THE PATH OF LEAST RESISTANCE: GUIDING LLM REASONING TRAJECTORIES WITH PREFIX CONSENSUS
Authors: Ishan Jindal
Sai Prashanth Akuthota
Jayant Taneja
SACHIN DEV SHARMA
Venue: ICLR 2026 Poster (2026)
Keywords: Speculative reasoning
LLM inference optimization
Primary area: generative models

Abstract: Large language models achieve strong reasoning performance, but inference strategies such as Self-Consistency (SC) are computationally expensive, as they fully expand all reasoning traces. We introduce PoLR (Path of Least Resistance), the first inference-time method to leverage prefix self-consistency for compute-efficient reasoning. PoLR clusters short prefixes of reasoning traces, identifies the dominant cluster, and expands only a subset of promising paths, preserving the accuracy benefits of SC while substantially reducing token usage and latency. Our theoretical analysis, framed via mutual information and entropy, explains why early reasoning steps encode strong signals predictive of final correctness. Empirically, PoLR consistently matches or exceeds SC across GSM8K, Math500, AIME 2024/2025, and GPQA-Diamond, reducing token usage by up to 60% and wall-clock latency by up to 50%. Moreover, PoLR is fully complementary to adaptive inference methods (e.g., Adaptive Consistency, Early-Stopping SC) and can serve as a drop-in pre-filter, making SC substantially more efficient and scalable without requiring model fine-tuning.

Presented as a conference paper at ICLR 2026
THE PATH OF LEAST RESISTANCE: GUIDING LLM REASONING TRAJECTORIES WITH PREFIX CONSENSUS
Ishan Jindal
Fujitsu Research India ishan. j nnddll fu fts.
Sai Prashanth Akuthotat, Jayant Tanejat, Sachin Dev Sharma Samsung R&D Institute media-Delhi {a. prashhahth, jataneja, sachin. dev) com
ABSTRACT
Large language models achieve strong reasoning performance, but inference strategies such as Self-Consistnccy (SC) are computationally expensive, as they fully expand reasoning traces. We introduce PoLR (Path of Leust Resistance), the first inference-time method to leverage prefix consistency for compute-efficient reasoning. PoLR clusters short prefixes of reasoning traces, identifies the domi- nant cluster, and expands all paths in that cluster, preserving the accuracy benefits of SC while substantially reducing token usage and latency. Our theoretical anal- ysis, framed via mutual information and entropy, explains why early reasoning steps encode strong signals predictive of final correctness, Empirically, PoLR con- sistently matches exceeds SC across GSM8K, MATI500,, AIME24/25, and GPQA-DIAMOND, reducing token usage by up to 60% and wall-clock latency by up 50%. Moreover, PoLR is fully complementary ods (e.g., Adaptive Consistency, Early-Stoppins SC) and can serve as drop-in pre-filter, making SC substantially more efficient and scalable without requiring model fine-tuning.
adaptive inference meth-
INTRODUCTION
Large Language Models (L..Ms) have recently achieved remarkable performance on complex rea- soning tasks Grattafiori et al. (2024); Yang et al.] (2025); Guo et al. (2025): Jindal et al. (2025), ranging from grade-school math (Cobbe et al. 2021) to graduate-level problem solving (Hendrycks) ctt al. 2021 Rein et al. 2023). Among inference-time strategies, Self-Consistency (SC) decoding (Wang et al. 2023) has emerged as strong default: by sampling multiple reasoning traces and taking majority vote over their final answers. SC substantially improves accuracy greedy or single-sample decoding. However, incurs substantial computational cost because all reasoning traces must be expanded to completion.
To reduce SC's compute requirements, several inference-time methods such as Adaptive Consis- tency (AC) Aggarwal et al. (2023) and Early-Stop Self-Consistency (ESC) Li et al. (2024) have been proposed. These methods expand reasoning traces sequentially and stop generating them only when sufficient final-answer agreement is observed. Though effective, they share fundamental limitation: answer-level agreement is only observable after full reasoning traces is generated. As result, they cannot exploit the rich structural information that might appear earlier in the reasoning process and their efficiency remains limited by the need to generate complete reasoning traces.
Recently, an alternative line of research shows that the early stages of reasoning traces carry dispro- portionately strong signals about the eventual solution, phenomenon known prefix consistency. Formally, if r, denotes reasoning trace, then its first L tokens ry[1 I.). termed as prefix, tend to exhibit similarity across reasoning traces, irrespective of their later steps. Ji et al. (2025) exploited this phenomenon at training time, that is, fine-tuning models on prefixes to improve reasoning while
Work done while SRID, +Contributed equally

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Presented as a conference paper at ICLR 2026
frnder dalon of karr or wetinal
Self consistancy
N Full Ressoning Traces with Responses
Fisil arswer sagrapaiion
locil sale?"
68
foer uraal amount bunkca
68
reAuee
decide 2
L&M
week mate afd upit Hicw tocal mestrrs
Riil Roppest
Accuracy
60
664
PoUR
Mi= PNl
Expanding Koc reasening traces
Final arswer
agEregation on
50.1
58
C
58
Red Reporss
20
40
60
80
100
of SC Tokens
Agplermehe Cheering
(b) Token-accuracy plot GPQA- Diamond
PoLR Overview
(SC) and PoLR. Top: SC expands all N sampled traces to completion (100% expansion), then aggregates answers via majority vote. Bottom: PoLR first generates N short prefixes of length Lp. embeds and clusters them, and selects the dominant cluster. All K < N traces from this cluster are expanded, after which majority voting is applied. (b) PoLR exceeds SC accuracy, while reducing token cost by approx 50%.
Figure 1: (a) Comparison of
reducing inference cost. However, this requires expensive tinettuning and cannot be applied directly at inference.
This gap motivates method that reduces Self- Self-Consistency cost by exploiting early steps of rea- soning traces rather than waiting for full trajectories. To address this need, we introduce PoLR (Path of Least Resistance), the first method to leverage prefix consistency for inference-time Self- Consistency. To leverage Prefix consistency, PoLR generates N short prefixes, embeds and clus- ters them, and only expands the prefixes to full reasoning traces for the dominant cluster, reducing wasted token generation and adaptively allocating compute to promising paths. This approach pre- serves SC's accuracy while cutting token usage and latency dramatically depicted in Figure I The key contributions of this work are:
PoLR is drop-in SC replacement that clusters partial reasoning traces and selectively expands the dominant cluster, substantially reducing inference cost.
Across math (GSM8K, MATH500, AIME24/25), commonsense, and science reasoning bench- marks (GPQA-DIAMOND)) and implicit knowledge retrieval benchmark (STaRTegYQA) PoLR shows up to 60% token reduction and 50% latency savings without accuracy loss, consis- tent across LLM families and scales (1-32B params).
PoLR is the first inference-time method to exploit prefix consistency for Self- Coff-ssssst,ny, com- plementing existing adaptive self-cone consistency methods further reducing the token generation. PoLR is robust different clustering methods, prefix lengths, and cluster selection strategies.
2 Do PREFIXES ENCODE EARLY CONSENSUS?
To understand if prefixes encode strong signals about the eventual solution, we conduct a preliminary analysis of reasoning prefixes. We generate 40 traces per question us- ing DeepSee--Distll--wen---
Table 1: Preliminary analysis MATH500 and GSM8K (DSQ7B, 40 samples).
(DSQ7B) on MATH500 and GSM8K, truncating traces at varying prefix lengths Lp Table [ We evaluate the fraction of traces that shares identical prefix Lp (Expansion rate) and compute majority-vott (accuracy). We also find the exact pre- fix match (EPM) that is number of problems where all 40 traces share identical prefixes. The results show that traces sharing the same prefix achieve nearly the same ac-
1y
Exyaminn nite
Accuracy
EPM
59.3
MAcH500
138
01:85
89.2
256
03.55
80.2
NC
1.00)
75.7
GSMAK
2

