Agent-Conditioned Routing: Diverse Reasoning Paths Within One Frozen Model

AI summary

Overview

Research area: Inference-time reasoning diversity for large language models, specifically controlling sparse mixture-of-experts (MoE) routing in a frozen model. Technical level: Intermediate — the paper is readable without deep MoE expertise, but the method (expert-eligibility masks, top-k routing) assumes familiarity with how sparse MoE layers dispatch tokens to experts. Scope: The paper introduces Agent-Conditioned Routing (ACR), a training-free inference mechanism that gives four parallel trajectories different expert-eligibility masks inside one frozen MoE, and measures how often those trajectories produce genuinely different correct solution methods on a screened 126-problem mathematics and physics benchmark.

What This Paper Is About

Generating several solutions to a problem often produces paraphrases of one dominant approach rather than genuinely different methods. The authors ask whether the conditional capacity already inside a frozen sparse MoE can supply real method diversity from a single problem prompt — with no user-assigned roles, no prescribed techniques, no fine-tuning, and no model copies. Their goal is "autonomous method diversification": the user supplies only the problem, and the system's four trajectories are scored by how often at least two of them reach the correct answer by distinct primary derivations.

Key Contributions

1. Agent-Conditioned Routing (ACR). A training-free inference mechanism that assigns each of m = 4 parallel trajectories a persistent, untrained shared/private expert-eligibility mask, while preserving the model's learned, input-dependent top-k token router. Nothing is trained and no parameters are updated.
2. A multi-mode reasoning benchmark for diversity. A 126-question benchmark spanning 12 mathematics and physics categories, screened from a hand-authored 200-problem candidate pool, evaluated with a metric (UCM@4) that counts distinct primary methods among soft-correct trajectories rather than answers or lexical variation.
3. Dual evaluation protocol. Full-benchmark judgments by two model judges (GLM 5.3 and GPT-5.6 Sol) complemented by a blinded four-expert human audit on a stratified 30-problem subset across three seeds, with correctness and mean UCM@4 reported alongside threshold counts.
4. Controls and ablations. Comparisons against temperature sampling, two routing-noise baselines (Expert-Sample and RoE), an informed sequential prompting arm, matched-eligibility mask ablations (persistence and structure), pool-size sweeps, a handoff comparison, and a second backbone.

Main Findings

• Roughly double the multi-method problems under GLM 5.3. At the main setting P = 160, ACR yields at least two correct primary methods on 37.3 of 126 problems versus 18.7 for the strongest temperature setting (T = 0.9), averaged over three seeds. Correctness is 95.77% versus 95.63%, and mean UCM@4 is 1.323 versus 1.159.
• 1.67-fold increase under GPT-5.6 Sol. ACR reaches 45.00 problems with at least two correct methods versus 27.00 for T = 0.9, both averaged over three seeds. Correctness is 97.69% versus 100.00%, and mean UCM@4 is 1.3915 versus 1.2328.
• Statistically supported paired gain. Under Sol, ACR's rate of multi-method problems is 35.71% versus 21.43% for T = 0.9, a gain of 14.29 percentage points (paired-bootstrap 95% CI [8.20, 20.37]; sign-flip p = 1.49 × 10⁻⁵).
• The blinded human audit agrees in direction, with a correctness cost. On 30 problems, Qwen ACR at P = 160 gives 12.0 multi-method problems versus 9.0 for temperature (1.33-fold), with correctness 96.4% versus 98.3%. Gemma ACR at P = 80 gives 14.0 versus 7.0 (twofold), with correctness 86.2% versus 100.0%.
• Routing-noise baselines do worse on diversity despite high correctness. Expert-Sample reaches 14.33 multi-method problems (99.80% correct) and RoE 17.67 (99.40% correct) under GLM, both below ACR's 37.33 at 95.77% correctness.
• The full mask construction beats matched-eligibility controls by modest margins. Fixing eligibility at 184 experts per trajectory per layer, hybrid ACR reaches 45.00 multi-method problems, token-resampled ACR 42.33, and independent-persistent masks 39.67. Token-resampled masks have higher correctness (99.21% versus ACR's 97.69%), a 1.52-percentage-point gap.
• Pool size matters, and a small pool damages correctness. P = 160 ranks above both P = 192 (32.33 under GLM, 37.67 under Sol) and P = 96, which collapses to 52.78% correctness under GLM and 60.71% under Sol.
• The effect transfers to a second backbone. On Gemma-4-26B-A4B (128 experts, top-8), the fraction-matched P = 80 setting yields 52 versus 21 multi-method problems in one seed, with a 2.7-percentage-point correctness reduction (84.9% versus 87.6%).
• Informed sequential prompting still wins on diversity. Showing later calls prior solutions and asking for a different method yields 124.33 multi-method problems under GLM and a 99.21% paired rate under Sol, versus ACR's 35.71% (Δ = −63.49 pp), but its calls depend on earlier attempts and it cannot be batched.
• Low overhead. ACR adds about 160 KiB of FP32 mask state (about 5 KiB packed). In a three-problem microbenchmark capped at 1,024 tokens on one 80 GB A100, ACR takes 86.3 s/problem versus 84.5 s for batched temperature sampling, with peak reserved memory of 66.39 GB versus 66.00 GB — within 3%.

