Test-time scaling improves large language model reasoning, but spends compute uniformly along a reasoning trace, even in stretches that are already stable. Motivated by the observation that reasoning failures show an early onset of uncertainty, we introduce DeepLook, a training-free decoding framework that monitors segment-level confidence, branches only at uncertainty bottlenecks, and ranks candidate continuations by Average Lookahead Confidence (ALC)---their mean confidence over fixed-horizon rollouts---before completing and voting over a pruned subset. On four competition mathematics benchmarks across four open models, DeepLook matches or exceeds the accuracy of DeepConf-low in 12 of 16 settings while generating 87.3% fewer tokens, showing that a model's own confidence is informative enough to decide where extra decoding compute is worth spending. On knowledge-intensive GPQA-Diamond the accuracy advantage disappears even though the token saving does not: coherent hallucinations also receive high ALC, so internal confidence localizes instability, not falsehood. Code is available at https://github.com/txyang1/deeplook.
Figures & tables
Figure 1: DeepLook conceptual overview and accuracy–token-cost frontier. Left: uniform brute-force scaling vs. selective lookahead at uncertainty bottlenecks. Middle: the DeepLook pipeline of segment monitoring, branching, and ALC ranking. Right: DeepLook on a higher-accuracy, lower-token-cost Pareto frontier, with an 87.3% average generated-token reduction relative to DeepConf-low (details in § 4.2 ).
Figure 2: Uncertainty diagnostics correlate with errors on DeepSeek-R1-8B. Wrong traces (orange) exhibit more uncertain segments (a) and an earlier uncertainty onset (b) than correct traces (blue), motivating early confidence drops as triggers for lookahead exploration.
Figure 3: DeepLook pipeline. (1) Token-level top- k log-probabilities are aggregated into a segment confidence Cˉ(Si) , which (2) is compared against a percentile threshold τi over a local history window Hi , so exploration fires only on a drop relative to the trace’s own recent history. (3) At a trigger, K branches are rolled forward over a horizon H and scored by Average Lookahead Confidence (ALC). (4) Branches are ranked and adaptively pruned, the best branch b∗ resuming as the primary trajectory while the other retained branches are completed. (5) All completed traces are majority-voted into the final answer.
Model
Dataset
Path@1
Cons@512
DeepConf-low
DeepLook @128 (Ours)
Tok
Acc
Tok
Acc
Tok
Δ%↓ (C / DC)
Acc
Δ (C / DC)
DeepSeek-R1-8B
AIME24
83.0%
3.55
86.7%
0.78
92.5%
0.121
(-96.6%/-84.5%)
93.3%
(+6.6/+0.8)
AIME25
76.9%
4.01
82.3%
1.24
86.4%
0.127
(-96.8%/-89.8%)
86.7%
(+4.4/+0.3)
BRUMO25
80.0%
3.56
93.3%
1.07
90.0%
0.124
(-96.5%/-88.4%)
90.0%
(-3.3/+0.0)
HMMT25
58.1%
4.49
69.8%
1.60
77.6%
0.213
(-95.3%/-86.7%)
73.3%
(+3.5/-4.3)
Qwen3-32B
AIME24
80.6%
2.00
84.8%
0.66
89.5%
0.102
(-94.9%/-84.5%)
90.0%
(+5.2/+0.5)
Table 1: Main results. Accuracy (%) and total generated-token cost (Tok, ×108 , all inference stages). For DeepLook @128, Δ%↓ and Δ give token and accuracy change vs. (C / DC) = (Cons@512 / DeepConf-low). Shading marks the best and second-best accuracy per row. All accuracies are measured on N=30 problems per benchmark.
Figure 4: Illustrative case summary (not a verbatim trace). Hand-condensed decisive steps of an HMMT25 problem, contrasting the consensus failure mode of Cons@512 with the DeepLook run that recovered the correct answer; the summarization convention is described in Appendix F .
Figure 5: Average nunc for correct vs. incorrect traces , DeepSeek-R1-8B on HMMT25, across four component variants under both readout regimes; G0 (greedy decoding) is shown as the two reference lines. The correct–incorrect gap ranges over 7.46 – 9.92 segments and never closes.
Figure 6: Ablation and scaling analysis. (a) Accuracy as components are integrated (variants G0–G4 of § 4.3 ); Δ is the gain over Greedy. (b) Accuracy as a function of the lookahead horizon H .
Appendix figures & tables18 assets
Supplementary material from the paper’s appendix.
Appendix
Hyperparameter
Value
Main segment length Lmain
512
Confidence top- k
20
Trigger window W
8 segments
Low quantile q
0.10
Warmup
4 segments
Hysteresis δ
0.02
Appendix
Table 2: Default DeepLook hyperparameters (corresponding to DeepLook@32 ). The @64 and @128 variants increase only K (to 32 and 64); all other values are unchanged.
Figure 7: Prompt logic for model_type=deepseek/qwen .
Figure 8: Prompt logic for GPT-OSS models with reasoning_effort .
