Language Model Decoding

Diffusion large language models promise parallel token generation, yet inference remains bottlenecked by deciding which masked tokens can be safely committed together. Fast-dLLM addressed this with KV caching and confidence-guided parallel decoding, but its decoding theory uses a homogeneous high-confidence assumption that effectively reduces each candidate set to its weakest selected token. We argue that this leaves speed on the table because real decoding steps exhibit heterogeneous confidence profiles. We propose \textbf{Fast-dLLM++}, a training-free extension that introduces \emph{Fréchet profile decoding}: selecting parallel commit sets from the full sorted confidence profile rather than a single worst-case confidence. The resulting rule is a heterogeneous-confidence generalization of Fast-dLLM's factor selector and it recovers the previous rule exactly in the equal-confidence case and adds a provable \emph{heterogeneity bonus} when the selected tokens have uneven confidences. Fast-dLLM++ leaves the model, diffusion process, and cache implementation entirely unchanged, making it a drop-in replacement for existing Fast-dLLM decoding. Experiments on GSM8K, MATH, HumanEval, and MBPP with the LLaDA-8B model show that the theoretical improvement translates directly into empirical gains: profile-aware selection improves the accuracy--throughput frontier by exploiting safe parallelism that weakest-token rules miss, achieving up to 37% higher throughput at comparable accuracy. Our code release is at https://github.com/Ringo-Star/FastdLLM_plusplus.

Order-agnostic language models (OALMs), including discrete diffusion language models (dLLMs), are trained to predict masked tokens under arbitrary conditioning sets, allowing sequences to be generated or scored under arbitrary reveal orders at inference time. In LLaDA-2.1, we report three findings. First, the learned conditionals are not exact factorizations of a coherent joint distribution: changing only the reveal order shifts target log-likelihood by up to 0.49 nats/token, so likelihood alone mixes content difficulty with path-dependent artifacts. Second, although confidence-first (CF) decoding is order-agnostic, its reveal orders are close to left-to-right (L2R) on content tokens. Third, we propose a complementary diagnostic based on the shape of the confidence trace. A uniform-spreading theorem shows that, at fixed total likelihood, target recoverability is maximized when per-step confidence is spread uniformly; the resulting deviation motivates $\mathrm{Var}(\log q_t)$ as a diagnostic for comparing decoding paths. Across C4 and four downstream benchmarks, low variance separates structured paths from random ordering, and variance is consistently associated with downstream correctness. These results support reporting mean confidence and confidence variance jointly when comparing OALM decoding paths.

Large Language Models (LLMs) have achieved strong performance across diverse natural language tasks, yet their outputs often suffer from hallucinations -- content that is misaligned with factual information. In this work, we conduct a comprehensive layer-wise analysis of the decoding process and reveal that hallucinations tend to originate from deeper decoder layers. To address this issue, we introduce \textbf{DeLask} (\textbf{De}coder \textbf{La}yer \textbf{Sk}ipping), a novel decoding framework that dynamically skips layers prone to producing hallucinations. DeLask leverages the theoretical insight that the forward computation of an $L$-layer Transformer is conditionally equivalent to $L$ steps of gradient descent. We define a \emph{driftance value} by computing the cosine similarity between gradients derived from consecutive decoder steps, identifying problematic layers when the descent direction reverses. Rather than discarding such layers entirely, DeLask partially aggregates their hidden states with preceding layers, thereby preserving consistency while suppressing erroneous signals. Extensive experiments across diverse LLMs and benchmarks demonstrate that DeLask consistently mitigates hallucinations and enhances overall reliability, providing a lightweight and generalizable decoding framework for improving the robustness of large-scale language models.

Large language models hallucinate even when the answer lies within their parameters. While inference-time scaling can surface this latent knowledge, the most effective methods require supervision: a trained verifier or reward model. We ask what can be done with only a base language model: which intrinsic signal best identifies correct outputs, and how should it be decoded? We cast this as a score~$\times$~decoder grid pairing four scores (perplexity, contrastive, power-distribution likelihood, and self-verification) with three decoding families (optimization, sampling, consensus), and evaluate every cell on MATH500 with the base and instruction-tuned Qwen3-1.7B. While self-verification, which prompts the model to judge its own answer and is sharpened by a training-free virtual-thinking prefix, works well in most settings, no score has a fixed quality: its value depends on the decoder that consumes it and on model capability. When no supervision is available, the score and the decoding family must be chosen together.