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Presented as a conference paper at ICLR 2026
euracy as full SC, meaning large fraction of token cost spent extra traces rarely contribute the final answer. These findings suggest that LLMs encode structural agreement well before generating complete answers. Detecting and leveraging this early consensus substantially reduce compute without compromising SC"s robustness.
3 PATH OF LEAST RESISTANCE (PoLR)
In this section, we present how PoLR (Path of Least Resistance) operates as an inference-time alter- native to Self-Consistency (SC). The name PoLR is motivated by natural principle: systems tend to follow the path of least resistance, avoiding unnecessary detours while conserving energy. Anal- ogously, instead of fully expanding all reasoning traces like SC, PoLR prunes unlikely redundant paths early and allocates computation only to the dominant prefix cluster.
3.1 MATHEMATICAL FORMULATION
Setup. Consider an input reasoning question æ posed to a language model M. In the standard SC baseline, we sample N complete reasoning traces of average length &y and then aggregate their final answers by majority vote. While effective, this incurs high inference cost because every trace must be expanded until completion, even if most are redundant.
prefix-based selection step. Specifically, we sample N short prefixes, each of length Lp tokens, and use their semantic structure to decide which subset of traces to fully expand. The key intuition is that reasoning traces often share overlapping initial steps (Ji et al. 2025), and these early structures correlate with the correctness of the final outcome. By clustering prefxxes, we can identify the dominant reasoning mode early, without generating all traces to completion. A step-by-ster implementation instructions presented in Appendix B (ppendiiB(Allorittaii (Algorithm
PoLR modifies this pipeline by introducing
Step 1: Prefix Sampling, Given the input question x and the M, we first generate N short rea- soning prefixes p; Prefix(M(s; f4), Tup), i = 1,..., N, where is the sampling temperature, and Prefix(-) denotes truncating the LLM output to Lp tokens. In practice, this is implemented by setting max.new.
Lp-
Step 2: Embedding and Clustering. Each prefix ps is embedded into sparse vector represen- tation via TF-IDF bag-of-word. encoding over tokens. This choice lightweight, aogel--gnostic, and CPU-friendly, avoiding external neural encoders. We provide detailed comparison with neural encoder Table It is evident that neural encoders increase the clustering overhead way more than the TF-IDF encoders with diminishing returns on the accuracies.
We cluster } into C = [CI,..., Cm using Agglomerative Hierarchical Clustering with cosine similarity. This well-suited for small N (11-51), it requires no pre-specified m and produces interpretable groupings. That is C* arg maxc, EC [Cyl, where U Cj = {pI..... PNv and e is the dominant cluster.
Step 3: Expansion. M(x pk), Pk C", k= 1,..., K.
We then expands all K prefixes from C* to full reasoning traces as Tk
Step 4: Self-Consistency Voting. Let be the extracted answer from trace rk- PoLR returns à arg maxy Σk1 1[ax y]. Thus PoLR strictly generalizes SC: if K - and clustering is bypassed, it reduces to standard SC.
Token Efficiency: Let Ep average prefix length, & full reasoning length. Number of tokens generated for SC Tsc N f,, and for PoLR TPAI N ln + K (er tp). We compute the token efficiency as:
TPOLR Tsc
N lp + (l, ep) =1
11 =
N N.
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m clusters Presented as a conference paper at ICLR 2026
3.2 THEORETICAL JUSTIFICATION
PoLR relies on the intuition that early prefixes already contain useful signals about the final rea- soning trajectory. We formalize this intuition by considering two complementary properties: (i) correctness alignment, which determines whether restricting to a dominant cluster preserves accu- racy, and (ii) structural skew, which governs the magnitude of efficiency gains.
3.2.1 CORRECTNESS ALIGNMENT AND ACCURACY PRESERVATION
Let Y E (0, }} denote the correctness of final reasoning trajectory (1 if correct, 0 otherwise), and let Z denote the cluster assignment of a sampled prefix. The critical condition for PoLR is that Z carries information about Y, i.e. [2; Y) >> O, where I -(: denotes mutual information. Intuitively, prefixes cluster a way that is at least weakly predictive correctness, then restricting expansion to the dominant cluster will not systematically degrade accuracy. In this view, self-consistency (SC) can be seen as an unbiased estimator of E{Y]] while PoLR acts as a variance- reduued estimator that focuses high-probatin probability clusters.
Formally, the conditional entropy of correctness given the cluster assignment can be written as H(Y = Σ. P(Z = HY 2). If H(Y Z) is small, then cluster identity reliably predicts correctness. Our empirical results (Section 5) show that T [(2; Y) and H( 2) remain non-trivial across models, which explains why PoLR consistently matches SC accuracy.
3.2.2 STRUCTURAL SKEW AND EFFICIENCY
While correctness alignment governs accuracy preservation, our experiments reveal that it does not explain the magnitude of efficiency gains. Instead, efficiency is driven by the structural skew in the prefix cluster distribution. Define the skew for given instance as k. NN
|C"| where |C*| is the size of
the dominant cluster and N is the number of sampled prefixes. If large, the majority of prefixes fall into one cluster, and ignoring the smaller clusters eliminates substantial redundant expansions. Conversely, clusters are balanced (i x 1/m), dominant cluster's traces' expansion yields more token savings but poorer quality.
At the dataset level, the expected efficiency gain is thus directly tied to the expected skew E[y] x ]] Empirically, we observe strong correlation between and token savings, whereas NMI between clusters and correctness weakly correlated with efficiency. This indicates that PoLR's efficiency derives from structural dominance rather than correctness alignment.
The combined picture as follows:
Accuracy preservation requires that I(Z;Y) > 0, i.e., that clusters are not adversarially misaligned with correctness. Even modest alignment is sufficient, SC's voting ensures that errors do not amplify.
Efficiency magnitude depends on structural skew k: the more dominant the largest cluster, the more redundant expansions PoLR can safely ignore.
This separation of concerns reconciles our theory and empirical findings: mutual information guar- antees safety, while skew determines savings. Our experiments across GSM8K with multiple models (1.5B-7B) confirm this in Section 5.5 where NMI remains low (s 0.18), yet efficiency saturates around 50-58%. precisely because prefix clusters exhibit strong structural skew.
We now make the connection between cluster skew and efficiency gains explicit.
Proposition 1. Let N denote the number of sampled prefixes, partitioned and let C* denote the dominant cluster with size \C*).
(Ci...., Cm) with sizes [Cil,.... Assume PoLR expands K continuations from C*, while Self-Consistenyy (SC) expands M continu- ations from all N prefixes (with M K). Then the expected token efficiency gain of PoLR relative to SC satisfies
2
K where x.
16"1 N
is the dominance ratio (skew).
M
Sketch. SC requires expanding M continuations distributed across all prefixes. m clusters expanded proportionally, each prefix contributes average m/N expansions. PoLR instead
4

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Presented as a conference paper at ICLR 2026
expands only K continuations from the dominant cluster C Normalizing by M, the relative cost K is M |C- M K x-1 Thus the efficiency gain relative to SC is at least 1 M x x! Equality
K
holds when expansions are exactly proportional across clusters.
This bound formalizes the empirical observation that efficiency gains scale monotonically with x: the more dominant the largest cluster, the more redundant expansions can be ignored.
4 MAIN EXPERIMENTS
Backbone LLMs. We evaluate the efficiency and generality of PoLR Path of Least Resistance across diverse open-source LLMs spanning different architectures, scales, and training paradigms. Specifically,
(DSQ) (7B, 1.5B) (Guo et al. 2025), distilled from maasoning-specialiinn LLMs; QWQ32B (Team 2023 Yang et al. 2024a), a Qwen2.5 variant trained
CrepSeek-R1-Distilll-e
with reinforcement learning for problem solving; MiMo-7B-RL-U55.
(Xiaomi 2025) and Phi-4-
15B Abdin et al. (2025), an open-source GPTT-style model trained with large-scale supervised data; and Qwen2.5-Math-77 (Ynng et al. (024b), a math suth-speccalized instruction- tunndd model. These choices cover architectures (Qwen, MiMo, Phi-4, DeepSeek), parameter scales (1.5B-32B), and training paradigms (distillation, RL, supervised fine-tuning).
Benchmarks. We evaluate multi-step reasoning tasks: GSM8K (Cobbe et al. 2021 grade- school arithmetic word problems: MATH500 (Lightman et al. 2023), a set 500 challenging math problems; AIME24/25 (of Problem Solving. 2024 2025), school olympiad-leve math prob- lems;
(Rein et a 2024). a graduate-level STEM reasoning benchmark covering
physics, chemistry, and biology; and STRATEGYQA (Geva al. 2021), multi-hop reasoning and implicit knowledge retrieval task.
Evaluation Metrics. We follow standard metrics from prior reasoning literature: Exact Match (EM) on GSM8K (Habib et al., 2023); Pass@1 1 on Math500 and AIME24/25; Accuracy (binary correctness) on GPQA-Diamond. We also measure Token Efficiency relative to Self-Consistency (SC): 7 1 Teaa.
Path Expansion (PExp) denoting the number of full reasoning traces used for majority voting, and PoLR Overhead (kt). which includes TF-IDF vectorization and clustering.
Tse
(SC) (Wang et al. 2023). which samples multiple chain-of-thought independently and selects the majority answer. SC is widely adopted standard inference-ting tireeneeeiieeeeeee ensemble for reasoning tasks. We also report single-sample greedy decoding (Chain-of- -Chain-of-Thought, CoT) as lower-bound reference and compare PoLR with Adaptive Consistency (AC) Aggarwal et al. (203). and Early-Stopping Self-Consistency (ESC) Li et al. 2024).
Baselines. The primary baseline is Self-Consiste
All experiments are repeated 10 times with different random seeds (sampling order and tempera- ture) and we report mean performance and standard deviation across runs for all metrics: accuracy, EM, Pass @ 1, token efficiency, and latency. Further hyperparameter details are provided in Ap- pendix A All PoLR evaluations use Lp 256 unless stated otherwise. Empirically, we find that Lp 256 achieves good balance between PoLR accuracy and token efficiency gains.
Main Results. Table 2 presents the performance of PoLR compared to Self-Consistency (SC) across five reasoning benchmarks (GSM8K, MATH100, AIME24, AIME25, GPQA-DIAMOND) and multiple LLM families. The results reveal clear advantages of PoLR. First, PoLR drastically reduces token usage while preserving accuracy. Across all datasets and models, token efficiency 77 typically ranges between 40-60% effectively cutting token consumption by roughly half. For example, on GSM8K with QWQ32B at N = 51, PoL. achieves the same accuracy as SC (90.8%) while using only half the tokens (1) 47.6 47.6%). The additional clustering overhead ky is minimal, just few milliseconds, so the savings directly translate into faster inference. Second, accuracy is preserved and occasionally improved. Despite discarding up to half of the reasoning paths, PoLR matches SC's accuracy and sometimes surpasses it. On MATU500,, for instance, PoLR improves
For hrevity, standard deviations not included in the main table. All reported gains statistically significant. Detailed standard deviation values provided in Appendix
5

