Chain-of-Thought (CoT) has become a cornerstone of reasoning in large language models, yet its effectiveness is constrained by the limited expressiveness of discrete token sampling. Recent latent reasoning approaches attempt to alleviate this limitation by replacing discrete tokens with soft embeddings (probability-weighted mixtures of token embeddings) or hidden states, but they commonly suffer from two issues: (1) global activation injects perturbations into high-confidence steps, impairing reasoning stability; and (2) soft embeddings quickly collapse toward the highest-probability token, limiting exploration of alternative trajectories. To address these challenges, we propose SeLaR (Selective Latent Reasoning), a lightweight and training-free framework. SeLaR introduces an entropy-gated mechanism that activates soft embeddings only at low-confidence steps, while preserving discrete decoding at high-confidence steps. Additionally, we propose an entropy-aware contrastive regularization that pushes soft embeddings away from the dominant (highest-probability) token's direction, encouraging sustained exploration of multiple latent reasoning paths. Experiments on five reasoning benchmarks demonstrate that SeLaR consistently outperforms standard CoT and state-of-the-art training-free methods.
Figures & tables
Figure 1: Normalized entropy distributions of decoding steps across five reasoning benchmarks using Qwen3-8B. Each subplot shows the density of step-wise entropy values, revealing a clear long-tail structure: the majority of steps concentrate in a low-entropy region (deterministic steps), while a smaller tail extends toward higher entropy values (exploratory steps).
Figure 2: Overview of SeLaR. At each decoding step, we compute the normalized entropy over top- k tokens. If entropy falls below threshold τ (deterministic step), standard discrete decoding is applied. Otherwise (exploratory step), we construct a soft embedding from top- k candidates and apply contrastive regularization to push it away from the dominant token, encouraging exploration of alternative reasoning paths.
Method
GSM8K
MATH500
GPQA
AIME24
AIME25
Avg
Qwen3-1.7B Yang et al. (2025a)
CoT (Sampling)
90.07
92.00
39.39
50.00
33.33
60.96
CoT (Greedy)
88.32
90.60
31.31
40.00
30.00
56.05
Soft Thinking
89.46
91.00
33.83
36.67
36.67
57.53
SwiR
89.84
92.00
37.88
46.67
23.33
57.94
SeLaR
90.60
92.60
35.35
53.33
36.67
61.71
Table 1: Detailed results on reasoning benchmarks. Results highlighted in green indicate performance comparable to or better than CoT (Sampling). Results highlighted in red indicate a performance drop relative to CoT (Sampling).
Figure 3: Computational overhead of SeLaR and SwiR relative to CoT (Sampling) on Qwen3-8B. (a) Tokens per correct answer: SeLaR beats SwiR on 4 of 5 benchmarks, most notably on AIME 2024/2025. (b) Average tokens on correctly-answered samples. (c) Average tokens on wrongly-answered samples.
Figure 4: Layer-wise top- k overlap ( k=10 ) between the soft-embedding forward pass and single-token reference passes, aggregated over N=200 branching steps from AIME 2025 on Qwen3-8B. Shaded bands denote standard error. Left: without contrastive regularization, Otop1 dominates Otop2 in deep layers, reproducing the collapse behavior of Wu et al. (2025) . Right: with contrastive regularization, both overlaps remain non-zero and comparable, indicating multiple reasoning trajectories coexist rather than a single one being swapped.
Method
GSM8K
MATH500
GPQA
AIME24
AIME25
Avg
CoT (Sampling)
95.45
98.00
61.62
76.67
66.67
79.68
SeLaR (Full)
95.83
97.00
61.62
83.33
80.00
83.56
Component Ablation
w/o Selective Activation
95.14
95.80
57.58
76.67
66.67
78.37
w/o Contrastive Reg.
94.92
96.20
57.58
70.00
60.00
75.74
Table 2: Ablation study on Qwen3-8B. We evaluate the contribution of each component in SeLaR.
Figure 5: Activation frequency analysis on Qwen3-8B. Exploratory steps (high entropy) account for 6.2%–13.8% of total reasoning tokens.
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
k
τ
GSM8K
MATH500
GPQA
AIME24
AIME25
Avg
Varying τ (fixed k=3 )
3
0.3
95.00
96.40
53.03
76.67
80.00
80.22
3
0.4
95.22
96.60
54.55
83.33
70.00
79.94
3
0.5
95.60
97.00
55.05
76.67
80.00
80.86
3
0.6
95.83
96.00
60.10
76.67
70.00
79.72
3
0.7
95.53
96.40
60.10
76.67
56.67
77.07
Appendix
Table 3: Sensitivity analysis on Qwen3-8B. We vary the entropy threshold τ and top- k value while keeping other settings fixed.
Figure 6: Case study on an AIME 2025 geometry problem. Standard CoT computes Arc HJ = 23° at the critical exploratory step, leading to an incorrect final answer of 334 . SeLaR activates selective latent reasoning at this exploratory step, correctly computing Arc HJ = 24° and yielding the correct answer 336 .