As retrieval-augmented generation (RAG) systems scale, it becomes increasingly challenging to ensure faithful grounding in external evidence. Large language models may still prioritize parametric knowledge over retrieved information when conflicts arise. We propose a novel training-free decoding framework, \emph{Grounded Decoding}, designed to improve factual consistency in RAG without modifying model parameters. Unlike standard approaches that rely on a single conditional distribution, our method constructs two matched-prompt distributions at every generation step: (1) a full RAG distribution conditioned on the query, retrieved documents, and generated prefix, and (2) a retrieval-only distribution conditioned solely on retrieved evidence and the same prefix. The final next-token distribution is derived as the unique solution to a KL-barycenter objective over the probability simplex, yielding a normalized geometric fusion of the two distributions.This formulation naturally recovers standard RAG when the grounding weight is zero and smoothly shifts probability mass toward retrieved evidence as grounding strength increases. We further introduce a conflict-aware adaptive weighting scheme that dynamically adjusts grounding based on distributional disagreement and retriever confidence. Experiments on ALCE, Natural Questions, and FActScore demonstrate consistent improvements in factual accuracy and citation quality over standard RAG and competitive decoding-time baselines, while maintaining fluency. Our results indicate that probability-level fusion provides a strong and efficient alternative to logit-level intervention methods for faithful RAG decoding.

Temperature-zero BF16 LLM inference is often treated as reproducible, yet the same request can emit different tokens when decoded alone or inside a larger batch. Existing fixes use batch-invariant operators or LLM-42's per-token verification, incurring cost even when most steps are stable. We ask whether verification can be applied exclusively to flipped tokens. Across five models, batch-induced token flips are sparse on the flip-rate benchmarks: on MATH500, Llama-3.1-8B flips on $0.48\%$ of synchronous decode steps, and all tested models stay within the 0.3-1.3% range on MATH500, GSM8K, and HumanEval. K/V perturbations remain flat before flips, while low top-1/top-2 logit margins expose much of the flip risk. MarginGate turns these observations into a verifier policy: it keeps BF16 decoding on high-margin steps, verifies only low-margin steps, and repairs confirmed mismatches by replacing the current K/V column. We evaluate on four datasets, calibrating on MATH500 and transferring to GSM8K, SharedGPT, and HumanEval. MarginGate restores 100% sequence-level deterministic decoding on Llama-3.1-8B and Qwen2.5-14B with 18.56%/15.05% verifier trigger rates, reducing LLM-42's latency increment by 2.23x/1.99x relative to always-on verification. On DSR1-Distill-Qwen-7B, the same policy reaches determinism in a harder regime at 49.50% triggers.

Large language models (LLMs) are increasingly used to generate software artifacts across many software engineering (SE) tasks, yet ensuring the semantic validity of these artifacts remains a fundamental challenge. Existing constrained decoding techniques can enforce syntactic correctness and, in some cases, specific semantic rules, but lack a general representation that bridges LLM-generated text with the reasoning required for semantic validation in SE. In this paper, we propose projectional decoding, a novel conceptual framework that integrates domain semantics directly into the generation process by maintaining, alongside text, a partial graph model as the primary artifact representation throughout generation. This abstract representation enables incremental semantic validation by explicitly capturing uncertainty and natively supporting error detection, while guiding generation toward semantically valid outputs with provable guarantees. We present preliminary results on a program generation task which demonstrate the potential of this approach to improve the semantic validity of LLM-generated artifacts. We also discuss how projectional decoding can enable verifiable automation with LLMs across various SE activities.