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Presented as a conference paper at ICLR 2026
Table 2: Performance comparison of PoLR versus SC across datasets (GSM8K, MATH500, AIME24, AIME25, GPQA-DIAMOND and model sizes. The table shows accuracy differences (green improvement, red drop), token efficiency 7) (%), sample size N, and PoLR overhead k (ms).
DSQ1.5B
DSQ7B
QWQ32B
GSM8K (1319)
N
SC
PoL.
o(%)
Rg (ms)
SC
PoL.R
k, (ms)
SC
Pol.R
x(X)
4 (ms)
73.2
0.2
26.5
31
73.2
0.0
41.1
6.0
80.0
-0.4
27.2
4,3
90.9
-0.6
48.6
5.8
72.6
2.3
0.0
28.1
DBQ1.5B
DSQ7B
QWQ32B
MATH500
Pol.R
((%)
(ms)
SC
Pol.R
R, (ms)
Pol.R
(ms)
(500)
51
76.2
-0.8
52.4
6.5
89.8
-0.4
48.7
7.6
91.8
0.2
51.8
11.2
76.4
52.0
4,4
89.6
0.1
48.5
5.1
91.9
0.0
54.2
5.7
11
75.9
-1.6
52.0
2.0
89.4
0.0
48.4
2.2
91.6
60.5
2.2
DSQ7B
Phi-4-15B
QWQ32B
AIME24
N
SC
PoLR
9(%)
(ms)
SC
PoLR
xy(%)
R2 (ms)
SC
PoLR
o(%)
k. (ms)
(30)
51
53.3
-6.7
50.9
6.3
50.0
3.3
49.5
12.1
80.0
0.0
59.7
10.8
53.3
-3.0
51.5
3.3
49.7
0.3
51.5
5.3
78.3
61.6
6.2
11
54.3
-3.3
49.8
2.0
50.3
-5.3
58.6
2.2
78.3
-2.0
66.6
12.8
DSQ7B
Pli Phi-4-15B
QWQ32B
AIME25
N
SC
PoLR
Ag (ms)
SC
PoLR
nx%)
k (ms)
SC
Pol.R
x(X)
4, (ms)
(30)
33.3
7.8
0.0
11.0
76.7
31
35,3
0.0
48.4
3.9
32.0
4.0
54.8
5,9
75.0
-4.0
59.5
6.9
33.7
48.9
2.2
35.7
2.3
60.5
2.3
74.7
-6.0
65.3
DSQ7B
MiMo-RL-7B
QWQ32B
GPQA
PoLR
o(%)
(ms)
SC
PoL.
(x%)
& (ms)
PoL.R
4; (ms)
DIAMOND
(198)
51
57.1
-1.5
57.1
9.5
65.7
-0.5
51.4
9.0
68.7
1.5
53.8
17.4
55.3
-1.2
55.8
5.7
64.9
-1.2
$1.7
5.9
68.2
0.0
56.9
7.3
54.1
-1.7
55.4
2.4
64.6
0.0
48.9
2.5
67.9
64.3
2.5
QWQ32B from 91.8% 92.0% N 51, and DSQ7B from 89.6% 89.7% at N 31. On AIME25, PoLR boosts accuracy by +3 percentage points for DSQ7B (33.7% - 36.4%) and Phi- 4-15B (32.0% + 36.0%). These gains occur because PoLR emphasizes the dominant, coherent reasoning clusters while filtering out noisy or inconsistent paths. On few occasions, PoLR down- grades the SC accuracy by small magnitudes except on the AIME25 dataset, where for QWQ32B PoLR is 10 points below SC. This amounts to dropping accuracy only 3 samples out of total 30 samples in this dataset. In Appendix H we find that these instances are inherently challenging, with SC succeeding only by narrow margin.
Finally, PoLR's 's benefits are consistent across models, datasets, and trace expansion budgets. On challenging benchmarks like DAAAADDDMOOND PoLR improves QWQ32B accuracy from 68.7% to 70.2% % at N = 51, while reducing token usage nearly by half (1) = 53.8%). Even on math- intensive datasets such MATH500, AIME24, and A AIME25, PoLR maintains high efficiency and accuracy, demonstrating robustness across reasoning domains and model scales. Additionally, PoLR shows consistent gains over mon-math/STEM task, STRATEGY discussed in Appendix G
In summary, PoLR halves token usage, preserves or improves accuracy, and adds negligible overhead, offering practical, training-free approach to make Self-Consistency substantially more efficient for real-world deployment.
ANALYSIS AND DISCUSSION
5.1 POLR AS A COMPLEMENT TO ADAPTIVE REASONING.
We evaluate whether PoLR can improve adaptive inference methods such as Adaptive Consistency (AC) Aggarwal al. (2023) and Early-stopping Self-Consistency (ESC) the GPQA-DIAMOND benchmark. Table 3 reports accuracy and the number of path expansions (PExp) across three LLMs and different initial sample budgets N.

