Adaptivity Under Realizability Constraints: Comparing In-Context and Agentic Learning

TL;DR

This paper investigates how adaptivity influences task approximation in neural networks, revealing that the benefits of adaptivity depend on representational constraints and differ between unrestricted and realizable regimes.

Contribution

It systematically compares in-context and agentic learning under various regimes, highlighting how neural network constraints affect adaptivity's effectiveness.

Findings

Adaptivity never hinders approximation performance.

Four distinct scenarios of adaptivity advantage are identified.

Representational constraints significantly influence adaptivity effects.

Abstract

We compare in-context learning with fixed queries and agentic learning with adaptive queries for uniform approximation of task families. We consider two settings: an unrestricted regime, where querying and approximation are arbitrary functions, and a realizable regime, where we require these operations to be implemented by ReLU neural networks. In both settings, adaptivity never hinders approximation performance. However, this advantage can change when one passes from the unrestricted regime to the realizable regime. We identify four distinct approximation scenarios, each witnessed by an explicit task family: (a) no advantage of adaptivity; (b) an advantage in the unrestricted regime that persists under ReLU realizability; (c) an advantage that arises only under realizability; and (d) an advantage that disappears under realizability. This demonstrates that representational constraints interact profoundly with the effect of adaptivity.