While LLM-based Automatic Speech Recognition (ASR) achieves high accuracy, its speed is limited by sequential autoregressive decoding. Diffusion Language Models (DLMs) offer a parallel alternative, yet their decoding strategies remain under-explored in ASR contexts. This paper analyzes three decoding schemes for DLM-based ASR: fixed-number, static confidence threshold, and dynamic confidence threshold. We introduce a round-wise analysis of decoding progress using Negative Log-Likelihood-based uncertainty as a proxy for prediction reliability. Our results show that both threshold-based strategies provide a better accuracy-speed trade-off than fixed-number schemes. This behavior is associated with the more concentrated confidence distribution observed in the evaluated ASR settings: many tokens reach high confidence early, enabling multiple tokens to be committed in early decoding rounds while lower-confidence tokens are deferred to later rounds. The static-threshold strategy achieves accuracy close to autoregressive decoding at lower decoding cost.

Chain-of-thought reasoning helps autoregressive models solve complex problems by generating intermediate steps that support later predictions. Masked diffusion models (MDMs) offer a similar opportunity through arbitrary-order generation: they can ideally reveal intermediate results along logical dependencies. In practice, however, standard decoding simply prioritizes high-confidence tokens, which need not align with this dependency order. We identify this discrepancy as the \emph{confidence shortcut}: models commit with high certainty to plausible tokens while neglecting long-range dependencies. In multi-digit addition, models predict higher-order digits without properly tracking carries through long chains. Controlled pretraining across diverse reasoning tasks confirms that confidence-guided ordering often selects suboptimal sequences, and confidence-aligned training schemes can exacerbate these failures---for example, increasing addition error rates by an order of magnitude. Our findings caution against relying solely on confidence to choose generation orders and against training objectives that reinforce this preference. The experimental code is available at https://github.com/jinha2536/mdm-arithmetic.

Diffusion language models decode text by iteratively denoising masked token sequences, making the choice of which positions to decode a central inference-time decision. Most training-free decoding strategies use model confidence for position selection, assuming that high-confidence positions are ready to be decoded. In this work, we revisit this assumption by studying when confidence misleads fully non-autoregressive (fully non-AR) decoding. EOT tokens can receive high confidence and cause incomplete generation; inserting a suffix anchor can mitigate this issue but introduces local overconfidence near the anchor, causing anchor-adjacent tokens to be decoded too early. To address these issues, we propose Suffix-Anchored Confidence Modulation, a simple training-free method that inserts a short suffix anchor to encourage response completion and modulates confidence near the anchor according to decoding progress. This preserves the response-completion benefit of suffix anchoring while reducing premature decoding of anchor-adjacent tokens. Across text-only reasoning, vision-language reasoning, and code-generation benchmarks, our method consistently improves confidence-based fully non-AR decoding, outperforms explicit EOT suppression, and preserves the parallel decoding advantage of fully non-AR generation.

With the rapid progress of large language models (LLMs), reliably evaluating the capabilities of pre-trained LLMs has become increasingly important. The challenge is that base pre-trained models are optimized for next-token prediction and often fail to follow instructions or produce well-formed answers under standard prompting and direct decoding. As a result, benchmark performance can conflate model capability with decoding-induced failures to produce task-oriented outputs, while exposing such behavior often relies on costly post-training. Recent decodingonly approaches attempt to reshape output distributions, but such methods can be inefficient and brittle across open-ended tasks. To address these limitations, we propose Energy-Based Decoding (EBD), a training-free, reward-guided framework for activating task-oriented behaviors from frozen pre-trained LLMs across both open-ended and objective tasks. EBD augments decoding with an external lightweight reward model, steering generations toward high-utility responses while anchoring them to the pre-trained model prior through a reward-tilted target distribution. We show that EBD shifts base-model outputs toward more instructionfollowing behavior, increasing behavioral similarity to post-trained counterparts and enabling a fairer inference-time evaluation of accessible pre-trained-model behavior. Empirically, EBD outperforms baselines across five models and six benchmarks, improving Qwen3-8B-Base on AlpacaEval2.0 from 8.8 to 44.5, reducing Mistral-7B Math500 latency by 18.9x relative to prior decoding work, and remaining robust to reward-model size.

