The use of Large Language Models (LLMs) for reasoning and planning tasks has drawn increasing attention in Artificial Intelligence research. Despite their remarkable progress, these models still exhibit limitations in multi-step inference scenarios, particularly in mathematical and logical reasoning. We introduce PREGU (Partial Reasoning Guided by Uncertainty). PREGU monitors the entropy of the output distribution during autoregressive generation and halts the process whenever entropy exceeds a defined threshold, signaling uncertainty. From that point, a localized search is performed in the latent space to refine the partial reasoning and select the most coherent answer, using the Soft Reasoning method. Experiments conducted with LLaMA-3-8B, Mistral-7B, and Qwen2-7B across four reasoning benchmarks (GSM8K, GSM-Hard, SVAMP, and StrategyQA) showed performance greater than or similar to Soft Reasoning, indicating that entropy can serve as an efective signal to trigger selective refinement during reasoning.
Large Language Models (LLMs) have demonstrated notable reasoning capabilities, often enhanced by
techniques like Chain-of-Thought (CoT) prompting [
Traditional reasoning strategies often operate in the vast space of tokens, which can be ineficient due to the immense number of possible token combinations. An alternative is performing search in the latent space, where representations are more abstract, compressed, and lower in dimensionality, avoiding successive natural language encoding and decoding.
The Soft Reasoning (SR) [
This research proposes PREGU (Figure 1), an adaptive extension of Soft Reasoning. PREGU dynamically identifies points of uncertainty during generation and triggers a focused search in the latent space only at those specific critical junctures.
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ISSN1613-0073 ) generates multiple partial reasoning paths in the token space. When the entropy of the output distribution ( ) exceeds the threshold ( ), the generation halts, marking a region of uncertainty. Each partial reasoning sequence is then refined in the latent space using the Soft Reasoning method, producing candidate responses ( 1, 2, … , ), from which the highest-reward answer is selected.
The latent space (or embedding space in the context of Large Language Models) is an abstract, multidimensional mathematical representation of input data (such as words or phrases) that encodes semantic, syntactic, and contextual information. Operating within this space allows LLM agents to function more eficiently by using compressed and abstract representations of environmental dynamics.
Soft Reasoning performs a search by applying controlled Gaussian perturbations ( ) to the
embedding of the first token, . This exploration is guided by Bayesian Optimization using the Expected
Improvement (EI) acquisition function [
() = verifier ( ) + coherence( ),
where verifier determines correctness — typically by employing the LLM itself as a black-box verifier
through the Multi-Generate approach [
A standard method for quantifying an LLM’s internal uncertainty is by analyzing the probability distribution of its output tokens. The metric employed here is the Shannon Entropy ( ), defined as:
A higher entropy value signifies a flatter or more uniform probability distribution, indicating greater
ambiguity or indecision in selecting the next token. By setting an entropy threshold ( ), the model’s
autoregressive process can be interrupted when high uncertainty is detected, thereby activating an
auxiliary reasoning mechanism. This approach mimics human dual cognition models (System 1:
fast/inencounters an impasse or high doubt [
=1 = − ∑
() log2 () .
Inspired by dual-process theories of cognition, PREGU mirrors the interaction between intuitive and analytical reasoning systems: a fast, heuristic mode during confident segments and a slower, deliberative intervention when uncertainty peaks. In this view, the entropy threshold acts as a computational analogue of metacognitive control, triggering a shift from automatic generation to reflective reasoning.
Unlike prompt-based diversification strategies such as Chain-of-Thought [
PREGU (Partial Reasoning Guided by Uncertainty) is designed to overcome the limitation of Soft Reasoning (SR), which optimizes only the initial token embedding. PREGU integrates entropy-based detection with latent space refinement in a two-stage process (Figure 1).
Stage 1: Partial Reasoning Generation (Token Space) We denote by a pretrained language model with parameters . The language model performs autoregressive generation to produce candidate reasoning paths. At each decoding step , we monitor the Shannon entropy of the next-token distribution. For each path, generation is interrupted at most once, exactly at the first token whose entropy crosses the threshold (i.e., the first such that ≥ ), yielding a partial reasoning prefix.