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Presented as a conference paper at ICLR 2026
Table 3: PoLR complements Adaptive Consistency (AC) and Early-Stopping Self-Consistency
(ESC) on GPQA-DIAMOND. In the hybrid setting, PoLR ignores low-qual low-quality reasoning paths (PExp) before adaptive allocation. Results for three LLMs and multiple budgets N show reduced PExp while preserving or improving accuracy. Bold indicates the best result.
LLMs
DSQ7B
MiMo-RL--B8
QWQ32B
N
51
31
51
31
51
31
Acc
PExp
Acc
PExp
Acc
PExp
Acc
PExp
Acc
PExp
Acc
PExp
CoT
54.55
1.00
54.54
1.00
63.64
1.00
63.18
1,00
68.69
1,00
68.33
1.00
SC:
57.07
51.00
55.25
31.00
65.66
51.00
64,90
31.00
69.00
51.00)
68.19
31.00)
PoLR
35.56
20.79
54.04
13:01
65.16
24.12
63.74
14.62
70.20
21.83
67.80
12.58
AC
56.57
18.05
55.20
13.54
65.66
13.15
64.85
10.64
69.70
10.43
68.13
9.66
PoLR+AC
55,36
10.58
55.56
10.53
65.15
9.70
65.15
9.75
70.71
8.11
70.61
8.05
ESC
56.06
24.69
55.81
18.04
65.40
19.00
64,80
14.33
68.54
16.90
67.58
13.02
PoLR-ESC
54.85
$3.99
9.54
65.10
11.79
8.93
69.90
67.17
8.05
The results show that PoLR effectively ignores low-quality reasoning paths before applying adap- tive methods, reducing the number of expansions required without compromising accuracy. For example, in DSQ7B with N = 31, PoLR+AC reduces PExp from 13.54 (AC alone) to 10.53, while maintaining comparable accuracy (55.56% vs. 55.20% Similar patterns hold across MiMo-RL-7B and QWQ32B, with PoLR+AC and PoLR+ESC consistently lowering path expansions by 31,4% (on average) while preserving or slightly improving performance.
These findings indicate that PoLR can serve as an efficient pre-processing step for adaptive reasoning methods. By combining PoLR with adaptive allocation, the hybrid approach achieves substantial computational savings (75% on average as compared to SC) while retaining solution quality, making it practical enhancement for inference-time reasoning in large language models. All results report mean accuracies over 10 random trials. Table i in Appendix (D)odiddd standard errors, showing that PoLR yields more precise results with lower variance. We also conducted the same comparison on MATH500, observing consistent patterns (Table g Appendix D), confirming the robustness of PoLR across datasets.
5.2 LIGHTWEIGHT PREFIX EMBEDDINGS ARE SUFFICIENT FOR PoLR.
We evaluate the effect of different prefix embeddings on PoLR performance. Ta- ble 4 compares lightweight TF-IDF features with dense semantic embeddings from tomaarsen/mpnet base-aselll- aii-matrrosshke generating 64-dimensional sentence embed- ding.
The results show that TF-IDF achieves nearly identical accuracy and token efficiency dense embed- dings while incurring dramatically lower clustering overhead (5-11 vs. 220 ms). This indicates that lightweight representations are suf- ficient for PoLR's 's prefix clustering: they capture enough structural simi- larity among reasoning paths. Dense embeddings, while semantically richer, provide little benefit for short prefixes and introduce substantial computational cost. For longer pre- fixes or highly heterogeneous tasks, denser embeddings may be advantageous, but for the current reasoning benchmarks, lightweight features offer the best trade-off between efficiency and accuracy.
Table 4: Impact of different embeddings on PoLR accuracy on GSM8K,
and Math500 datasets.
SC
TF-IDF
Mauyoshka
Model
Acc
Acc
k
Acc
k
DSQ1.5B
73.2
73.2
40.1
11.3
73.3
38.7
219.8
GSMSK
DSQ7B
79.8
5.9
219.0
QWQ32B
90.8
90.8
47.6
11.2
90.8
45.8
221.4
DSQ7B
$7.1
55.6
57.1
9.5
54.0
52.4
209.3
GPQA
MIM07B
65.7
65.2
51.4
9.0
47.7
221.5
DIAMOND
QWQ32B
68.7
70.2
53.8
17.4
70.7
54.1
218.5
DSQ1,5B
76.2
75.4
52.4
6.5
76.2
47.5
219.7
MATH500
DSQ7B
89.8
89.4
48.7
7.6
90.0
44.7
220.6
QWQ32B
91.8
92.0
51.8
11.2
51.4
218.9
ryoshka