Figure 7: Activation frequency analysis on DeepSeek-R1-Distill-Llama-8B. Exploratory steps account for 8.8%–15.3% of total reasoning tokens, higher than Qwen3-8B (6.2%–13.8%).
Method
GSM8K
MATH500
GPQA
AIME24
AIME25
Avg
DeepSeek-R1-Distill-Llama-8B DeepSeek-AI et al. (2025)
CoT (Sampling)
89.01
90.20
42.93
36.67
30.00
57.76
CoT (Greedy)
85.29
83.60
30.30
30.00
26.67
51.17
Soft Thinking
85.67
82.20
32.83
30.00
23.33
50.81
SwiR
89.31
87.80
45.96
50.00
23.33
59.28
SeLaR
90.22
88.20
40.91
46.67
36.67
60.53
Appendix
Table 4: Results of DeepSeek-R1-Distill-Llama-8B. Results highlighted in green indicate performance comparable to or better than CoT (Sampling). Results highlighted in red indicate a performance drop relative to CoT (Sampling).
Large Language Models (LLMs) increasingly rely on intermediate reasoning, yet explicit Chain-of-Thought (CoT) suffers from a linguistic space bottleneck: each thought must be decoded into tokens, causing high inference overhead. Latent reasoning moves deliberation into continuous space, but existing methods mostly learn deterministic or reward-maximizing paths, lacking a principled way to allocate probability across trajectories with different correctness and costs. We propose Latent Thought Flow (LTF), which models reasoning as variable-length continuous trajectories and trains a sampler to match a reward-induced posterior over answer quality and computation cost. We instantiate this with a continuous GFlowNet using stochastic latent transitions. To handle sparse answer supervision, we introduce an Entropy-Weighted Subtrajectory Balance objective for intermediate rewards and a reference-prior regularizer to anchor exploration. Experiments under finetuning and transfer learning settings show that LTF outperforms explicit CoT and latent reasoning baselines, improving accuracy by 9.5% while reducing reasoning length by 27.2% on average compared with strong latent reasoning baselines.
Explicit chain-of-thought (CoT) reasoning substantially improves the reasoning ability of large language models (LLMs), but incurs high inference cost due to lengthy autoregressive traces. Existing latent reasoning methods offer a promis- ing alternative, yet they often treat reasoning as uniformly compressible, causing precision-critical intermediate steps to be overly compressed and thereby degrading reasoning accuracy. In this work, we propose Selective Latent Thinking (SLT), a reasoning paradigm that selectively compresses redundant reasoning spans into latent representations while preserving precision-critical spans as explicit CoT within the same reasoning trajectory. Our primary instantiation uses a lightweight decoder to anticipate a short upcoming reasoning span and applies confidence- based gating to determine the longest span that can be reliably compressed; the resulting selective compression policy is further optimized with trajectory-level reinforcement learning to balance answer correctness against reasoning cost. Ex- periments across four mathematical reasoning benchmarks show that which spans are compressed is critical: with the same compressor, compressing arbitrary spans reduces the GSM-Hard accuracy of Qwen3-4B from 54.7% to 17.3%, whereas keeping numerical tokens explicit retains 51.8%. SLT reduces explicit reasoning length by 58.4% with only a 2.8-point accuracy drop compared to explicit CoT on Llama-3.2-1B. Notably, the principle extends beyond this design: instantiated within existing latent reasoning models via a learned compression gate, it improves accuracy at equal reasoning length (+2.6 points over Latent-SFT) and at shorter length (+5.6 points over Latent-GRPO with 13% fewer tokens).
Hui Xie, Jie Liu, Ziyue Qiao +1
Eindhoven University of Technology, Netherlands · School of Computing and Information Technology, Great Bay University, China
Recent work has explored continuous representations in place of discrete tokens during Chain-of-Thought (CoT) reasoning, often referred to as soft CoT. This is motivated by the idea that a mixture of token embeddings can represent a superposition of multiple reasoning possibilities within a single step. However, it remains challenging to train large language models to realize this potential. Existing work has explored reinforcement learning (RL)-style training for soft CoT. However, these approaches treat soft tokens as actions in a Markov decision process rather than as differentiable intermediate computation steps. Thus, they do not propagate gradients across the soft tokens and miss out on the signal of how the choice of one soft token affects the next. In this paper, we propose a sparse relaxation method for RL (called SpaRLax), which leverages the differentiability of soft-CoT reasoning over time steps and makes training more stable and effective. We adopt an entmax sparsity method that adaptively determines the degree of softness, which truncates long-tail noise at confident steps while retaining multiple plausible candidates when uncertain. Across nine reasoning benchmarks, our method achieves the highest average performance compared with baseline methods. Further analyses validate the effective use of soft-token superposition in our approach, and also demonstrate the contribution of adaptive sparsity in our approach.
Jiabin Fan, Matthias Lindemann, Zita Marinho +2
University of Alberta · Alberta Machine Intelligence Institute (Amii) · Instituto de Telecomunicações +3