Methodology in Plain English

A sparse MoE model does not run all of its parameters on every token; a learned router picks a small top-k subset of experts for each token. ACR leaves the router intact but restricts which experts it is allowed to choose from, giving each of four trajectories its own allowed set. At each MoE layer, a seeded permutation picks a shared core of size P; the remaining experts are split round-robin into disjoint private sets, one per trajectory. Trajectory a may use the shared core plus its own private set, so at P = 160 on Qwen3.6-35B-A3B each trajectory can reach 184 of 256 experts per layer (208 at P = 192). The router still picks its usual top-k = 8 within that eligible set, decoding is deterministic, and the mask persists for a 2,000-token prefix before the trajectory continues with unrestricted routing in the same frozen model. All four trajectories run in one batched request over one model instance with separate KV caches.

The benchmark was built by screening a 200-problem, 12-category pool with six temperature samples per problem and retaining only the 126 problems that showed multiple solution paths and at least one correct solution. Judges read the complete raw predictions and marked a trajectory "soft-correct" if it reached the right answer anywhere in its reasoning, ignoring LaTeX and boxed-answer formatting slips. Diversity is counted as substantive differences in executed mathematical steps, not rephrasing or reordering; each trajectory contributes at most one method. Two model judges scored the full benchmark, and four human experts scored a stratified 30-problem subset with model and setting identities hidden.

Why This Matters

The paper reframes inference-time scaling: instead of treating extra samples as extra lottery tickets for the same answer, it asks whether extra samples can cover different methods, which is what matters when a single approach has systematic blind spots. It shows that a routing-level control inside a frozen model can shift the distribution of derivations without fine-tuning, role prompts, or multiple model copies — and it gives the field a measurement protocol (correctness-filtered method counts, plus a human audit) for diversity claims that answer-level metrics cannot check.

Real-world applications:

• Scientific and engineering problem solving, where a wrong answer often traces to a flawed method rather than arithmetic, and surfacing a Lagrangian versus a Newtonian derivation can expose the error.
• Verification and review workflows, where independent derivations of the same result give reviewers more to cross-check than repeated identical proofs.
• Educational tutoring systems, where showing a student several valid solution routes to one problem is more useful than one route restated four times.
• Resource-constrained deployment, since the approach adds roughly 160 KiB of mask state and stays within 3% of batched sampling in latency and peak VRAM on the tested microbenchmark, making it viable where multi-model ensembles are not.

Industry relevance centers on serving economics: ACR is a single-backbone, single-batched-request intervention that preserves the top-k active-expert count, in contrast to multi-agent systems that need separate weights, communication, or sequential calls. The informed sequential prompting baseline reached far higher diversity but took 323.6 s/problem in the microbenchmark versus 86.3 s for ACR and cannot be batched — a direct trade-off between diversity and throughput that deployment teams would have to price.

Future Directions

• Assess intermediate-step validity. The current metric filters on final-answer correctness only; the authors explicitly leave expert assessment of whether intermediate steps are valid to future work.
• Broader task and model coverage. The benchmark is deliberately conditioned on problems with multiple solution paths, and the human audit covers 30 problems with reviewer agreement not quantified; generalizing beyond this selected population is untested.
• Layer-specific masks and resource scaling. The paper uses uniform shared/private masks across all 40 MoE layers and notes layer-specific masks and resource scaling as open questions.
• Downstream selection or aggregation. The paper generates diverse trajectories but does not study how to pick among them or combine them, and it notes that masks constrain computation without assigning semantic specializations, so trajectories may still converge on the same method.

Target Audience

Researchers and engineers working on inference-time compute, reasoning diversity, and sparse MoE architectures will get the most from this paper, particularly those evaluating multi-sample or multi-agent strategies and looking for a cheaper alternative to separate models or role prompts. It is also useful for practitioners who need to reason about the correctness–diversity trade-off in deployed reasoning systems, and for evaluation researchers interested in method-level rather than answer-level metrics. Readers without background in MoE routing will need to pick up the top-k expert-selection concept first.

Authors’ abstract

Generating several solutions can expose alternative methods, but additional trajectories often paraphrase one dominant approach. We investigate whether the conditional capacity of a frozen sparse mixture-of-experts (MoE) model can provide such diversity from one problem prompt, without user-assigned roles, prescribed methods, fine-tuning, or model copies. Agent-Conditioned Routing (ACR) assigns $m$ parallel trajectories persistent, untrained shared/private expert-eligibility masks while preserving the learned, input-dependent token router. On a screened 126-question multi-mode mathematics and physics benchmark, with model judges reading the reported derivations in full, we count the number of problems yielding at least two distinct primary methods among soft-correct solutions in four trajectories. ACR reaches approximately twice as many such problems as the strongest temperature setting under GLM 5.3 (37.3 versus 18.7), and 1.67 times as many under GPT-5.6 Sol (45.00 versus 27.00), at matched output budgets. A blinded four-expert audit on a stratified sample of 30 problems also finds more multi-method solutions with ACR on both backbones, with lower correctness. Matched-eligibility ablations show modest multi-method count advantages for ACR, while token-resampled masks attain higher correctness. An informed sequential prompt elicits more diversity still, using previous solutions and explicit requests for alternative methods. ACR adds about 160 KiB of mask state. In a three-problem microbenchmark capped at 1,024 tokens, its latency and peak VRAM usage remain within 3% of batched temperature sampling.