Entropy is estimated over the top- tokens (with = 50 ), balancing computational cost and representativeness; very low-probability tokens contribute minimally to the total uncertainty. Minimum Prefix ( min): the model must generate at least min tokens before uncertainty detection is allowed, ensuring suficient semantic context.
Stage 2: Refinement (Latent Space) Each partial reasoning sequence generated in Stage 1 is treated as an extended prompt root ( ). This partial reasoning is then refined independently using the Soft Reasoning method. The search is focused on the latent space starting from the point of interruption, allowing Bayesian Optimization to specifically address the ambiguity that triggered the halt.
The process yields multiple candidate answers ( 1, 2, … , ), and the final solution ( ∗) is selected based on the highest reward computed by the equation 1.
This structure combines breadth exploration (through multiple partial reasoning paths) with focused depth exploration (via latent space refinement), enabling a more adaptive and uncertainty-aware reasoning process.
Experiments were conducted using three intermediate-scale (7–8 billion parameter) open-source LLMs
under a zero-shot setting: LLaMA-3-8B [
Baselines. We compare PREGU and Soft Reasoning against standard prompting and decoding
baselines on GSM8K, GSM-Hard, SVAMP, and StrategyQA. CoT (Chain-of-Thought) encourages step-by-step
reasoning by prompting the model to generate intermediate rationale before the final answer [
Zero-Shot 58.5 ± 0.0 64.7 ± 0.7 59.9 ± 2.0 54.4 ± 2.6 63.0 ± 3.7 64.6 ± 1.6 67.2 ± 0.7 68.6 ± 0.7 63.0 ± 0.0 67.1 ± 1.5 67.5 ± 0.7 67.0 ± 1.0 62.0 ± 0.0 69.3 ± 1.5 64.2 ± 1.0 64.9 ± 1.0 64.2 ± 1.0 63.5 ± 1.5 66.1 ± 1.9 68.1 ± 1.9 • Search width: = 5 partial reasoning paths • Soft Reasoning parameters: = 5 samples, projected latent dimension = 50
The results in Table 1 indicate that PREGU generally matches or improves upon Soft Reasoning across the evaluated benchmarks. We observe small regressions in isolated settings (e.g., Qwen-2-7B on GSM8K and LLaMA-3-8B on SVAMP), while maintaining gains on GSM-Hard, StrategyQA, and most remaining cases. Across five runs, the method remained stable and did not exhibit systematic performance degradation, suggesting that combining entropy-guided interruption with localized latent-space refinement may improve reasoning consistency across domains, especially on multi-step inference chains such as GSM-Hard.
Notably, performance on the GSM-Hard dataset improved, where PREGU showed robustness on long, multi-step inference chains. Even with the search being initiated only at the first point of uncertainty, the method successfully refined reasoning trajectories, suggesting entropy is an efective critical-point selection metric.
An analysis of the detected points of uncertainty revealed a clear linguistic correlation. Tokens exhibiting the highest average entropy—such as “For”, “Given”, and “Since”—frequently marked logical transitions, the introduction of sub-problems, or causal relations. Other high-entropy tokens, including “First” and “According”, were also observed to initiate new reasoning steps. These tokens correspond precisely to structural moments in reasoning where the model must choose among multiple plausible logical continuations.
At these critical junctures, the probability distribution over output tokens becomes notably dispersed, reflecting the model’s indecision regarding the most coherent semantic direction.
These entropy spikes frequently coincide with discourse connectives (e.g., “for”, “since”, “given”), suggesting that the model’s uncertainty aligns with structural transitions in linguistic reasoning. Such correspondence supports the view that entropy can reveal moments of linguistic introspection, where the model implicitly evaluates competing semantic paths before proceeding.
This pattern supports the hypothesis that entropy functions as an indicator of local cognitive complexity: points where fast, automatic generation (System 1) gives way to slower, more analytical reasoning (System 2). Thus, the entropy-based mechanism efectively monitors internal signals of cognitive hesitation, transforming them into opportunities for reflective refinement.
The distribution of high-entropy tokens is visualized through a word cloud (Figure 2), highlighting terms associated with logical transitions in reasoning. This linguistic correspondence suggests that the method captures internal traces of hesitation within the model’s own generative process, approximating a primitive form of introspection.
