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

Ananth Kalyanasundaram; Ankush Kadu; Athira Gopal; Aswanth Krishnan

cs.AIOct 27, 2026

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

Authors: Ananth Kalyanasundaram, Ankush Kadu, Athira Gopal, Aswanth Krishnan

Organizations: QpiAI, India

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.

Figures & tables

Figure 1: Architecture of ACR . Four copies of an identical prompt share one frozen MoE backbone. Persistent shared/private masks give trajectories distinct expert eligibility while preserving the learned token router.

Arm	Seconds/problem	Throughput (tok/s)	Peak alloc	Peak reserved
Temperature, batched	84.5	48.4	65.82 GB	66.00 GB
ACR ( $P{=}160$ )	86.3	47.4	66.10 GB	66.39 GB
Expert-Sample	95.2	43.0	65.82 GB	66.00 GB
RoE ( $N{=}8$ )	417.0	9.8	66.46 GB	66.99 GB
Multi-agent, sequential	323.6	12.7	65.52 GB	65.58 GB

Table 1: Latency and VRAM at matched budget (four completions per problem, 3 screened problems, max

1{,}024

new tokens, single 80 GB A100, torch fallback, warmup excluded; means over problems). “Throughput” counts total generated tokens divided by elapsed wall-clock time.

Arm	Seeds	$N_{\geq 2}$	$N_{\geq 3}$	Correct (%)	UCM@4
Temp. $T=0.5$	2	25.00	1.50	100.00	1.2103
Temp. $T=0.9$	3	27.00	2.33	100.00	1.2328
Expert-Sample	1	21.00	2.00	100.00	1.1825
RoE	1	12.00	1.00	100.00	1.1032
ACR ( $P=96$ )	1	24.00	2.00	60.71	1.0873
ACR ( $P=160$ )	3	45.00	4.00	97.69	1.3915

Table 2: GPT-5.6 Sol benchmark: 126 problems, four trajectories per problem. Values are averaged over the listed seeds.

N_{\geq 2}

and

N_{\geq 3}

count problems.

Arm	$N_{\geq 2}$	$N_{\geq 3}$	Correct (%)	Mean UCM@4
Temp. $T{=}0.5$	15.67	0.67	93.84	1.130
Temp. $T{=}0.9$	18.67	1.33	95.63	1.159
Temp. $T{=}1.1$	16.67	0.33	97.42	1.150
Expert-Sample	14.33	1.00	99.80	1.127
RoE	17.67	0.00	99.40	1.140
ACR ( $P{=}96$ )	25.33	3.00	52.78	1.248

Table 3: GLM 5.3 benchmark: counts of problems with at least two correct methods, correctness, and secondary diversity metrics on the screened 126-problem benchmark. All results are averaged over three seeds.

Comparator	Rate (%)	$\Delta$ (pp)	95% CI (pp)	$p$
RoE	9.52	+26.19	$[19.58,\,32.80]$	$3.74\times 10^{-12}$
Expert-Sample	16.67	+19.05	$[11.64,\,26.46]$	$1.93\times 10^{-6}$
DivPrompt	99.21	$-63.49$	$[-69.84,\,-56.88]$	$1.23\times 10^{-32}$
Temperature $T=0.5$	19.84	+15.87	$[9.92,\,21.96]$	$6.75\times 10^{-7}$
Temperature $T=0.9$	21.43	+14.29	$[8.20,\,20.37]$	$1.49\times 10^{-5}$

Table 4: Paired comparisons of the rate of problems with at least two methods under GPT-5.6 Sol. ACR (

P=160

) has a 35.71% rate; seed counts are given in Table 2 . Differences and paired-bootstrap 95% CIs are in percentage points;

\Delta

is ACR minus comparator. The final column reports sign-flip

p

-values.

Figure 2: GLM multi-method problem counts versus correctness at matched output budgets. Points are three-seed means from Table 3 ; lines connect tested settings. ACR $P=160$ reaches 37.3 multi-method problems versus 18.7 for temperature $T=0.9$ .

Setting	$N_{\geq 2}$	$N_{\geq 3}$	Correctness (%)	Mean UCM@4
Qwen temperature	9.0	1.0	98.3	1.33
Expert-Sample	6.0	2.0	99.2	1.27
RoE	4.0	0.0	99.2	1.13
Qwen ACR ( $P=96$ )	10.0	5.0	57.5	1.33
Qwen ACR ( $P=160$ )	12.0	2.3	96.4	1.51
Qwen ACR ( $P=192$ )	9.7	2.7	97.5	1.43

Table 5: Blinded human audit on 30 problems. Threshold columns report mean problem counts out of 30 across three seeds; UCM@4 reports mean method counts. Four experts evaluated outputs with model and setting identities hidden.

Route	Distinguishing equations	ACR	Temperature
Newtonian	$mg\sin\alpha-f=ma$ , $fR=I\ddot{\theta}$ , $a=R\ddot{\theta}$	Primary: 2–4	Primary: 1–4
Lagrangian	$mg\sin\alpha-ma+\lambda=0$ , $I\ddot{\theta}+R\lambda=0$	Primary: 1	Absent
Energy	$\frac{d}{dt}[\frac{1}{2}m(1+\kappa)v^{2}-mgx\sin\alpha]=0$	Check: 1, 2	Absent

Table 6: Rolling down an incline: ACR

P=160

versus temperature

T=0.9

, four trajectories each. Equations summarize the raw derivations with normalized notation; secondary checks receive no extra primary-method credit.