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Presented as a conference paper at ICLR 2026
1.0
1.0
1.5
0.5
-9.6 10.0
0.8
110
1..
11.7
126/78
.... SC Accuracy
-02
0.2
124778
.... Accuracy
-0.
125778
.... SC Accuracy
0.2
PoLR_Acourae
POLR AUR_Accuracy
05401
5B
expanaton)
USC1
oxpansion)
USG1.55
expansion)
0.8
0.0
0.0
0.8 0.0
0.0
Distance Threshaid
Distance Threshald
Distance Threshald
(a) GPQA Diamond
(b) GSM8K
(c) Math500
Figure Impact of different cluster threshold selection.
5.3 IMPACT OF DISTANCE THRESHOLD CLUSTERING.
In PoLR, agglomerative clustering applied to TF-IDF embeddings of reasoning prefixes, with the distance threshold controlling the granularity of clusters. To study its effect, we vary the threshold from 0.5 1.0 while fixing the number of samples at N 51, and report accuracy and token efficiency y GPQA-DIAMONT in Figure 2a GSM8K in Figure 2b and MATH500 in Figure 2c across different LLMs.
Across all thresholds, we find that accuracy remains nearly identical to SC, confirming that prefix consensus is strong enough that the precise clustering granularity does not affect the final outcome. However, the token efficiency is sensitive to the threshold: lower thresholds lead to tighter clusters, which reduce the size of the dominant cluster and hence the number of traces that need be expanded. This naturally improves token efficiency.
The magnitude efficiency gains also depends on model capacity. Weaker models such as DSQL.5B show the largest improvements (up duce more redundant and low-quality traces that can be easily filtered. In contrast, stronger models such as QWQ32B, which generate more diverse yet usefull reasoning steps, leave less redundancy to exploit, yielding smaller efficiency gains (~ 40%). This behavior is consistent with the intuition that PoLR benefits most when the model's s reasoning space noisy and contains many unpromising paths. We choose threshold of 1.0 for our main experiments as strikes a balance between effi- ciency and accuracy: at this setting, the accuracy either matches or slightly exceeds SC, while still providing substantial token savings, whereas lower thresholds could marginally improve efficiency but risk fragmenting clusters unnecessarily.
60% token savings), since they tend pro-
5.4 PoLR Is ROBUST TO CLUSTERING METHODS
Table 5 shows that the choice of clustering method has minimal impact on accuracy, but strongly affects PoLR's efficiency metrics. Across GSMSK, MATH500 and GPQA-DIAMOND datasets and different model sizes. density- based methods (DBSCAN and HDBSCAN) yield the better token efficiency (1)) indicating more effective reuse prefix consensus. These gains come with a modest increase in overhead (kz). Larger models such as QWQ32B benefit most,
Table 5: Impact of different clustering methods on PoLR.
SC
Agglomerative
DBSCAN
HDBSCAN
GSM8K
Acc
Acc
Ace
k
Acc
7
Ar
DSQ1.5B DSQ7B QWQ32B
40.1
72.7
12.0
73.5
61.5
12.9
79.8
80.0
26.5
05.9
80.1
36.4
06.9
80.4
33.4
07.1
90.8
90.8
47.6
11.2
90.8
64.6
11.4
91.0
56.9
12.0
SC
Agglomerative
DBSCAN
HDBSCAN
GPQA
Acc
Acc
Ace
h.
Acc
DSQ7B MIM07B
$7.1
57.1
09.5
56.1
69.9
10.2
53.5
71.8
11.0
65.7
65.2
51.4
09.0
64.1
65.3
10.1
63.6
67.0
10.5
QWQ32B
68.7
70.2
53.8
17.4
68.2
52.2
14.9
68.2
55.2
15.3
SC
Agglamerative
DBSCAN
HDBSCAN
Acc
Acc
Acc
h
Acc
k
DSQL.5B DSQ7B
76.2
75.4
52.4
76.2
68.7
7.2
76.0
67.4
7.7
89.8
89.4
48.7
7.6
89.6
54.6
8.2
89.2
63.5
9.7
achieving both high accuracy
QWQ32B
91.8
92.0
51.8
11.2
92.0
71.3
12.6
92.2
63.1
12.6
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Presented as a conference paper at ICLR 2026
Average Cluster Skew
Effiiency Gain
Average Cluster Skew
Effiiecc Gain
Average Cluster Skew
Efficiency Gain
0.8
Efficiency Gain
Aug
Efficiency Gain
Aug
0.6
Efficlenty Gein
0.6
0.6
Cluste Snew
0.4
Rug
0.2
2000
4000
2000
4000
2000
4000
Prefix Length (takens)
Prefix Length (tokens)
Prefix Length (tokens)
Qwen2.5-ne meen2.5-math-77 (95%)
(b) DSQ7B (80%)
(c) DSQ1.5B (73%)
Figure 3: Efficiency gains of PoLR across three models on GSM8K as function of prefix length.
models achieve over 50% token savings by 256-512 prefix tokens.
and strong efficiency improvements. Overall, we observed that the clustering methods mainly impact the officiency-overheedd trade-off, not the accuracy, showing that the PoLR is robust different clustering methods.
5.5 EFFECT OF PREFIX LENGTH ON EFFICIENCY AND CLUSTER STRUCTURE.
To further understand the role of prefix information, we varied prefix length from 4096 tokens on GSM8K with different LLMs. Figure 3 shows the resulting efficiency gains, cluster skew, and NMI. Raw numbers are provided in Appendix Table
We observe that efficiency improves monotonically with prefix length up to 512 tokens, achieving 58% token savings over Ceff-Consistency, after which it saturates. Cluster skew, by contrast, decreases sharply from ~ 0.96 at length 2 to 0.52 at 256, stabilizing thereafter. NMI increases slowly with prefix length but remains relatively low (~ 0.18 at 4096).
These results highlight two insights that efficiency is primarily governed by structural dominance (skew) rather than correctness alignment (NMI). Even with weak NMI, PoLR achieves substantial token savings whenever a dominant cluster exists. Second, prefix length trades off skew and NMI. Short prefixes yield high skew but low predictiveness; longer prefixes reduce skew while slightly improving correctness alignment. PoLR's efficiency benefits emerge in the mid-range, when skew remains sufficient for pruning yet prefixes capture more reasoning structure.
We compared PoLR across three LLMs for GSM8K dataset with differing accuracies (73%-952) 95%). Across all models, efficiency gains eventually plateau around 50-55%, but the trajectory differs. Lower-capacity models achieve large savings even very short prefixes (2-16 tokens), whereas the higher-accuracy Qwen2.5-Math- requires longer prefixes (256-512) before efficiency saturates. Importantly, cluster skew consistently predicts efficiency gains, while NMI remains low across all models. This highlights that PoLR's 's benefits stem from structural dominance of prefix clusters rather than their correctness alignment, and that model capacity mainly shifts the prefix length required to realize these savings.
5.6 CLUSTER SIZE BETTER ACCURACY
To further understand which cluster's reasoning traces should be expanded, we perform the majority voting for all the formed clusters for all dataset model combinations. We observed that the dominant cluster (by cluster size) cap- tures more accurate traces while the remain- ing clusters tend to have lower accuracies com- pared to the dominant cluster, second dominant cluster being typically ranking second in accu- racy, and
Table 6: Correlation coefficient between clus- ter sizes and accuracy for DSQ7B and QwQ32B (N = 51, Lp 256).
GSMNK MATH500
AIME24
AIME25
GPQA
DSQ-7B QwQ-32B
0.90
0.88
0.87
0.78
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Presented as a conference paper at ICLR 2026
We further find the Pearson correlation coefficient p between the cluster sizes and the corresponding accuracies for all the dataset in Table [6] We observe a strong correlation for all dataset model combinations p > 0.75. Therefore, in PoLR, cluster size is the best indicator of the cluster to be expanded. We provide the prefix length-wise dominant cluster accuracy for all dataset model combinations in Figure A
We refer the reader to Appendix ! for further analysis of the impact of other hyperparameters on PoLR.
6 RELATED WORK
We focus on two main directions relevant to our work: (I) methods that utilize answer consistency to reduce inference cost, and (2) methods that exploit early reasoning prefixes.
Soff-Consitteccy (SC) Wang et al. (2023) has become standard approach for improving the reliability of chain-of-thoughe reasoning by sampling multiple solution paths and selecting the majority answer. Other verifier-based methods include [Cobee et al.
Methods Exploiting Answer Consistency
(202T) Uesato et al. (2022); : Yao et al. (2023). While effective, SC is inefficient: accuracy improves roughly linearly with the number of samples N, but decoding cost scales proportionally, Icading to substantial redundancy when many trajectories repeat similar reasoning patterns.
Several methods aim to mitigate this overhead. Adaptive Consistency (AC) Aggarwal et al. (2023) monitors answer agreement samples arrive, allocating fewer trajectories to "easy" problems where consensus forms quickly. Early-Stopping
Coffisssssttncy (ESC) [i et al. (2024) halts sampling confident majority is detected, avoiding the cost of decoding all N samples. Reasoning- Aware Self-Consistency (RASC) Wan et al. (2025) evaluates reasoning paths based on a set of features and aggregates answers using weighted majority voting after collecting high-quality paths.
Both AC and ESC reduce compute by relying on answer-level agreement, but they act after full trajectories are decoded. In contrast, PoLR exploits structural signals much earlier: by clustering prefixes before expansion, it avoids generating redundant modes upfront rather than waiting for consensus at the answer level. This is crucial because when agreement delayed or split across modes, AC and ESC still expend tokens unnecessarily, whereas PoLR prevents this overhead entirely. Our experiments show that PoLR and AC are complementary: prefix clustering removes redundant modes, while adaptive stopping controls allocation within the dominant cluster, achieving the strongest cfficiency-accuree parallelizable, leading to higher throughput in practice since multiple promising prefixes can be expanded simultaneously without waiting for sequential majority-vote checks.
trade-offs. Moreover, unlike itcrative methods, PoLR is highly
Methods Exploiting Early Prefixes Another line of work leverages the predictive power of early prefixes. Path Consistency Zhu et al. (2024) estimates the confidence of partial reasoning paths and guides subsequent generations toward promising branches. In contrast, PoLR does not rely external confidence estimators or guided decoding. Instead, clusters multiple short prefixes to capture naturally emerging consensus among independent samples and applies self-consistency vot- ing only within that cluster. This preserves SC's majority-vote principle while substantially reducing computational cost.
Similarly, UPFT Ji et al. (2025) shows that prefixes contain rich signals and uses them at training time for supervision. PoLR transfers this insight to inference, demonstrating that prefixes can be exploited unsupervised and training-fret to reduce inference cost while maintaining SC-level accuracy. Orthogonal to mefix-based methods, several trainable approaches iteratively leverage LLM outputs to improve model performance Zelikman et al. (2022): Yuan et al. (2023).
7 CONCLUSION
In this work, we present PoLR, which leverages prefix clustering to drastically reduce reasoning cost while preserving or improving accuracy, providing a training free, inference-time enhancement to Self-Consistency.
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A HYPERPARAMETER SETTINGS
In this section we provide the hyperparameter settings for PoLR and the other comparative methods. All experiments were conducted using Lighteva[Hain Habib et al. (2023), supporting 7,000+ evaluation tasks across multiple domains and languages. We performed all experiments 48GB memory cards. We now define the core parameters for each method used in this work. For the comparative methods used the hyperparameters configurations yielding the best performance.
4 NVIDIA L40S
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Algorithm Path of Least Resistance (PoLR)
Require: Question z; LLM M, prefix length Lp. #prefixes N, #expansions K
Ensure: Final answer à
1: Prefix Sampling:
2: for = I... N do
3: p; <- Prefix M(x,
4: end for
5: Clustering:
6: Embed prefixes: 6; t Embed(pi)
7: C Cluster( (=))==))
8: C* + arg max Cyy
9: Expansion:
10: Select K prefixes {pI..... PK] C C
for k 1...K K do
12: Tk < Max p&)
D Complete reasoning trace
dg ExtractAnnswer(r))
14: end for
15: Self-Consistency Voting:
16: à + arg max, > lax = y)
17: return
PoLR
top-p=0.9,
temperature=0.6,
max-token=32K,
prefix-Length=256.
clustering parameters:
clustering distance threshold=1.0
feature downsampling dim=10
linkage=average,
metric=cosine,
Adaptive Consistency (AC) Aggarwal et al. (2023)
top-p=0.9,
temperature=0.6.
max-token=32K,
stop criteria: 3-confidence threshold=0.95.
Early-stopping Self-consistency (ESC)
et al. 2024
top-p=0.9,
00
max-token=32K,
window-size=5.
A.1 LLM USAGE
We used ChatGPT and Claude for grammar reviews and language style polishing. In certain cases we used these models in analyzing and summarizing tables. These summaries are then verified and updated manually for correctness.
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B POLR ALGORITHM
Algorithm D provide the step-by-step instruction implement PoLR. PoLR is model agnostic and wokrs for any LLM.
C POLR PERFORMANCE VS PREFIX LENGTHS
Following the structure of Table 2 we report mean accuracies and standard deviations for both PoLR and SC across different prefix lengths L, E {1, 21,2.4, 2,4, and two sampling budgets N E (51,31) (Figure
16, 32, 64, 128, 256, 512, 1024, 2048, 4096)
Overall, PoLR exhibits remarkable robustness to the initial number of samples: for both N 51 and N = 31, token efficiency follows nearly identical curves. In both settings, we observe sharp improvement in efficiency once prefix lengths reach the range 128-512, after which efficiency plateaus or declines slightly. The drop at very long prefixes arises because many instances do not require extended prefixes to reach a stable answer-coe expending them wastes computation without improving consensus. This trend consistent across dataset-LLM pairs we tested.
In terms of quality, PoLR generally matches outperforms SC across prefix lengths. The gains most stable on math and commonsense datasets (e.g.. GSM8K, MATH500, AIME24/25), where prefix consensus is especially strong. The only exception is GPQA -DIAMODD where accuracy drops slightly for longer prefixes. We attribute this to the nature GPQA problems: they often require multi-step reasoning and longer prefixes often contains specialized technical terms that leads to less informative lexical overlap between prefixes. Potential solutions could include expanding top-m clusters instead of the dominant cluster or switching semantic neural embeddings. We leave this for future work.
D PoLR COMPARISON WITH EXISTING APPROACHES
D.1 POLR COMPLEMENTS ADAPTIVE AND EARLY-STOPPING CONSISTENCY ACROSS DATASETS
Tables 7 and evaluate PoLR in combination with Adaptive Consistency (AC) and Early- Stey-Sttopiing Consistency (ESC) on two contrasting benchmarks: GPQA-DIAMOND (STEM reasoning with highly diverse, less predictable traces) and MATH500 (structured math reasoning with strong prefix regularities).
GPQA-DIAMOND. On GPQA, prefixes are less predictive of correctness, making consensus weaker. Here, PoLR alone already reduces expansions substantially (e.g.. DSQ7B: 20.79 vs. under SC at N = 51), but occasionally trails SC in accuracy. However, when combined with AC or ESC, PoLR consistently lowers PExp by additional 30-40% while preserving or even slightly improving accuracy. For instance, Po with DSQ7B cuts expansions to 10.58 from 18.05 under AC, with no loss in performance. This highlights PoLR's role as pruning front-end that removes clearly redundant reasoning paths before adaptive allocation.
MATH500. On structured math problems, prefix clusters are highly reliable. PoL. alone reduces expansions by more than half (e.g.. DSQ7B: 22.47 vs. 51 at N -11) while matching SC accuracy. When combined with AC, expansions drop low as 5.69 per problem (DSQ7B, N 51) with- out measurable accuracy loss, achieving up to 5x efficiency gains. ESC also benefits: PoLR+ESC consistently reduces expansions (e.g., 9.23 vs. 10.66 on QWQ32B) while retaining SC-level perfor- mance.
Takeaway. The contrast between GPQA-DIAMONT and MATI150 illustrates the conditions un- der which PoLR is most effective. On tasks with highly structured reasoning (MATH500). PoLR nearly lossless and compounds the efficiency of adaptive strategies to yield massive savings. On tasks with more diverse or less predictable reasoning paths (GPQA), PoLR still reduces redundancy and enhances existing adaptive methods, though accuracy gains are less pronounced. Together, these
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165
145
50%
22%
24
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GSM8K: 5BQL.B
(b) GSM8K: DSQ7B
(c) GSM8K: QWQ32B
80%
60%
Derb Laggh
Pudt Lengh
MATH500: DSQ1.SB
(e) MATH500: DSQ7B
MATH500: QWQ32B
60%
30%
30
20
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Pud Lengh Aaga
(g) AIME24: DSQ7B
(h) AIME24: Phi thi44-155 15B
(i) AIME24: QWQ32B
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30
20
Longh Mad
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(i) AIME25: DSQ7B
(k) AIMB25: Phi 15B
(I) AIME25: QWQ32B
30%
30
30%
2
g0
60%
new log meac
(n) GPOA-DIAMOND: MiMo-RL-
Pude www.ggghhhiin log
(m) EPQA-DIAMOND DSQ7B 7B
(0) GPQA DIAMOND: QWQ32B
Figure 4: Performance comparison of PoLR versus SC across datasets (GSM8K, MATH500, AIME24, AIME25, GPQA-DIAMONDİ and model sizes. The table shows accuracy differences (green improvement, red = drop), token efficiency n (%), and sample size N as a function of different prefix lengths Lp-
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Table PoLR complements Adaptive Consistency (AC) and Early-Stopping Consistency (ESC) on GPQA-DIAMOND In the hybrid setting, PoLR prunes low-quality reasoning paths (PExp) before adaptive allocation. Results for three LLMs and multiple budgets N show reduced PExp while preserving or improving accuracy.
(a) DSQ7B
LLMs
DSQ7B
N
51
31
Acc
PExp
Acc
PExp
CoT
54.54 0.00
1.00
0.00
54.54 0.00
1.00 + 0.00
SC
57.07 = 0.00
51.00 + 0.00
55.25 + 0.93
31.00 0.00
PoLR
55.55 0.00
40.79
54.04 = 1.96
13.01 0.15
AC
56.57 = 0.00
18.05 0.00
55.20 0.90
13.54 + 0.34
PoLR + AC
55.56 0.00
10.58 + 0.00
55.56 0.00
10.53 + 0.06
ESC
56.06 + 0.78
24.69 + 0.87
55.80 1.51
18.04 + 0.63
PoLR+ESC
54.84 + 0,40
13.48 + 0.36
53.99 + 1.72
9.53 + 0.25
(b) MiMo-RL-7B
LLMs +
MiMo-RL-7B
N +
51
31
Acc
PExp
Acc
PExp
CoT
63.63 + 0.00
1.00 + 0.00
63.18 = 0.00
1.00 + 0.00
SC
65.65 0.00
51.00 0.00
64.89 1.08
31.00 + 0.00
PoLR
65.15 0.00
24.11 + 0.00
63.73 + 0.97
14.62 0.14
AC
65.66 0.00
13.15 + 0.00
64.84 1.11
10.64 0.26
PoLR + AC
65.15 + 0.00
9.70 + 0.00
65.15 + 0.00
9.75 + 0.06
ESC
65,40 + 0.60
19.01 + 0.98
64.79 + 0.93
14.32 + 0.57
PoLR+ESC
65.10 = 0.35
11.78 0.45
64.49 0.84
8.93 + 0.15
(c) QWQ32B
LLMs
QWQ32B
N +
51
31
Acc
PExp
Acc
PExp
CoT
68.68 + 0.00
1.00 + 0.00
68.33 + 0.00
1.00 + 0.00
SC
69.00 0.00
51.00
0.00
68.18 0.78
31.00 + 0.00
PoLR
70.20 + 0.00
21.83 0.00
67.87 + 1.19
12.57 0.19
AC
69.70 + 0.00
10.43 + 0.00
68.13 1.02
9.65 + 0.33
PoLR + AC
70.71 + 0.00
8.11 0.00
70.61 0.20
8.05 + 0.05
ESC
68.53 + 0.71
16.90 + 0.67
67.57 + 0.95
13.02 + 0.43
PoLR+ESC
69.89 0.68
11.13 = 0.24
67.17 0.87
8.05 + 0.12
16

