# Routing Is Least Learnable Where It Is Most Valuable: Bounds on Representation Routing for Web Agents

arXiv: https://arxiv.org/abs/2608.06171 · HTML: https://mlsanity.com/paper/2608.06171/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 15 of its 22 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 15 of 15)

- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Mind2Web: Towards a Generalist Agent for the Web](https://mlsanity.com/paper/2306.06070/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [GPT-4V(ision) is a Generalist Web Agent, if Grounded](https://mlsanity.com/paper/2401.01614/) (2024)
- [Navigating the Digital World as Humans Do: Universal Visual Grounding for GUI Agents](https://mlsanity.com/paper/2410.05243/) (2024)
- [Language Model Cascades: Token-level uncertainty and beyond](https://mlsanity.com/paper/2404.10136/) (2024)
- [AgentRewardBench: Evaluating Automatic Evaluations of Web Agent Trajectories](https://mlsanity.com/paper/2504.08942/) (2025)
- [Understanding and Mitigating Numerical Sources of Nondeterminism in LLM Inference](https://mlsanity.com/paper/2506.09501/) (2025)
- [Dynamic Model Routing and Cascading for Efficient LLM Inference: A Survey](https://mlsanity.com/paper/2603.04445/) (2026)
- [Adaptive Vision-Language Model Routing for Computer Use Agents](https://mlsanity.com/paper/2603.12823/) (2026)
- [Are Online Skill and Memory Modules Always Worth Their Tokens? A Budget-Constrained Study of Web Agents](https://mlsanity.com/paper/2606.15017/) (2026)
- [WebRouter: Query-specific Router via Variational Information Bottleneck for Cost-sensitive Web Agent](https://mlsanity.com/paper/2510.11221/) (2025)

## Built on by (most cited first, 1 of 1)

- [What Can Component-Replacement Evidence Establish? A Critical Scoping Review of Local Decisions in LLM Agents](https://mlsanity.com/paper/2609.39989/) (2026)

## Abstract (arXiv)

Web agents observe a browser through text, pixels, or both, and the choice is usually fixed once for all tasks. We measure six observation modes across eight site-model combinations (cells) on VisualWebArena and WebArena and ask what choosing per task would buy. The modes are complementary: each solves tasks the others miss, they fail in structurally different ways, and the best choice reverses between task sets. The obvious prize, an oracle that picks a winning mode for every task, looks large but is inflated by run-to-run noise: rerunning the same mode on the same tasks changes 12-14% of outcomes, so a second run of a mode already in hand gains about as much as adding a new one. What survives is a cost bound: sending only the tasks no mode solves to the cheapest mode cuts cost by 9.5-30.6% in 8 of 8 cells at unchanged success. We then test five routing policies (picking the mode, deciding when to spend on the strong mode, a zero-cost rule read off the task text, a confidence cascade, and pooled cost tiers), and none robustly beats simply fixing one well-chosen mode; the one exception is a fragile result in our sparsest cell. The central obstruction is that routing supervision is produced at the agent's success rate: the weaker the agent, the fewer labels a router gets, exactly where routing would be most valuable. This limit belongs to today's agents rather than to routing itself. Label supply and routing opportunity rise together (correlation 0.95 across cells), so a stronger agent can overturn the result, and we report the rerun noise bands and the full measurement protocol.