Language Model Decoding

Self-consistency boosts inference-time performance by sampling multiple reasoning traces in parallel and voting. However, in constrained domains like math and code, this strategy is compute-inefficient because it samples with replacement, repeatedly revisiting the same high-probability prefixes and duplicate completions. We propose Distinct Leaf Enumeration (DLE), a deterministic decoding method that treats truncated sampling as traversal of a pruned decoding tree and systematically enumerates distinct leaves instead of sampling with replacement. This strategy improves inference efficiency in two ways. Algorithmically, it increases coverage of the truncated search space under a fixed budget by exploring previously unvisited high-probability branches. Systemically, it reuses shared prefixes and reduces redundant token generation. Empirically, DLE explores higher-quality reasoning traces than stochastic self-consistency, yielding better performance on math, coding, and general reasoning tasks.

Structured sequence generation often requires a model to satisfy several input-derived constraints in a single output. Standard decoding methods may assign high probability to fluent continuations while placing low mass on continuations that realize all required anchors jointly. We study this regime as a rare-event sequential inference problem. LatticeBridge combines a compact prefix language model, instance-compiled surface automata, and a twisted sequential Monte Carlo (SMC) decoder with resampling, multilevel splitting, and a source-support proposal term derived from instance-provided phrases. The constraint representation is compiled from each input instance and does not rely on manually curated lexical classes. On 2,610 attainable validation tasks spanning CommonGen, E2E NLG, and WikiBio, the particle decoder improves exact anchor satisfaction and mean anchor coverage over greedy, beam-filtered, and best-of-k ancestral baselines under a shared proposal model. Since exact anchor satisfaction alone does not rule out unsupported attribute substitutions, the evaluation reports required-anchor coverage, source coverage, source-intrusion diagnostics, overlap, runtime, and particle statistics jointly. The benchmark characterizes the faithfulness-overlap-latency frontier under a fixed proposal model.

Query auto-completion (QAC) has been widely studied in the context of web search, yet remains underexplored for in-document search, which we term DocQAC. DocQAC aims to enhance search productivity within long documents by helping users craft faster, more precise queries, even for complex or hard-to-spell terms. While global historical queries are available to both WebQAC and DocQAC, DocQAC uniquely accesses document-specific context, including the current document's content and its specific history of user query interactions. To address this setting, we propose a novel adaptive trie-guided decoding framework that uses user query prefixes to softly steer language models toward high-quality completions. Our approach introduces an adaptive penalty mechanism with tunable hyperparameters, enabling a principled trade-off between model confidence and trie-based guidance. To efficiently incorporate document context, we explore retrieval-augmented generation (RAG) and lightweight contextual document signals such as titles, keyphrases, and summaries. When applied to encoder-decoder models like T5 and BART, our trie-guided framework outperforms strong baselines and even surpasses much larger instruction-tuned models such as LLaMA-3 and Phi-3 on seen queries across both seen and unseen documents. This demonstrates its practicality for real-world DocQAC deployments, where efficiency and scalability are critical. We evaluate our method on a newly introduced DocQAC benchmark derived from ORCAS, enriched with query-document pairs. We make both the DocQAC dataset (https://bit.ly/3IGEkbH) and code (https://github.com/rahcode7/DocQAC) publicly available.

Large language models (LLMs) can answer questions and summarize documents when conditioned on external contexts (e.g., retrieved evidence), yet context use remains unreliable: models may overwrite an already-correct output (neutral regression) even when the context is non-informative. We formalize neutral regression as a do-no-harm requirement and quantify it by measuring accuracy drops on baseline-correct items under answer-consistent contexts. We propose No-Worse Context-Aware Decoding (NWCAD), a decode-time adapter built on a two-stream setup with a two-stage gate: it backs off to no-context decoding when the context is non-informative, and otherwise uses context-conditioned decoding with a CAD-style fallback under uncertainty. We evaluate NWCAD on benchmarks that separate do-no-harm reliability from context utilization (accuracy gains on genuinely helpful contexts). NWCAD prevents neutral regression on baseline-correct items while preserving strong context-driven accuracy on helpful contexts.

The quality of text generated by large language models depends critically on the decoding sampling strategy. While mainstream methods such as Top-$k$, Top-$p$, and Min-$p$ achieve a balance between diversity and accuracy through probability-space truncation, they share an inherent limitation: extreme sensitivity to the temperature parameter. Recent logit-space approaches like Top-$nσ$ achieve temperature invariance but rely on global statistics that are susceptible to long-tail noise, failing to capture fine-grained confidence structures among top candidates. We propose \textbf{Min-$k$ Sampling}, a novel dynamic truncation strategy that analyzes the local shape of the sorted logit distribution to identify "semantic cliffs": sharp transitions from high-confidence core tokens to uncertain long-tail tokens. By computing a position-weighted relative decay rate, Min-$k$ dynamically determines truncation boundaries at each generation step. We formally prove that Min-$k$ achieves strict temperature invariance and empirically demonstrate its low sensitivity to hyperparameter choices. Experiments on multiple reasoning benchmarks, creative writing tasks, and human evaluation show that Min-$k$ consistently improves text quality, maintaining robust performance even under extreme temperature settings where probability-based methods collapse. We make our code, models, and analysis tools publicly available.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable reasoning capabilities yet continue to suffer from hallucination, where generated text contradicts visual content. In this paper, we introduce Dual-Anchor Introspective Decoding (DaID), a novel contrastive decoding framework that dynamically calibrates each token generation by mining the model's internal perceptual discrepancies. Specifically, DaID identifies a Spotlight layer to amplify visual factual signals and a Shadow layer to suppress textual inertia. By leveraging visual attention distributions to guide this dual-anchor selection process, our method ensures precise, token-specific adaptation. Experimental results across multiple benchmarks and MLLMs demonstrate that DaID significantly mitigates hallucination while enhancing general reasoning capabilities.