---

Presented as a conference paper at ICLR 2026
Table PoLR complements Adaptive Consistency (AC) and Early-Stopping Consistency (ESC) on MATH500, In the hybrid setting, PoLR prunes low-quality reasoning paths (PExp) before adaptive allocation. Results for three LLMSs and multiple budgets N show reduced PExp while preserving or improving accuracy.
DSQL.5B
LLMs 7
DSQ1.5B
N
51
31
Acc
PExp
Acc
PExp
CoT
73.00 0.00
1.00
0.00
72.88
0.00
1.00 + 0.00
SC
76.20 = 0.00
51.00 + 0.00
76,40
= 0.49
31.00 + 0.00
PoLR
75.40 0.00
22.13 0.00
75.70 0.77
13.39 0.14
AC
78.60 = 0.00
12.20 0.00
77.84 - 0.45
10.19
PoLR + AC
76.20 = 0.00
8.63 - 0.00
76.14 = 0.09
8.67 0.04
ESC
76.26 0.09
27.42 + 0.58
76.22 + 0.51
19.69 + 0.24
PoLR+ESC
75.66 + 0.23
15.83 + 0.26
76.12 + 0.60
11.26 + 0.15
DSQ7B
LLMs +
DSQ7B
N +
51
31
Acc
PExp
Acc
PExp
CoT
89.20 + 0.00
1.00 = 0.00
89.12 = 0.00
1.00 + 0.00
SC
89.80 0.00
51.00 0.00
89.56 0.32
31.00 + 0.00
PoLR
89.40 0.00
22.47 0.00
89.68 + 0.36
13.71 0.10
AC
90.00 0.00
7
89.94 0.28
6.24 0.08
PoLR + AC
89.40 + 0.00
5.69 + 0.00
89.48 + 0.10
5.61 + 0.04
ESC
89.82 + 0.06
14.64 + 0.24
89.62 + 0.24
11.84 0.19
PoLR+ESC
89.40 = 0.00
10.77 0.11
89.68 0.45
9.25 + 0.06
(c) QWQ32B
LLMs
QWQ32B
N +
51
31
Acc
PExp
Acc
PExp
CoT
92.00 + 0.00
1.00 + 0.00
91.94 + 0.00
1.00 + 0.00
SC
91.80 0.00
51.00
0.00
91.86 0.13
31.00 0.00
PoLR
92.00 + 0.00
22.78 1 0.00
91.74 - 0.18
1..24
AC
92.20 + 0.00
4.87
91.74
0.06
PoLR + AC
92.00 = 0.00
4.67 0.00
92.00 0.00
4.65
ESC
91.79 + 0.00
10.66 0.12
91.88 + 0.15
9.62 0.08
PoLR+ESC
92.00 0.00
9.23 0.05
91.92 # 0.24
8.42 0.03
17