Recent advances in large language models have accelerated open-vocabulary EEG-to-imagined-text decoding, where non-invasive neural activity recorded during visual perception is translated into coherent natural language descriptions of viewed stimuli. However, existing systems remain highly vulnerable to biological noise, where corrupted neural projections induce hallucinated or semantically unstable generation in frozen language models. We introduce SYNAPSE (Symbolic Neural Alignment for Precise Semantic Extraction), a lightweight neuro-symbolic framework that stabilizes neural text generation through inference-time symbolic regularization. By purifying EEG-derived semantic candidates using commonsense graph structure and latent exemplars, SYNAPSE improves semantic stability without end-to-end LLM fine-tuning. Experiments across popular EEG decoding benchmarks and multiple frozen LLM backends demonstrate consistent gains over unconstrained prompting baselines, robustness under object-label ablation, and performance commensurate with substantially more resource-intensive fine-tuned systems, while preserving biometric privacy by localizing raw EEG processing entirely within the encoder stack.

Modern Large Language Models (LLMs) are often criticized for producing repetitive and homogeneous text, despite possessing vast latent vocabularies. While previous research has focused on model knowledge and training data, we investigate the role of decoding mechanics in suppressing linguistic diversity. We introduce the Word Coverage Score (WCS), a metric that quantifies the extent to which contextually appropriate human vocabulary is mathematically pruned by standard sampling filters (e.g., Top-$p$, Top-$k$, and Min-$p$). Rather than assessing static knowledge, the WCS measures the lexical survival rate of low-frequency, high-information human words as a function of sampling parameters. By auditing open-weight models on human-authored corpus fragments, we identify which logical lexical choices are rendered unreachable by the decoder, even when they reside within the probability space. Our results provide quantitative evidence that industry-standard sampling defaults act as unintended censorship mechanisms, smoothing the unique textures of human expression into a homogenized discourse. The WCS offers a rigorous framework for optimizing the trade-off between text coherence and lexical richness, providing a diagnostic tool for preserving the diversity of human language in generative models.

Diffusion-based multimodal large language models (dMLLMs) decode by iteratively predicting tokens at multiple masked positions in parallel. This turns each decoding step into a position-selection problem: the model must choose not only which predictions are reliable in isolation, but also which positions should be committed together as context for later decoding steps. Existing confidence-based decoding ranks masked positions independently and commits the top-K positions, largely ignoring whether the committed tokens provide complementary visual grounding. We identify a step-level limitation of this strategy in multimodal settings: high-confidence tokens selected in the same step can rely on overlapping visual grounding, introducing visual redundancy among the committed tokens and leaving less complementary visual grounding available for later decoding. To quantify this effect, we introduce the Visual Redundancy Index (VRI), which measures visual grounding overlap among tokens committed in parallel. To control this redundancy during decoding, we propose Visual-Redundancy-Controlled Decoding (VRCD), a training-free inference-time decoding method that uses token-to-image attention to prioritize visually complementary positions. Across diverse multimodal benchmarks, VRCD reduces visual redundancy and remaining-position entropy with modest runtime overhead. In longer decoding experiments, it also achieves relative accuracy gains of up to 18.8% on M^3CoT and 6.9% on MMBench over confidence-based decoding. Code is available at https://github.com/infiniteYuanyl/VRCD.

Backtesting large language models (LLMs) on historical financial data is unreliable because pre-training cuts off after the events happened. An LLM trained in 2024 already "knows" which way 2018-2020 stocks moved. We name this failure parametric look-ahead bias and propose FinCAD, an inference-time adaptation of Context-Aware Decoding that suppresses an LLM's memory of historical outcomes without retraining. FinCAD pairs an adversarial bias-discovery pipeline that learns a model-specific memory-activating prior prompt with an entity- and date-adaptive rule that scales the CAD strength to per-(entity, date) memorisation, so the penalty fires on memorised in-sample dates and decays to zero out-of-sample. Across five 7-14B LLMs and five mega-cap equities, FinCAD cuts in-sample backtest returns by up to -67.1% on memorised dates while leaving 2025 out-of-sample returns within $8K and Sharpe within 0.10 of baseline, and preserves general-purpose reasoning within 1.7 pts. On an eleven-model leaderboard, it raises the in-sample / out-of-sample Spearman correlation from +0.779 to +0.846, recovering rankings that genuinely predict out-of-sample performance.