PREGU successfully achieved its objective by developing an adaptive architecture that integrates partial reasoning generation in the token space with localized refinement in the latent space, guided by entropy. The approach validates the hypothesis that internal uncertainty can serve as a metacognitive control mechanism to direct computational efort toward regions ofering the highest potential for informational gain.
PREGU inherits certain limitations from the original Soft Reasoning approach. First, the scope of Bayesian Optimization remains restricted, as it operates only on the initial embedding following a detected uncertainty point, thereby constraining refinement to a localized region of the latent space. Second, the method’s reliance on the internal verifier ( verifier )—which employs the LLM itself to assess the correctness of its own outputs—can introduce bias, particularly in complex mathematical verification tasks. Finally, the fixed entropy threshold ( ) constitutes a sensitive hyperparameter: inadequate calibration may either cause premature fragmentation of reasoning sequences or reduce the frequency of uncertainty detection, efectively reverting the behavior toward that of the original Soft Reasoning method.
Future research should aim to expand the scope of optimization within the latent space to encompass a window of multiple embeddings following the point of uncertainty, rather than a single one. This broader search may enable smoother and more contextual refinements. Another promising direction involves designing new reward metrics that reduce dependence on the LLM’s self-evaluation, for instance by integrating external or symbolic verifiers for mathematical reasoning. Additionally, dynamically calibrating the entropy threshold ( )—adapting it to the problem’s complexity and context—and quantifying explicit cost-benefit metrics (e.g., execution time, inference cost per correct solution) represent important steps toward improving PREGU’s eficiency, interpretability, and robustness.
This work has been fully/partially funded by the project Research and Development of Digital Agents Capable of Planning, Acting, Cooperating and Learning supported by Advanced Knowledge Center in Immersive Technologies (AKCIT), with financial resources from the PPI IoT/Manufatura 4.0 / PPI HardwareBR of the MCTI grant number 057/2023, signed with EMBRAPII
During the preparation of this work, the author(s) used ChatGPT (GPT-5.2) to assist with translation and language editing (grammar, spelling, and clarity). The author(s) reviewed and edited the output and take full responsibility for the final content.
All experiments were executed on an NVIDIA DGX-H100 system equipped with 8× H100 GPUs (80 GB each).
The models evaluated were LLaMA-3-8B, Mistral-7B, and Qwen2-7B, selected for their architectural diversity and open accessibility. All experiments followed the same inference configuration, including token truncation to the top-k ( = 50 ) logits for entropy estimation and a fixed entropy threshold of = 3.0 bits. Uncertainty detection followed min = 5 (minimum prefix), and we trigger at most one interruption per path (first token where ≥ ).
For the latent-space optimization phase, Bayesian Optimization was applied over a projected subspace of = 50 dimensions, using the Expected Improvement (EI) acquisition function. Each refinement round sampled = 5 latent perturbations per reasoning path, guided by the composite reward function in Eq. 1.
To account for stochasticity in both token sampling and latent perturbation, each experimental configuration was executed across multiple independent runs with distinct random seeds. All results were reported as mean and standard deviation to capture the natural variability of large language model inference. Benchmarks included GSM8K, GSM-Hard, SVAMP, and StrategyQA under the zero-shot setting, following the standard prompt structures described in the methodology.
For each benchmark, a random subset of 200 problems was uniformly sampled from the full dataset at the beginning of each run. This random selection ensured that diferent executions explored distinct subsets while maintaining comparable task dificulty distributions. The random seed controlling the sampling process was synchronized with the inference seed, guaranteeing consistency between data selection and generation randomness across runs.
Finally, representative examples from diferent benchmarks are included in the Appendix to illustrate the full execution trace of PREGU. Each example shows both stages of operation—entropy-based interruption and latent-space refinement—highlighting how uncertainty localization leads to structured reasoning improvements. These examples provide a transparent depiction of the reasoning process and facilitate independent verification of the experimental pipeline.
Note. The examples reported here correspond to raw model outputs. Therefore, they may include hallucinations or other generation artifacts (e.g., spurious claims or incoherent fragments), and are provided solely to illustrate the behavior of the proposed pipeline.
Initial Question. Mayor: head of municipal government such as a town or city. Are Mayors safe from harm from the federal government?