---

Presented as a conference paper at ICLR 2026
Table 9: Efficiency gains PoLR across three models on GSM8K as a function of prefix length. All models achieve over 50% token savings by 256-512 12 prefix tokens. Here PEff denotes 1 PÉ32
DSQ7B (80%)
DSQI.5B (73%)
Qwen2.5-math-78 (95%)
Lp
PFff
avg skew
avg nmi
PFf
avg skew
avg nmi
PFff
avg skew
avg nmi
0.336
0.644
0.066
0.270
0.662
0.067
0.043
0.963
0.009
4
0.375
0.594
0.070
0.346
0.614
0.066
0.065
0.937
0.012
8
0.415
0.551
0.074
0.368
0.556
0.075
0.097
0.896
0.016
16
0.440
0.520
0.080
0.412
0.516
0.081
0.187
0.791
0.038
0.469
0.494
0.091
0.443
0.488
0.096
0.343
0.619
0.087
64
0,500
0.469
0.107
0.475
0.468
0.114
0.409
0.567
0.111
128
0.529
0.462
0.123
0.501
0.462
0.127
0,442
0,545
0.129
256
0.524
0.463
0.142
0.516
0.471
0.146
0.537
0,514
0.157
512
0.528
0.473
0.150
0.525
0.478
0.158
0,579
0,515
0.176
1024
0.526
0.471
0,151
0,520
0.475
0.161
0.558
0.522
0.184
2048
0.528
0.471
0.150
0.530
0.478
0.162
0.548
0.532
0.187
4096
0.534
0.470
0.151
0.537
0.477
0.165
0.545
0.532
0.187
Table 10: Efficiency gains of PoL.R on STRATEGYQA DSQ7B combination as compared to SC.
1p
2
32
64
128
256
512
1024
2048
4096
SC (%)
59.8
59.8
59.8
59.8
59.8
59.8
59.8
59.8
59.8
59.8
59.8
59.8
PoLR (5)
60.0
59.0
59.0
59.8
57.9
57.9
57.6
59.6
59.8
61.1
60.5
61.8
PET
0.185
0.275
0.313
0.361
0.470
0.565
0.646
0.662
0.657
0.655
0.651
0.656
7
0.110
0.107
0.146
0.192
0.290
0.383
0.430
0.315
0.150
0.063
0.058
0.061
An
1.3
1.5
1.7
3.7
7.4
11.2
9.4
12.2
12.1
13.0
13.1
results show that PoLR is both strong standalone alternative SC and a universal enhancer for adaptive consistency methods across reasoming domains.
E EFFECT OF PREFIX LENGTH ON EFFICIENCY AND CLUSTER STRUCTURE
In this section, we provide the cluster skew, NMI and efficiencies gains with varying prefix lengths for GSMSK dataset. The plots are provided Section 5.5 in Figure For reproducibility, we are providing the raw numbers in Table for each of the plots in Figure
F CLUSTER SIZE IS THE INDICATOR OF BEST PERFORMANCE
Following the structure of Table 2 we report the cluster-wise self coffsssssittncy across different prefix lengths Lp E 21,2,4, 4, 8, 16, 32, 64. 128, 256, 512, 1024, 2048, 4096), cluster being the dominant cluster with highest number consistently delivers best accuracies across the model dataset prefix length combinations except for the AIME24/25 dataset. It is likely because these benchmarks (e.g., AIME with only 30 samples) relatively small, reducing statistical robustness. Therefore, the plots for AIME seems be bit noisy. However, for all the combinations we observed strong correlation between the cluster sizes and the corresponding accuracies for all the dataset p 0.75. Therefore, in PoLR, clustering cardinality is the best indicator of the cluster to be expanded.
Figure 5 We observe that dominant cluster reasoning prefixes,
G POLR EVALUATION ON NON-MATH DATASETS
To further evaluate the generality of our observations beyond math/STEM settings, also experi- mented with a mattttt/TTTEM QA dataset, STRATEGY with DSQ7B model. We find that PoLR continues to match SC accuracy preserving the token efficiency benefits as depicted in Table 10
18

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Presented as a conference paper at ICLR 2026
(a) GSM8K: 5SQL.B
(b) GSM8K: DSQ7B
(c) GSM8K: QWQ32B
(d) MATH500: DSQ1.5B
(e) MATH500: DSQ7B
(f) MATH500: QWQ32B
@ AIME24: DSQ7B
(h) AIME24: Phi-4-15B
AIME24: QWQ32B
(i) AIME25: DSQ7B
(k) AIME25: Phi-4-15B
AIME25: QWQ32B
(m) GPQA-D: DSQ7B
GPQA-D: MiMo-RL-7B
(0) GPQA-D: QWQ32B
Figure 5: Cluster-wise self-consistency for (GSM8K, MATH500, AIME24, AIME25, GPQA-
DIAMOND) datasets with different model sizes.
19

---

Presented as a conference paper at ICLR 2026
Table 11: Instance-level error analysis of PoLR on AIME25 dataset QWQ32B model combination.
Cluster number
Cluster
% Correct Within
SC consensus %
Correct
Incorrect
size
0
20
9
11
45.0%
Failure
10
53.0%
53.0%
case 1
2
12
8
67.0%
0
22
9
13
41.0%
Failure
15
11
73.0%
59.0%
case 2
2
14
10
71.0%
9
11
45.0%
Failure case 3
1
13
8
62.0%
63.0%
11
85.0%
3
5
4
80.0%
Random correct
0
27
26
96.0%
19
19
100.0%
96.0%
case
2
80.0%
21.77
14.6
7.2
66.1%
Average case
1
14.63
10.1
4.6
68.5%
67.9%
9.70
7.0
2.7
65.3%
Across prefix lengths, PoLR maintains accuracy comparable to slightly better than SC, while achieving strong token efficiency improvements (17), consistent with our observations on other math and STEM datasets.
H PoLR INSTANCE-LEVEL ERROR ANALYSIS
To better understand the observed 10% accuracy drop for QwQ32B on AIME2025 dataset, per- form an instance-level analysis of the cases where SC passes but PoLR fails. Though this drop seems large, AIME2025 contains only 30 samples, meaning 10% drop corresponds to deviation of just three problems. Given this small sample size, even a few challenging instances can produce noticeable fluctuations.
In this analysis, for each incorrect instance, we inspect the cluster structures formed by PoLR. For each failure instance, We compute the number of correct reasoning traces within each cluster and compared it against the SC consensus in Table II We observe that the SC consensus for these failure cases is substantial low as compared the average case (last row block in Table I indicating that these instances are inherently difficult, even for the SC baseline. Further, all these failure case shows weaker cluster purity making PoLR's selection task more ambiguous. However, the primary contribution of PoLR remains to be the substantial improvements in token efficiency and cost reduction, rather than surpassing SC raw accuracy. Therefore, for the challenging problems where even the SC baseline solves the task only narrowly, PoLR is not expected to outperform SC in accuracy.
I IMPACT OF TEMPERATURE SAMPLING
To evaluate whether dynamically adjusting the prefix length based on the sampling temperature can improve performance, conduct controlled study MATH500 using DSQ7B. We vary prefix lengths from to 4096 and LLM sampling temperatures from 0.2 to 1.0 in Table 12
Across all temperatures and prefix lengths, the accuracy varies only within narrow band of +1 points, showing no consistent trend that correlates temperature with an optimal prefix length sug- gesting that sampling temperature does meaningfully interact with prefix length, and the best- performing prefix lengths for DSQ7B remain effectively constant.
20

---

Presented as a conference paper at ICLR 2026
Table 12: PoLR is robust to different temperature samplings.
Sampling Temperatures
Lp
0.2
0.4
0.6
0.8
88.0
89.4
89.2
89.2
89.0
88.0
89.4
89.2
89.2
88.8
88.2
89.4
89.0
88.6
88.2
88.2
89.2
89.2
88.8
88.0
16
88.2
89.6
89.0
88.8
89.4
32
88.2
89.2
89.4
89.0
89.2
64
88.0
89.0
89.0
89.4
88.4
128
87.6
89.4
89.0
88.6
88.6
256
88.4
89.4
89.4
88.6
88.0
512
88.4
90.0
89.6
89.4
89.0
1024
88.2
88.6
89.2
89.0
88.6
2048
88.2
89.4
89.2
89.0
88.6
4096
88.6
89.6
89.2
88.6
88.4
SC
88.0
89.4
89.2
89.2
88.8
21