Chain-of-thought (CoT) reasoning has become the default strategy for enhancing LLM capabilities, yet its application raises a fundamental question: when is explicit reasoning actually beneficial? Empirical evidence reveals a striking paradox: CoT often provides marginal or even negative gains on factual and open-ended tasks while multiplying token consumption. In this work, we show that LLM reasoning is not a static property of tasks or models, but a \emph{dynamic decoding state} that emerges during generation. Through systematic analysis, we find early-stage entropy dynamics provide a reliable signal of this state: tasks benefiting from CoT exhibit consistent entropy reduction, while others display unstable or increasing patterns. This behavior can be interpreted as a phase-transition-like shift from a high-entropy exploratory regime to a low-entropy structured reasoning regime. Based on these insights, we propose \textbf{EDRM} (Entropy Dynamics-based Reasoning Manifold), a lightweight and training-free routing framework that leverages early decoding entropy to adaptively select inference strategies. EDRM embeds entropy trajectories into a compact and interpretable manifold representation, enabling both zero-shot deployment and fine-grained instance-level adaptation. Across 15 benchmarks and 4 LLMs of varying scales and architectures, EDRM consistently outperforms static baselines. At the dataset level, EDRM achieves \textbf{41--55%} token reduction while improving accuracy with as few as 50 calibration samples. At the instance level, it further improves accuracy by up to \textbf{4.7%} while maintaining \textbf{27--45%} token savings. These results suggest that reasoning should be invoked selectively rather than by default, and demonstrate the effectiveness of entropy-driven decoding control for efficient and adaptive LLM inference.

Test-time scaling is an important mechanism for improving large language models, especially on tasks with deterministic verifiers. Code translation is a canonical example: the source program constrains valid outputs, while compilers, type check- ers, and behavioral checks provide exact pass/fail feedback. Existing approaches typically apply these verifiers only after generation, which is inefficient because early errors corrupt the autoregressive context and are rarely corrected later. We introduce Decoding Time Verification (DTV), a framework that treats structural boundaries as meta steps for verifier-guided decoding. DTV interleaves generation with verifier calls under a state-machine controller that enforces valid prefixes, using structural-boundary checks and structure-aware rollback to prevent error propagation while reducing wasted tokens. We evaluate DTV on C-to-Rust and JavaScript-to-TypeScript translation. Using Qwen3-4B as the primary generator under matched token budgets, DTV improves pass rates from 72.3% to 82.0% on C-to-Rust and from 33.3% to 46.0% on JavaScript-to-TypeScript relative to matched self-refinement baselines, while using fewer tokens per case; the same trend largely transfers to Gemma-4-E4B. In the evaluated cost-matched grid, DTV achieves a more favorable pass-rate-cost tradeoff than post-hoc verification or sampling-based scaling. These results show that verifier-guided decoding is an effective use of inference-time compute for code translation.

While large language models (LLMs) are trained to align with human values, their generations may still violate safety constraints. A growing line of work addresses this problem by modifying the model's sampling policy at decoding time using a safety reward. However, existing decoding-time steering methods often intervene unnecessarily, modifying generations that would have been safe under the base model. Such unnecessary interventions are undesirable, as they can distort key properties of the base model such as helpfulness, fluency, style, and coherence. We propose a new test-time steering method designed to reduce such unnecessary interventions while improving the safety of unsafe responses. Our approach filters tokens using a value-based safety criterion and provides an explicit bound on the probability of false interventions. A single threshold hyperparameter controls this bound, allowing practitioners to trade off higher rates of unnecessary intervention for better output safety. Across multiple datasets and experiments, we show that our value-filtered decoding method outperforms existing baselines, achieving better trade-offs between safety, helpfulness, and similarity to the base model.

Flow Language Models (FLMs) are a recently introduced class of language models which adapt continuous flow matching for one-hot encoded token sequences. Their denoisers have a special structure absent from generic continuous diffusion models: each block of the denoising mean is a posterior marginal distribution over the clean token at that position. Standard DDPM-style samplers collapse these marginals to a single conditional-mean endpoint and bridge toward this simplex-valued point, which is generally not a valid one-hot sequence. We argue that the natural sampler for an FLM is instead posterior-predictive. At each reverse step, we sample a clean one-hot endpoint from the factorized posterior defined by the FLM token marginals, and then sample the next continuous state from the analytic Ornstein--Uhlenbeck bridge conditioned on that endpoint. The method is training-free, uses the same model evaluations as standard sampling, and gives a principled interface for token-level decoding controls such as temperature scaling and nucleus truncation. We show that, under exact posterior marginals, the endpoint approximation error is exactly the conditional multi-information among token positions. The induced one-step bridge kernel preserves all token-wise posterior-predictive marginals and loses only the residual cross-position dependence. Finally, we prove a Girsanov path-space comparison showing that the marginal-conditioned bridge has a no-larger denoising-error term than the frozen conditional-mean bridge, with strict improvement whenever intermediate coordinate-wise bridge observations reveal additional information about the clean token. Experiments with FLMs show that the sampler improves the quality--diversity tradeoff. Code is available at: github.com/imbirik/mcb.