Table 3: Licenses and terms for existing assets. Dataset and model licenses are taken from the linked public asset pages.
Figure 9: Accuracy vs. token cost trade-offs across benchmarks. Each panel plots dataset-level token cost against accuracy for one benchmark. Colors identify the base model, with DeepLook @128 shown as prominent stars and the corresponding Path@1 , DeepConf-low , and Cons@512 references shown with lighter markers. Faint colored segments connect Path@1 to DeepConf-low within the same model, visualizing the baseline accuracy–cost frontier that DeepLook @128 pushes beyond. Across AIME24, AIME25, BRUMO25, and HMMT25, DeepLook @128 consistently lies in the low-cost, high-accuracy region: it uses far fewer tokens than DeepConf-low and Cons@512 , while matching or exceeding their accuracy in most model–dataset settings. Path@1 is shown as the no-search reference point, plotted at the mean per-trajectory cost implied by Cons@512 (its token total divided by 512), which is the cost matching a single sampled trajectory.
Model
Dataset
Cons@512
DeepConf-high
DeepConf-low
DeepLook @32
DeepLook @64
DeepLook @128
Tok
Acc
Tok
Acc
Tok
Acc
Tok
Acc
Tok
Acc
Tok
Acc
DeepSeek-R1-8B
AIME24
3.55
86.7%
1.45
86.7%
0.78
92.5%
0.036
86.7%
0.064
86.7%
0.121
93.3%
AIME25
4.01
82.3%
2.37
81.4%
1.24
86.4%
0.027
83.3%
0.072
83.3%
0.127
86.7%
BRUMO25
3.56
93.3%
2.17
93.3%
1.07
90.0%
0.033
86.7%
0.065
90.0%
0.124
90.0%
HMMT25
4.49
69.8%
3.43
70.0%
1.60
77.6%
0.040
66.7%
0.082
70.0%
0.213
73.3%
Qwen3-32B
AIME24
2.00
84.8%
0.88
86.4%
0.66
89.5%
0.018
86.7%
0.046
86.7%
0.102
90.0%
Appendix
Table 4: Full benchmark results. Accuracy (%) and token cost (Tok, ×108 ) for Cons@512 , DeepConf baselines, and DeepLook budgets.
Table 6: Token cost breakdown on AIME25 (DeepSeek-R1-8B). Stage-wise share of DeepLook ’s dataset-level generated-token budget. The lookahead evaluation (ALC scoring) accounts for under 24% of total tokens.
Figure 10: Token- vs. segment-level confidence. Each segment spans two lines for readability (segment length 32 tokens for illustration). The segment background encodes segment-level confidence Cˉ , where red backgrounds indicate uncertain segments. Individual token colors ( Ct ) reveal local confidence fluctuations, motivating segment-level aggregation for robust detection of reasoning failures.
Figure 11: Motivating analysis on Qwen3-32B. Incorrect traces show both more frequent uncertainty and earlier uncertainty onset than correct traces.
DeepLook-Recursive
DeepLook
Dataset
Tok
Acc
Tok
Acc
AIME24
0.019
83.3
0.018
86.7
AIME25
0.039
76.7
0.038
80.0
Appendix
Table 7: Search strategy: DeepLook-Recursive vs. DeepLook . Tok ( ×108 ) and Acc (%) on Qwen3-32B.
Hyperparameter
Setting
Acc (%)
Tok (M)
Trig.
Ablation baseline
83.3
5.0
5.5
Robust: accuracy within one problem of baseline
Low quantile q
0.05
80.0
4.5
4.2
0.25
80.0
7.5
7.3
Window size W
4
80.0
5.5
6.4
32
80.0
6.9
8.5
Appendix
Table 8: Trigger parameter sensitivity on AIME25 (DeepSeek-R1-8B). One parameter varied at a time; all others held at the ablation baseline ( q=0.10 , W=8 , δ=0.02 , k=10 , Lmain=512 , warm-up 4 , K=16 , Rmax=10 ). This ablation baseline differs from the default configuration of Table 2 in k and Rmax , so its absolute token counts are not comparable to those of Table 9 . Tok in millions; “Trig.” is the mean number of trigger firings per problem.
Rounds
Tok ( ×108 )
Acc (%)
2
0.0270
83.3
4
0.0437
83.3
6
0.0545
83.3
8
0.0649
83.3
Appendix
Table 9: Branching-round sensitivity on AIME25 (DeepSeek-R1-8B). K=16 . Bold marks the default Rmax .
ρ
Tok ( ×108 )
Acc (%)
0.10
0.0180
80.0
0.25
0.0438
80.0
0.50
0.0850
83.3
0.75
0.1204
83.3
Appendix
Table 10: Keep-ratio sensitivity on AIME25 (Qwen3-32B). K=16 , Rmax=2 ; static keep ratio ρ .
Figure 12: Illustrative summary: DeepLook exposes global constraints that self-consistency misses. In this HMMT combinatorics example, Cons@512 repeatedly selects the locally plausible odd-vertex heuristic and converges to 202. By intervening at the unstable pairing step, DeepLook uses lookahead to test whether the proposed edge removals remain globally consistent, detects the boundary-parity obstruction, and redirects the solution to the correct answer 200.
