Entropy-Based Decoding

Multimodal large language models (MLLMs) have demonstrated remarkable progress on cross-modal reasoning tasks, yet they continue to suffer from hallucinations in long-chain reasoning processes. In this work, we revisit hallucination in MLLMs from the perspective of reasoning generation dynamics. We argue that entropy is not merely a static measure of uncertainty but a structured signal that reflects how modality information is integrated throughout decoding. Through systematic analysis, we identify two characteristic entropy patterns associated with hallucination behaviors: (1) a generally high-confidence regime corresponds to premature convergence to inappropriate multimodal interactions; and (2) local abrupt entropy transitions are associated with reasoning instability and hallucination onset. Building on these observations, we propose an entropy-aware self-introspective framework for MLLM reasoning. Our method continuously tracks entropy dynamics during decoding and performs targeted visual re-alignment when suspicious hallucination states are detected, encouraging the model to re-examine salient visual evidence at critical reasoning stages. Extensive experiments across six multimodal reasoning benchmarks spanning nine distinct evaluation settings demonstrate that our approach delivers robust improvements in reasoning accuracy and hallucination robustness, while providing new insights into the generation dynamics underlying MLLM failures. The code is available at: https://github.com/jden4524/SelfRetrospectiveDecoding.

Solutions based on large language models (LLMs) often rely on temperature sampling to improve accuracy and stability by aggregating multiple samples from the completion distribution. However, this memoryless approach is inherently suboptimal: because it lacks awareness of prior generations and their evaluations, it produces an increasing proportion of semantically duplicate answers as more samples are drawn, leading to diminishing returns. To address this limitation, we introduce FLEET, a novel method that integrates a memory mechanism into the generation process. FLEET represents each generation as a sparse trajectory through states whose entropy exceeds a predefined threshold and uses these trajectories to infer per-token utility scores that adjust the logits. Benchmark evaluations demonstrate that FLEET achieves the same accuracy as the repeated sampling baseline, with a 3x speedup, and substantially improves accuracy on complex coding tasks (LiveCodeBench Pass@32 increases from 59.9% to 66.2%) under the same budget. Furthermore, in the greedy-decoding configuration evaluated here, the approach is deterministic and uses a single calibration pass to derive its principal hyperparameters, requiring only minimal modifications to existing LLM pipelines.

Uniform discrete flow permits repeated updates at every generation position. While continued revision supports correction of wrong tokens, it also exposes correct intermediate predictions to later errors. An experiment on Sudoku puzzles shows that 9.4% of generated cells are correct at an intermediate step but incorrect in the final output. We introduce generation order into uniform discrete flow through selective absorption, which fixes chosen predictions while preserving the uniform flow velocity at active positions. To prioritize reliable predictions for absorption, we propose Low-Entropy Discrete Flow (LEDFlow), a training-free sampler that adaptively orders absorption by local entropy. By decomposing absorption error into joint dependence and conditional prediction terms, we show that, under entropy-error regularity, selecting the lowest-entropy positions under a fixed absorption count minimizes an upper bound on the conditional term. We further analyze sensitivity of global lookahead, whose worst-case decision-error bound grows with lookahead window under an imperfect denoiser. Across reasoning benchmarks, LEDFlow attains 0.845 Nikoli Sudoku solve accuracy, with largest gains on strongly constrained tasks. On a text-to-image generation benchmark it attains the best overall score among decode-time samplers, and on multimodal understanding it improves over the default sampler on all six benchmarks, at an inference cost comparable to standard flow sampling.

Large language models (LLMs) achieve remarkable generative performance, yet their output quality is dependent on the decoding strategy. While sampling-based methods (e.g., top-k, nucleus) and search-and-select based methods (e.g., beam search, best-of-n, majority voting) can improve upon greedy decoding, both approaches suffer from limitations: sampling generally commits to a single path, while search often expends excessive computation regardless of task complexity. To address these, we introduce Entropy-informed decoding (EDEN), a plug-and-play, model-agnostic decoding framework that adaptively allocates computation based on the model's own uncertainty, approximating higher-width beam search with fewer expansions. At each generation step, EDEN estimates the entropy of the output token distribution and adjusts the branching factor monotonically with the entropy, expanding more candidates in high-entropy regions and following a greedier path in low-entropy regions, improving token efficiency. Experiments across complex tasks, including mathematical reasoning, code generation, and scientific questions, demonstrate that EDEN consistently improves output quality over existing decoding strategies, achieving better accuracy-expansion trade-offs than fixed-width beam search. By treating next-token selection as a noisy maximisation problem, we prove that branching factors monotone in entropy are guaranteed to find better (i.e. more probable) continuations than any fixed branching factor within the same total expansion budget, and derive explicit regret rates characterising the benefit of the adaptive allocation.

Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive (AR) models for language modeling, allowing flexible generation order and parallel generation of multiple tokens. However, this flexibility introduces a challenge absent in AR models: the decoding strategy -- which determines the order and number of tokens generated at each iteration -- critically affects sampling efficiency. Among decoding strategies explored in practice, confidence-based methods, which adaptively select which and how many tokens to unmask based on prediction confidence, have shown strong empirical performance. Despite this success, our theoretical understanding of confidence-based decoding remains limited. In this work, we develop the first theoretical analysis framework for confidence-based decoding in DLMs. We focus on an entropy sum-based strategy that continues unmasking tokens within each iteration until the cumulative entropy exceeds a threshold, and show that it achieves $\varepsilon$-accurate sampling in KL divergence with an expected number of iterations $\widetilde O(H(X_0)/\varepsilon)$, where $H(X_0)$ denotes the entropy of the target data distribution. Notably, this strategy yields substantial sampling acceleration when the data distribution has low entropy relative to the sequence length, while automatically adapting to the intrinsic complexity of data without requiring prior knowledge or hyperparameter tuning. Overall, our results provide a theoretical foundation for confidence-based decoding and may inform the design of more efficient decoding strategies for DLMs.

Decoding strategies play a central role in shaping the reasoning ability of large language models (LLMs). Traditional methods such as greedy decoding and beam search often suffer from error propagation, while sampling-based approaches introduce randomness without adequate robustness. Self-consistency improves reliability by aggregating multiple rollouts, but incurs significant computational overhead. We propose an entropy-guided decoding framework that introduces token-level adaptivity into generation. At each step, the model computes the entropy of the token distribution, identifies high-uncertainty positions, and selectively branches on these vulnerable points. A dynamic pool of partial rollouts is maintained and expanded until solutions are completed, concentrating computation where uncertainty is greatest and avoiding unnecessary exploration in confident regions. To enable efficient termination, we apply a rollout-level Entropy After </Think> (EAT) stopping criterion by performing entropy evaluation after the full reasoning trace, rather than incrementally at every step. Experiments on GSM8K, AMC2023, and their perturbed variants demonstrate that our method achieves consistently strong accuracy. Notably, on smaller LLMs, performance is comparable to GPT-5 while operating at a fraction of the cost.

Recent advancements in multimodal large reasoning models (MLRMs) have significantly improved performance in visual question answering. However, we observe that transition words (e.g., because, however, and wait) are closely associated with hallucinations and tend to exhibit high-entropy states. We argue that adequate contextual reasoning information can be directly extracted from the token probability distribution. Inspired by superposed representation theory, we propose leveraging latent superposed reasoning to integrate multiple candidate semantics and maintain latent reasoning trajectories. The hypothesis is that reliance on discrete textual inputs may drive the model toward sequential explicit reasoning, underutilizing dense contextual cues during high-entropy reasoning stages. Therefore, we propose constructing rich semantic representations from the token probability distributions to enhance in-context reasoning. With this goal, we present Latent Entropy-Aware Decoding (LEAD), an efficient plug-and-play decoding strategy that leverages semantic context to achieve reliable reasoning. The heart of our method lies in entropy-aware reasoning mode switching. The model employs probability-weighted continuous embeddings under high-entropy states and transitions back to discrete token embeddings as entropy decreases. Moreover, we propose a prior-guided visual anchor injection strategy that encourages the model to focus on visual information. Extensive experiments show that LEAD effectively mitigates hallucinations across various MLRMs on multiple benchmarks.

Speculative decoding (SD) accelerates large language model (LLM) inference by using a lightweight draft model to propose tokens and a stronger target model to verify them. However, standard SD is mainly designed for acceleration, and its output quality is typically constrained by the target model. In this work, we propose Entropy-Aware Speculative Decoding (EASD), a lightweight and training-free extension of SD that improves reasoning quality through token-level entropy-guided rejection. EASD detects cases where both draft and target models exhibit high uncertainty while strongly overlapping in their top predictions. In such uncertain-agreement cases, EASD rejects the aligned token and resamples from the target distribution, preventing low-confidence errors from propagating. Experiments on challenging reasoning benchmarks show that EASD consistently improves accuracy over standard SD and reward-guided variants while maintaining comparable inference efficiency. Notably, EASD can surpass the standalone performance of the target model, suggesting that speculative decoding can serve not only as an acceleration method but also as an effective mechanism for improving reasoning quality. The code is available at https://github.com/ECNU-Text-Computing/EASD.