We introduce Orthrus, a simple and efficient dual-architecture framework that unifies the exact generation fidelity of autoregressive Large Language Models (LLMs) with the high-speed parallel token generation of diffusion models. The sequential nature of standard autoregressive decoding represents a fundamental bottleneck for high-throughput inference. While diffusion language models attempt to break this barrier via parallel generation, they suffer from significant performance degradation, high training costs, and a lack of rigorous convergence guarantees. Orthrus resolves this dichotomy natively. Designed to seamlessly integrate into existing Transformers, the framework augments a frozen LLM with a lightweight, trainable module to create a parallel diffusion view alongside the standard autoregressive view. In this unified system, both views attend to the exact same high-fidelity Key-Value (KV) cache; the autoregressive head executes context pre-filling to construct accurate KV representations, while the diffusion head executes parallel generation. By employing an exact consensus mechanism between the two views, Orthrus guarantees lossless inference, delivering up to a 7.8x speedup with only an O(1) memory cache overhead and minimal parameter additions.

Large language models accumulate extensive parametric knowledge through pre-training. However, knowledge conflicts occur when outdated or incorrect parametric knowledge conflicts with external knowledge in the context. Existing methods address knowledge conflicts through contrastive decoding, but in conflict-free scenarios, static approaches disrupt output distribution. Other dynamic decoding methods attempt to measure the degree of conflict but still struggle with complex real-world situations. In this paper, we propose a two-stage decoding method called Dynamic Cognitive Reconciliation Decoding (DCRD), to predict and mitigate context-memory conflicts. DCRD first analyzes the attention map to assess context fidelity and predict potential conflicts. Based on this prediction, the input is directed to one of two decoding paths: (1) greedy decoding, or (2) context fidelity-based dynamic decoding. This design enables DCRD to handle conflicts efficiently while maintaining high accuracy and decoding efficiency in conflict-free cases. Additionally, to simulate scenarios with frequent knowledge updates, we constructed ConflictKG, a knowledge conflict QA benchmark. Experiments on four LLMs across six QA datasets show that DCRD outperforms all baselines, achieving state-of-the-art performance.

Power capping is the standard GPU energy lever in LLM serving, and it appears to work: throughput drops, power readings fall, and energy budgets are met. We show the appearance is illusory for the phase that dominates production serving: autoregressive decode. Across four attention paradigms -- GQA, MLA, Gated DeltaNet, and Mamba2 -- on NVIDIA H200, decode draws only 137--300,W on a 700,W GPU; no cap ever triggers, because memory-bound decode saturates HBM bandwidth rather than compute and leaves power headroom untouched. Firmware-initiated clock throttling compounds the illusion: these deviations can corrupt any throughput measurement that attributes them to the cap. SM clock locking dissolves both confounds. By targeting the lever that is actually on the critical path, clock locking Pareto-dominates power capping universally, recovering up to 32% of decode energy at minimal throughput loss. We identify three architecture-dependent DVFS behavioural classes and characterise a common energy pattern across novel attention replacements: a heavy prefill cost recouped by efficient decode, eventually halving total request energy relative to GQA at production batch sizes.