Figure 13: Illustrative summary: DeepLook concentrates compute on fragile enumeration steps. In this AIME 2024 counting example, Cons@512 preserves a mechanically plausible inclusion-exclusion error and overcounts the rotational cases, giving 373. DeepLook identifies the low-confidence overlap calculation as the decision point, uses lookahead rollouts to reveal duplicated symmetry classes, and prunes the overcounted branch to recover the correct answer 371.
Figure 14: Illustrative summary: the knowledge-boundary failure mode of § 4.6 . A hallucinated physical fact yields a coherent continuation that scores high ALC; internal confidence localizes instability, not falsehood.
Figure 15: Illustrative summary: DeepLook rejects deceptive algebraic branches through lookahead verification. In this continuous-math example, Cons@512 treats the result of repeated squaring as reliable and outputs an extraneous root. DeepLook instead evaluates the downstream stability of that branch, checks the candidate against the original equation and domain behavior, and switches to the globally valid conclusion that no real solution exists.
Recent work on test-time scaling for large language model (LLM) reasoning typically assumes that allocating more inference-time computation uniformly improves correctness. However, prior studies show that reasoning uncertainty is highly localized: a small subset of low-confidence tokens disproportionately contributes to reasoning errors and unnecessary output expansion. Motivated by this observation, we propose Thinking by Subtraction, a confidence-driven contrastive decoding approach that improves reasoning reliability through targeted token-level intervention. Our method, Confidence-Driven Contrastive Decoding, detects low-confidence tokens during decoding and intervenes selectively at these positions. It constructs a contrastive reference by replacing high-confidence tokens with minimal placeholders, and refines predictions by subtracting this reference distribution at low-confidence locations. Experiments show that CCD significantly improves accuracy across mathematical reasoning benchmarks while substantially reducing output length, with minimal KV-cache overhead. As a training-free method, CCD enhances reasoning reliability through targeted low-confidence intervention without computational redundancy. Our code will be made available at: https://github.com/bolo-web/CCD.
Lexiang Tang, Weihao Gao, Bingchen Zhao +4
Peking University, Beijing, China · University of Edinburgh, Edinburgh, UK.
As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers. Current methods for estimating the confidence of large language models are generally based on probabilities of selected key tokens, but the underlying mechanism remains unclear. Our pilot study finds that replacing selected token probabilities with coarse substitutes can also improve calibration, motivating us to further explore effective signals of model confidence. We introduce Divergent Token Confidence (DTC), a framework that estimates confidence by counting tokens at which two models strongly disagree during decoding. DTC identifies these divergent tokens using the Jensen-Shannon divergence between next-token distributions evaluated along the same reasoning trajectory. We find that their count is almost negatively associated with answer accuracy, thereby serving as a simple yet effective signal for uncertainty quantification. DTC supports both white-box and black-box evaluation using auxiliary models, without explicit training and affecting the generation process. Experiments across multiple model families and six mathematical benchmarks demonstrate improved calibration over probability-based and verbalized baselines. Under white-box evaluation, the count-only estimator achieves an average expected calibration error of 13.0%, compared with 32.7%-42.4% for standard full-sequence confidence methods. In black-box settings, it also improves calibration over the original verbalized scores. For example, mean expected calibration error falls from 32.1%-40.2% to 13.7%-16.3% on DeepSeek-V3.2. These findings provide new insights for improving reasoning uncertainty quantification in large language models. The code is released at https://github.com/szu-tera/DTC.git.
Feiyang Li, Shengjing Liu, Qi Zhan +7
College of Computer Science and Software Engineering, Shenzhen University · Tsinghua University · Behavioral and Spatial AI Lab, Peking University & Tongji University
Large language models (LLMs) have demonstrated impressive reasoning capabilities by scaling test-time compute via long Chain-of-Thought (CoT). However, recent findings suggest that raw token counts are unreliable proxies for reasoning quality: increased generation length does not consistently correlate with accuracy and may instead signal "overthinking," leading to performance degradation. In this work, we quantify inference-time effort by identifying deep-thinking tokens -- tokens where internal predictions undergo significant revisions in deeper model layers prior to convergence. Across four challenging mathematical and scientific benchmarks (AIME 24/25, HMMT 25, and GPQA-diamond) and a diverse set of reasoning-focused models (GPT-OSS, DeepSeek-R1, and Qwen3), we show that deep-thinking ratio (the proportion of deep-thinking tokens in a generated sequence) exhibits a robust and consistently positive correlation with accuracy, substantially outperforming both length-based and confidence-based baselines. Leveraging this insight, we introduce Think@n, a test-time scaling strategy that prioritizes samples with high deep-thinking ratios. We demonstrate that Think@n matches or exceeds standard self-consistency performance while significantly reducing inference costs by enabling the early rejection of unpromising generations based on short prefixes.