(Entropy pause marked as [STOP]. Rewards refer to the partial prefix quality.)
1) Mayors are[STOP]
1) Mayor is a position of municipal government. 2) The municipal government,[STOP] Path 2 (Selected) 1) The mayor is the head of a municipal government. 2) The federal government is a higher level of government. 3) The constitution grants[STOP]
The Mayor is the local leader of a city or town. A federal government[STOP]
1) The Mayor is the leader of the local government and not part of the federal government. 2) No[STOP]
(Each path is refined in latent space and yields a complete answer.)
... auge officials of municipal governments, which are part of the state government, not the federal government. 2) The federal government has no direct authority over municipal governments, but it can influence them through various means such as funding or laws. 3) However, the federal government does not have the power to harm mayors directly, as they are not federal officials.
Answer: True. Mayors are safe from harm from the federal government.
Path 1 — Complete Chain ... oroften, has its own laws and regulations, but it is part of the larger national government. 3) The federal government has the power to enforce laws and regulations, and it can intervene in the affairs of municipal governments if necessary. 4) However, the federal government is not typically involved in the day-to-day operations of municipal governments, and mayors are usually free to carry out their duties without interference from the federal government. 5) Therefore, mayors are generally safe from harm from the federal government, but there are exceptions if the mayor is breaking federal laws or if there is a national emergency. Answer: Mayors are generally safe from harm from the federal government, but there are exceptions. Answer: mayors are enerally safe from harm from the federal overnment but there are exceptions
... kh the power to the federal government to regulate the states and municipalities. 4) The federal government can use its power to investigate and prosecute individuals, including mayors, if they are suspected of violating federal laws. 5) However, the federal government is not allowed to arbitrarily harm or threaten mayors. Answer: False. Mayors are not safe from harm from the federal government if they are suspected of violating federal laws, but the federal government is not allowed to arbitrarily harm or threaten mayors.
... iederates over the entire country, not just a single city or town. Therefore, the federal government has the power to intervene in the affairs of a city or town, including the removal or replacement of the Mayor. So, Mayors are not safe from harm from the federal government.
Answer: False.
... dit: The Mayor is not a federal official, so they are not under the protection of the federal government. 3) The federal government has no direct authority over the Mayor unless there is a violation of federal law. 4) The Mayor is not immune from prosecution if they break federal law.
Answer: False. The Mayor is not safe from harm from the federal government if they break federal law.
Initial Question. Ashley’s pizza delivery costs $15. What is the total amount that Ashley should give the delivery man if she wants to give a tip that is equal to 1/5 of the amount she ordered?
(Entropy pause marked as [STOP].)
1/5 means Ashley should give 1/5 of the total price.[STOP]
1/5 of the ordered amount is the tip Ashley wants to give. So, to find the amount of the tip, we[STOP] Path 2 (Selected) Ashley's tip should be 1/5 of what she paid for a delivery, so the tip amount is 1/5 * $15.[STOP]
1/5 of Ashley's pizza delivery is her tip. So, to find the tip amount, we[STOP]
1/5 (twentieth) of the[STOP] (Each path is refined in latent space and yields a complete answer.)
... Now, to find the total amount Ashley should give the delivery man, we add the tip amount to the cost of the delivery: $15 + (1/5 * $15).
Answer: $18
... Luxury Real Estate in Dubai will divide the cost of the pizza delivery by 5. Then, we will add the tip amount to the cost of the pizza delivery to find the total amount Ashley should give the delivery man. Answer: $15 + ($15 / 5) = $15 + $3 = $18.
... imanager's cost is the tip. So, we need to find 1/5 of $15.
Answer: $3 Selection Rule. Each partial reasoning sequence generated in Stage 1 serves only as an exploratory prompt. The final selection among reasoning paths occurs after the complete refinements in the latent space (Stage 2), based on the final evaluation scores. The chosen path thus corresponds to the reasoning that achieved the highest overall reward according to the combined objective function. Discussion. The examples provided demonstrate the operational dynamics of PREGU, showing how uncertainty detection and localized latent-space optimization interact to enhance reasoning reliability. Together, they ofer a transparent view of the model’s decision process and its transition from intuitive to analytical reasoning.