Diversity is essential for language-model applications ranging from creative generation to scientific discovery, yet modern LLMs often collapse into a narrow subset of plausible outputs. While prior work has developed benchmarks for measuring this lack of diversity, less is known about how the step-by-step probability distributions at inference time cause the problem. We introduce a validity--diversity framework that attributes diversity collapse to how an LLM allocates probability mass across valid and invalid continuations during decoding. This framework decomposes the bottleneck into two complementary forms of miscalibration. First, order calibration: valid tokens are not reliably ranked above invalid tokens, so rank-based cutoff rules must trade off between recovering valid continuations and admitting invalid ones. Second, shape calibration: probability mass is overly concentrated only on few valid continuations while having a heavy-tail of mixed valid and invalid tokens, so maintaining high validity limits diversity. We formalize both mechanisms and show that local failures compound across decoding steps, producing strong sequence-level losses in diversity. Empirically, we develop controlled diagnostics for probing these bottlenecks, including tasks with exactly known valid sets and oracle cutoff baselines. Across 14 language models spanning multiple families and scales, we find that diversity collapse is not merely a limitation of particular sampling heuristics, but a consequence of order and shape miscalibration in the LLM distribution.

LLM decoding often relies on the model's predictive distribution to generate an output. Consequently, misalignment with respect to the true generating distribution leads to suboptimal decisions in practice. While a natural solution is to calibrate the model's output distribution, for LLMs, this is ill-posed at the combinatorially vast level of free-form language. We address this by building on the insight that in many tasks, these free-form outputs can be interpreted in a semantically meaningful latent structure, for example, discrete class labels, integers, or sets. We introduce task calibration as a paradigm to calibrate the model's predictive distribution in the task-induced latent space. We apply a decision-theoretic result to show that Minimum Bayes Risk (MBR) decoding on the task-calibrated latent distribution is the optimal decoding strategy on latent model beliefs. Empirically, it consistently improves generation quality across different tasks and baselines. We also introduce Task Calibration Error (TCE), an application-aware calibration metric that quantifies the excess loss due to miscalibration. Our work demonstrates that task calibration enables more reliable model decisions across various tasks and applications.

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.

Reliable text generation is critical for deploying large language models (LLMs) in real-world applications, particularly in high-stakes domains such as medicine. To improve factual reliability, various inference-time methods have been proposed, including logit-level methods that modify token probability distributions and representation-level methods that manipulate intermediate model representations. However, most existing approaches operate on a single decoding trajectory, limiting their ability to explore alternative reasoning paths and making them susceptible to error accumulation. To address this limitation, we propose Adaptive Path-Contrastive Decoding (APCD), an adaptive multi-path contrastive decoding framework that improves factual reliability without model retraining or fine-tuning. APCD comprises two key components: Entropy-Driven Path Expansion, which adaptively expands the decoding process only at high-uncertainty decision points, and Divergence-Aware Path Contrast, which dynamically regulates contrastive interactions among parallel decoding paths based on their distributional divergence to balance diversity and coherence. We evaluate APCD on four LLM backbones across eight benchmarks spanning both general-domain and medical question answering tasks. Experimental results demonstrate that APCD consistently outperforms strong inference-time baselines in factual accuracy while maintaining competitive inference efficiency. These results demonstrate the robustness and generalizability of APCD across diverse models and tasks, highlighting its effectiveness as a practical multi-path decoding framework for reliable LLM deployment, particularly in high-stakes domains such as medicine. Code is available at https://github.com/zty-king/APCD.

Agents built on large language models (LLMs) rely on a range of reliability techniques, including retry, majority voting, and self-consistency, that have been developed in parallel rather than within a common analytical framework. We observe that an LLM sampled at temperature $T$ is a discrete stochastic channel $p(y \mid x)$ in the sense of Shannon's coding theory, and use this identity as the entry point for such a framework grounded in communication theory. Each of these techniques is a special case of one of six classical reliability operators: diversity combining, hybrid retransmission, iterative generator-critic decoding, rateless sampling, structured redundant verification, and difficulty-adaptive routing. Within the framework we give two closed-form results: a noise-variance threshold above which uniform averaging beats quality-weighted averaging, and a contractivity criterion for generator-critic refinement, consistent with a contractive-to-divergent transition we observe between 3B- and 14B-parameter models. We further introduce a cost-aware semantic-nearest-neighbor router whose single Lagrangian knob traverses the quality-cost frontier without retraining. Across six channel configurations spanning local and cloud models on 69 hard tasks, no fixed model-technique-budget choice dominates, motivating per-task allocation. On a 300-item hard split of MMLU, GSM8K, and HumanEval, our router occupies the full empirical Pareto frontier: at matched quality, its normalized cost is ${\approx}56$% lower than the strongest fixed technique; at matched normalized cost, it improves quality by ${\approx}7$% ($26$% over single-shot decoding). These results argue for consolidating these reliability techniques into a single tunable layer informed by channel coding.