Reviews:
[{"review_id": "Cvdo9xJUnS", "reviewer": "Reviewer_w1dY", "summary": "This paper introduces PoLR, an inference-time optimization that tackles the high computational cost of Self-Consistency (SC). PoLR generates short reasoning prefixes, clusters them to find a consensus, and only extends the paths from the dominant cluster. This approach significantly reduces token usage and latency on complex reasoning tasks while maintaining or even improving accuracy.", "questions": "1. If the dominant cluster leads to incorrect reasoning, does PoLR amplify “high-confidence errors”? Could multi-cluster expansion or confidence estimation help?\n2. Could the prefix length be adjusted dynamically via sampling temperature for adaptive balance between easy and hard problems?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Innovative & Practical: Cleverly solves the high cost of SC by using prefix consensus to filter paths early, a novel and practical approach.\n- High Efficiency: Achieves impressive results, reducing token/latency costs by ~50% without sacrificing accuracy.\n- Well-Supported: Backed by solid theoretical analysis (information theory, structural skew) and extensive experiments across multiple models and benchmarks.\n- Plug-and-Play: A simple, training-free method that is easy to implement and complements other optimization techniques.", "weaknesses": "- While the MI and skew analyses are insightful, they are not empirically validated. Quantitative measures linking $I(Z;Y)$ to observed behavior are missing.\n- Cluster-Dependent: The method's success hinges on identifying the correct dominant cluster; it could potentially filter out correct but less common reasoning paths.\n- Limited on Certain Tasks: Shows weaker performance on tasks with low lexical overlap (e.g., GPQA-DIAMOND), where the prefix consistency signal is faint.\n- Hyperparameter Discussion: Could benefit from a deeper analysis of the clustering method choice and TF-IDF configurations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LW40Rit5oK", "reviewer": "Reviewer_yLoa", "summary": "The authors propose PoLR, a method to reduce the computational cost of SC decoding in LLMs. Instead of expanding all sampled reasoning paths, PoLR clusters short prefixes and expands only those in the dominant cluster. The method is shown to preserve accuracy while drastically reducing token usage and latency.", "questions": "NA", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 1, "contribution": 2, "strengths": "1. The paper conducts comprehensive experiments to demonstrate the effectiveness of the proposed method. The main results show that it consistently outperforms existing approaches.\n\n2. The idea is both novel and compelling, and PoLR is straightforward to implement and fully compatible with existing language models.", "weaknesses": "I don't have many comments regarding the weaknesses; however, the primary issue is that the paper is not well written and is difficult to follow. For instance, I had to consult referenced papers to understand prerequisite concepts such as the definition of a prefix and the detailed observations related to prefix consistency. It would be better if the paper were more self-contained. Nonetheless, given the strong experimental results, I lean toward a positive assessment of the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "C4GyMLSBSf", "reviewer": "Reviewer_jah9", "summary": "The paper introduces PoLR (Path of Least Resistance), an inference-time method that improves the efficiency of reasoning in large language models (LLMs) without sacrificing accuracy. The key idea is to exploit prefix consistency, i.e., the observation that early reasoning steps (prefixes) across different reasoning traces tend to converge before diverging.", "questions": "N/A", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper builds on a compelling empirical finding: early reasoning steps in LLMs already encode signals predictive of correctness. This observation is both intuitively appealing and empirically validated, where clustering short prefixes achieves nearly identical accuracy to full SC.\n2. The paper notes some accuracy drops (especially on AIME24/25) but doesn’t deeply analyze why PoLR fails there. Qualitative error analyses or visualizations of cluster distributions could clarify how prefix diversity correlates with performance loss.", "weaknesses": "1. Uses simple TF–IDF clustering, which may miss deeper semantic similarities between reasoning traces.\n\n2. Accuracy drops on some datasets (e.g., AIME24/25) are not fully explored or explained.\n\n3. Mutual information argument is mostly qualitative and lacks empirical validation.\n\n4. Clustering approach may not scale efficiently when many samples (large N) are generated.\n\n5. Some sections are dense, with mixed implementation and theoretical details; figures could be clearer.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "aBMJVEfyOq", "reviewer": "Reviewer_jggQ", "summary": "This paper proposes an inference method called PoLR to address the issue of high computational costs in the inference process of LLM. Traditional Self-Consistency decoding requires sampling and expanding multiple complete reasoning paths, which improves accuracy but incurs significant computational overhead. The core idea of PoLR is to utilize prefix consistency during inference: first, generate short prefixes of multiple reasoning paths, cluster them, and only expand the paths in the main clusters, thereby significantly reducing ineffective computations. This method does not require retraining the model and can be used as a plug-in during the inference stage. The main contributions of the paper include: proposing the first method that leverages prefix consistency to optimize self-consistency decoding in the inference stage, reducing the number of generated tokens by up to approximately 60% and inference latency by about 50% without compromising accuracy. Additionally, the authors explain through theoretical analysis from an information-theoretic perspective why early reasoning prefixes contain strong signals for predicting the final correct answer, and verify the effectiveness of the PoLR method on mathematical, common sense, and scientific reasoning benchmarks through extensive experiments.", "questions": "Generality to Non-Math Tasks: Most evaluations are on math, STEM, and QA-style reasoning. Have you tested PoLR on more open-ended tasks where prefix similarity may be weaker?\n\nVoting within Noisy Clusters: When the dominant cluster includes low-quality traces, SC’s  majority voting might fail. Has the team considered weighting cluster votes by internal consistency or agreement confidence?\n\nFailure Cases: While PoLR generally preserves accuracy, there are cases with slight degradation. Can the authors provide qualitative analysis or examples to understand what types of reasoning problems lead to this drop?\n\nCluster Selection Robustness: PoLR selects the dominant cluster for expansion. In settings where reasoning traces diverge meaningfully, how sensitive is performance to this choice? Did you try expanding the top-k clusters instead of only the largest one?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "This paper introduces a highly novel inference strategy. Unlike existing work that either requires model fine-tuning or adaptively halts sampling based on answer agreement, PoLR introduces clustering based on early-stage reasoning prefixes. This is the first method to leverage prefix consistency at inference time for self-consistency decoding. The proposed idea is distinct from prior approaches and presents a fresh, efficient angle for improving LLM inference.\n\nThe theoretical analysis is solid and well-motivated. Using mutual information and conditional entropy, the paper shows that prefix clusters carry predictive signals about final answer correctness. It introduces the notion of cluster skew and formally proves that higher skew leads to greater token efficiency. The paper successfully connects theory and practice, and the theoretical results help explain the method’s robustness and efficiency.\n\nThe experiments are comprehensive and convincing. PoLR is evaluated on GSM8K, MATH500, AIME24/25, and GPQA-DIAMOND, covering a broad spectrum of reasoning difficulty. It is tested on LLMs ranging from 1.5B to 32B parameters and across different architectures and training paradigms. Results consistently show 40–60% token savings without accuracy degradation—sometimes even improving accuracy. PoLR is also shown to complement adaptive methods, offering additional savings. Results are averaged over 10 runs with reported standard deviations, ensuring statistical reliability. This section is a strong point of the paper.", "weaknesses": "Limitations of the method's applicability: There is a high degree of consensus in the early steps of PoLR hypothesis reasoning, meaning that the prefixes of most sampling paths converge to the main pattern. However, this assumption may not be fully valid for certain tasks. If the problem-solving paths of a question are highly divergent or the reasoning path corresponding to the correct answer is not the mainstream pattern, PoLR may miss important reasoning branches, thereby affecting accuracy.\n\nDependency on hyperparameters and clustering strategies: PoLR needs to pre-set the prefix length Lp and the methods for embedding and clustering prefixes. The optimal prefix truncation length and clustering method may vary across different tasks. If the prefix is too short, it may fail to capture sufficient reasoning signals; if it is too long, it may introduce irrelevant information and affect the clustering effect. In addition, simple word frequency embedding may not cover diverse expressions with semantic equivalence. Although the authors tried dense vector embedding and pointed out that its gain is limited and the overhead is large, the parameter selection in the clustering step itself still needs to be carefully adjusted in practical applications to ensure robustness.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)