 3-colored 2-complex in the 4-ball whose boundary is a Klein foam and whose bicolored surfaces are oriented. We extend Gille-Robert's signature for 3-Hamiltonian Klein graphs to all totally oriented Klein graphs and develop an analogy of Murasugi's bounds relating the signature, slice genus and unknotting number of knots. In particular, we show that the signature of a totally oriented Klein graph produces a lower bound on the negative orbifold Euler characteristic of certain totally oriented Klein foams bounded by $\Gamma$. When $\Gamma$ is abstractly planar, these negative Euler characteristics, in turn, produce a lower bound on a certain natural unknotting number for $\Gamma$. Mutatis mutandi, we produce lower bounds on the corresponding Gordian distance between two totally oriented Klein graphs that can be related by a sequence of crossing changes. We also give examples of theta-curves for which our lower bounds on unknotting number improve on previously known bounds.

math.GT↗
arXiv2024

Strong Haken via Thin Position

We use thin position of Heegaard splittings to give a new proof of Haken's Lemma that a Heegaard surface of a reducible manifold is reducible and of Scharlemann's ``Strong Haken Theorem'': a Heegaard surface for a 3-manifold may be isotoped to intersect a given collection of essential spheres and discs in a single loop each. We also give a reformulation of Casson and Gordon's theorem on weakly reducible Heegaard splittings, showing that they exhibit additional structure with respect to certain incompressible surfaces. This article could also serve as an introduction to the theory of generalized Heegaard surfaces and it includes a careful study of their behaviour under amalgamation.

math.GT↗
arXiv2014

Bridge spectra of twisted torus knots

We compute the genus zero bridge numbers and give lower bounds on the genus one bridge numbers for a large class of sufficiently generic hyperbolic twisted torus knots. As a result, the bridge spectra of these knots have two gaps which can be chosen to be arbitrarily large, providing the first known examples of hyperbolic knots exhibiting this property. In addition, we show that there are Berge and Dean knots with arbitrarily large genus one bridge numbers, and as a result, we give solutions to problems of Eudave-Muñoz concerning tunnel number one knots.

math.GT↗
arXiv2012

C-essential surfaces in (3-manifold, graph) pairs

Let $T$ be a graph in a compact, orientable 3--manifold $M$ and let $Γ$ be a subgraph. $T$ can be placed in bridge position with respect to a Heegaard surface $H$. We show that if $H$ is what we call $(T,Γ)$-c-weakly reducible in the complement of $T$ then either a "degenerate" situation occurs or $H$ can be untelescoped and consolidated into a collection of "thick surfaces" and "thin surfaces". The thin surfaces are c-essential (c-incompressible and essential) in the graph exterior and each thick surface is a strongly irreducible bridge surface in the complement of the thin surfaces. This strengthens and extends previous results of Hayashi-Shimokawa and Tomova to graphs in 3-manifolds that may have non-empty boundary.

math.GT↗
arXiv2006

On non-compact Heegaard splittings

A Heegaard splitting of an open 3-manifold is the partition of the manifold into two non-compact handlebodies which intersect on their common boundary. This paper proves several non-compact analogues of theorems about compact Heegaard splittings. The main theorem is: if N is a compact, connected, orientable 3-manifold with non-empty boundary, containing no S^2 components, and if M is obtained from N by removing the boundary then any two Heegaard splittings of M are properly ambient isotopic. This is a non-compact analogue of the classifications of splittings of (closed surface) x I and (closed surface) x S^1 by Scharlemann-Thompson and Schultens. Work of Frohman-Meeks and a non-compact analogue of the Casson-Gordon theorem on weakly reducible Heegaard splittings are key tools.

math.GT↗