A recurring pattern in "reasoning without training" is that base LLMs already assign non-trivial probability mass to correct multi-step solutions; the bottleneck is locating these modes efficiently at inference time. Power sampling provides a principled way to bias decoding toward such modes by targeting p_theta(x)^alpha with alpha > 1, but practical approximations must account for future-dependent correction factors that determine which prefixes remain promising. We introduce Auxiliary Particle Power Sampling (APPS), a blockwise particle algorithm for approximating the sequence-level power target with a bounded population of partial solutions. APPS propagates hypotheses in parallel using proposal-corrected power reweighting and refines their survival through future-value-guided selection at resampling boundaries. This redistributes finite compute across competing prefixes rather than committing to a single unfolding path, while providing a direct scaling knob in the particle count and predictable peak memory. We instantiate the future-value signal with short-horizon rollouts and also study an amortized variant that replaces rollouts with a lightweight learned selection head. AMore broadly, APPS improves the accuracy--runtime trade-off of training-free decoding, further supporting the view that inference-time power approximation can recover gains often attributed to post-training.

Large language models pick up social biases from the data they are trained on and carry those biases into downstream applications, often reinforcing stereotypes around gender, race, religion, disability, age, and socioeconomic status. The standard fixes (retraining on curated data or fine-tuning with human feedback) are expensive, need access to model weights, and risk degrading the model on other tasks. In this paper we take a different route: we debias the model at decoding time, treating bias mitigation as a structured search over candidate tokens without ever touching model weights. A separate Process Reward Model (PRM) acts as a judge, scoring each candidate for both fairness and fluency. We design three schemes of increasing sophistication (Best-of-N selection, Sequential critique-and-revise, and Constitutional self-audit) and evaluate them on four models (GPT-4o-mini, Llama 3.2 3B, Gemma 3 4B, Qwen 2.5 3B) across a 200-prompt bilingual benchmark in English and Urdu covering eight bias categories. Sequential debiasing proves the most effective, raising mean bias scores by up to +0.40 over baseline while preserving (and sometimes improving) fluency. We then extend all three schemes to open-ended generation, where each token is debiased on the fly, and introduce a lightweight Bias Guard gate that fires only on potentially biased words, keeping overhead near 2x for well-calibrated models. A formal overhead metric that separates generator cost from judge cost reveals that Best-of-N is effectively free on the generator side in a native implementation. GPT-4o-mini, included as a strong proprietary anchor, confirms that the framework scales with model capability; the three open-weight models show where current small-scale LLMs still struggle.

Generating diverse responses is crucial for test-time scaling of large language models (LLMs), yet standard stochastic sampling mostly yields surface-level lexical variation, limiting semantic exploration. In this paper, we propose Exploratory Sampling (ESamp), a decoding approach that explicitly encourages semantic diversity during generation. ESamp is motivated by the well-known observation that neural networks tend to make lower-error predictions on inputs similar to those encountered before, and incur higher prediction error on novel ones. Building on this property, we train a lightweight Distiller at test time to predict deep-layer hidden representations of the LLM from its shallow-layer representations to model the LLM's depth-wise representation transitions. During decoding, the Distiller continuously adapts to the mappings induced by the current generation context. ESamp uses the prediction error as a novelty signal to reweight candidate token extensions conditioned on the current prefix, thereby biasing decoding toward less-explored semantic patterns. ESamp is implemented with an asynchronous training--inference pipeline, with less than 5% worst case overhead (1.2% in the optimized release). Empirical results show that ESamp significantly boosts the Pass@k efficiency of reasoning models, showing superior or comparable performance to strong stochastic and heuristic baselines. Notably, ESamp achieves robust generalization across mathematics, science, and code generation benchmarks and breaks the trade-off between diversity and coherence in creative writing. Our code has released at: https://github.com/LinesHogan/tLLM.