Arm	$N_{\geq 2}$	$N_{\geq 3}$	Correct (%)	Mean UCM@4
Independent-persistent	39.67	3.67	96.49	1.3212
Token-resampled ACR	42.33	3.33	99.21	1.3574
Hybrid ACR	45.00	4.00	97.69	1.3915

Table 7: Persistence and mask structure at matched eligibility: 184 experts per trajectory per layer, matching ACR

P=160

. Threshold columns are mean problem counts out of 126.

Arm	Problems $\geq 2$ methods	Problems $\geq 3$ methods	Mean UCM@4	Correctness	Reached EOS
$\mathrm{Switch}_{2000}$	17/20	3/20	2.00	93.75%	92.5%
No switch	17/20	3/20	2.00	92.50%	82.5%

Table 8: Matched handoff comparison on 20 problems at

P=160

, mask seed 0. Correctness and method diversity are judged by GPT-5.6 Sol; EOS completion is recorded directly from generated token IDs.

Arm	$N_{\geq 2}$	$N_{\geq 3}$	Correct (%)	Mean UCM@4
Temperature $T{=}1.1$	21	3	87.6	1.19
ACR ( $P{=}80$ )	52	11	84.9	1.49

Table 9: Backbone ablation: Gemma-4-26B-A4B (128 experts, top-8), one seed, 126 problems, four trajectories;

P{=}80

matches Qwen

P{=}160

’s shared-core fraction.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Comparator	UCM@4	$\Delta$	95% CI	$p$
RoE	1.1032	+0.2883	$[0.2196,\,0.3598]$	$3.56\times 10^{-13}$
Expert-Sample	1.1825	+0.2090	$[0.1243,\,0.2910]$	$3.59\times 10^{-6}$
DivPrompt	3.7222	$-2.3307$	$[-2.4312,\,-2.2275]$	$4.70\times 10^{-38}$
Temperature $T=0.5$	1.2103	+0.1812	$[0.1164,\,0.2474]$	$2.30\times 10^{-7}$
Temperature $T=0.9$	1.2328	+0.1587	$[0.0899,\,0.2302]$	$2.59\times 10^{-5}$

Appendix

Table 10: Paired UCM@4 comparisons.

\Delta

is ACR minus comparator; ACR uses

P=160

over three seeds, with mean UCM@4 approximately 1.3915. Point differences use the displayed means. Intervals are paired-bootstrap 95% CIs; the final column reports sign-flip

p

-values.

Panel of Figure 3 — Figure 3: Development and held-out probes. (a) Reported development comparison; method counts include all trajectories. (b) On a held-out Putnam problem, 50 temperature samples yield two observed methods while eight routed trajectories expose a third.

Pool $P$	Seed	Evidence	Trajectories	Problems
96	0	Estimated	276	103
160	0	Estimated	167	73
160	1	Estimated	66	43
160	2	Estimated	149	67
192	0	Estimated	123	56
192	1	Estimated	48	28

Appendix

Table 11: Saved-output handoff analysis. Counts are trajectories out of 504 and problems out of 126 with at least one affected trajectory. Estimated rows measure near-cap prefixes; the recorded row uses explicit switch flags.

Reasoning Diversity

Reasoning diversity studies how to represent, measure, and preserve distinct solution strategies in AI systems.

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May 8, 2026

When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models

Mixture-of-Experts (MoE) language models route each token to a small subset of experts, but whether the routes selected by a trained top-

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Department of Computer Science and Engineering, POSTECH, South Korea · Microsoft Research Asia, Beijing, China · Graduate School of Artificial Intelligence, POSTECH, South Korea

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Jun 22, 2026

Does the Same Token Mean the Same State? MoE Routing as Signal for Reasoning Control

In sparse Mixture-of-Experts language models, does the same token id imply the same router state and the same experts producing it? Holding the emitted token id fixed at repeated anchors, we find it does not: the experts that produce it still separate task context, trajectory history, and reasoning-effort mode. This residual structure supports test-time control: near boundary anchors (the final-response transition) and delimiter anchors (which open the answer, e.g.\ \texttt{\textbackslash boxed{} or code fences), routing neighborhoods already align with final-answer basins at a marker-only readout and strongest when the routing is read at the answer opening. We operationalize this as RAD (Routing Agreement Decoding), an answer-string-free multi-rollout selector: it locates a fixed anchor, represents each rollout by its anchor-window MoE routing states, and returns the densest Weighted-Jaccard

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Fudan University · Shanghai Innovation Institute

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Large language models (LLMs) demonstrate strong performance in math reasoning benchmarks, but their performance varies inconsistently across problems with varying levels of difficulty. This paper describes Adaptive Multi-Expert Reasoning (AMR), a framework that focuses on problem complexity by reasoning with dynamically adapted strategies. An agile routing system that focuses on problem text predicts problems' difficulty and uncertainty and guides a reconfigurable sampling mechanism to manage the breadth of generation. Three specialized experts create candidate responses, which are modified during multiple correction and finalization phases. A neural verifier assesses the correctness of responses, while a clustering-based aggregation technique identifies the final candidate answer based on a combination of consensus and answer quality. When evaluated on the GSM8K dataset, AMR achieved 75.28% accuracy while only using the original training data. This result outperformed the majority of comparable 7B models that were trained on synthetic data. This showcases that models using difficulty-based routing and uncertainty-driven aggregation are efficient and effective in improving math reasoning models' robustness.

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