Reasoning in knowledge-intensive domains remains challenging as intermediate steps are often not locally verifiable: unlike math or code, evaluating step correctness may require synthesizing clues across large external knowledge sources. As a result, subtle errors can propagate through reasoning traces, potentially never to be detected. Prior work has proposed process reward models (PRMs), including retrieval-augmented variants, but these methods operate post hoc, scoring completed trajectories, which prevents their integration into dynamic inference procedures. Here, we introduce Process Reward Agents (PRA), an inference-time method for providing domain-grounded, online, step-wise rewards to a frozen policy. In contrast to prior retrieval-augmented PRMs, PRA enables search-based decoding to rank and prune candidate trajectories at every generation step. Experiments on multiple medical reasoning benchmarks demonstrate that PRA consistently outperforms strong baselines, achieving 81.9% accuracy on MedQA with Qwen3-4B, a new state of the art at the 4B scale. Importantly, PRA generalizes to unseen frozen policy models ranging from 0.5B to 8B parameters, improving their accuracy by up to 25.7% without any policy model updates. More broadly, PRA suggests a paradigm in which frozen reasoners are decoupled from domain-specific reward modules, allowing the deployment of new backbones in complex domains without retraining.

Chain-of-Thought reasoning can enhance large language models, but it requires manually designed prompts to guide the model. Recently proposed CoT-decoding enables the model to generate CoT-style reasoning paths without prompts, but it is only applicable to problems with fixed answer sets. To address this limitation, we propose a general decoding strategy GCoT-decoding that extends applicability to a broader range of question-answering tasks. GCoT-decoding employs a two-stage branching method combining Fibonacci sampling and heuristic error backtracking to generate candidate decoding paths. It then splits each path into a reasoning span and an answer span to accurately compute path confidence, and finally aggregates semantically similar paths to identify a consensus answer, replacing traditional majority voting. We conduct extensive experiments on six datasets covering both fixed and free QA tasks. Our method not only maintains strong performance on fixed QA but also achieves significant improvements on free QA, demonstrating its generality.

We introduce a principled probabilistic framework for reward-guided decoding in large language models, addressing the limitations of standard decoding methods that optimize token-level likelihood rather than sequence-level quality. Our method defines a reward-augmented target distribution over complete sequences by combining model transition probabilities with prefix-dependent reward potentials. Importantly, the approach is training-free: it leaves model weights unchanged and instead modifies the inference distribution via reward potentials, with all gains arising purely from inference-time sampling. To sample from this distribution, we develop Sequential Monte Carlo algorithms, including a computationally efficient prefix-only variant and a lookahead variant whose intermediate targets match the exact marginals of the full sequence distribution. The framework also integrates resample-move updates with Metropolis-Hastings rejuvenation and supports block-wise generation, subsuming common decoding strategies such as temperature sampling and power-tempered objectives. Empirical results across three 7B models show significant gains. On code generation (HumanEval), our method improves base performance by up to 54.9% and surpasses the strongest sampling baselines by 9.1%-15.3%. On mathematical reasoning (MATH500), it achieves gains of up to 8.8%. Notably, it reaches 87.8% on HumanEval and 78.4% on MATH500 with Qwen2.5-7B, consistently outperforming the reinforcement learning method GRPO.

Can a large language model (LLM) improve at code generation using only its own raw outputs, without a verifier, a teacher model, or reinforcement learning? We answer in the affirmative with simple self-distillation (SSD): sample solutions from the model with certain temperature and truncation configurations, then fine-tune on those samples with standard supervised fine-tuning. SSD improves Qwen3-30B-Instruct from 42.4% to 55.3% pass@1 on LiveCodeBench v6, with gains concentrating on harder problems, and it generalizes across Qwen and Llama models at 4B, 8B, and 30B scale, including both instruct and thinking variants. To understand why such a simple method can work, we trace these gains to a precision-exploration conflict in LLM decoding and show that SSD reshapes token distributions in a context-dependent way, suppressing distractor tails where precision matters while preserving useful diversity where exploration matters. Taken together, SSD offers a complementary post-training direction for improving LLM code generation. Our code is available at https://github.com/apple/ml-ssd

Multimodal large-language models (MLLMs) often experience degraded safety alignment when harmful queries exploit cross-modal interactions. Models aligned on text alone show a higher rate of successful attacks when extended to two or more modalities. We propose a simple conditional decoding strategy, CASA (Classification Augmented with Safety Attention) that uses internal representations of MLLMs to predict a binary safety token before response generation. The classification is guided by a safety attention mechanism that computes attention between a dedicated query prompt and the input to scale the classification logits, sharpening the model's ability to detect malicious queries. Our design ensures robust safety alignment without relying on any external classifier or auxiliary head, and without modality-specific safety fine-tuning. Unlike prior safety-decoding methods that attach an external classifier or moderation head, or rescale every generated token with a reward model, CASA makes a single, internal, attention-gated safety decision over the shared multimodal representation, which is precisely what lets safety learned from text-only training transfer to image and audio inputs. Compared against 4 baseline models across 7 attack types spanning text, image, and audio modalities, evaluated on benchmarks such as MM-SafetyBench, JailbreakV-28k, and adversarial audio tests, CASA lowers the average attack success rate by >90% relative when paired with a standard safety prompt (applied to all baselines for fair comparison), and by 54--61% using its internal safety mechanism alone. Our empirical evaluations also show that CASA~maintains strong utility on benign inputs, validated through both automated and human evaluations (via 13 trained annotators). Together, these results highlight CASA as a simple and generalizable framework to improve multimodal LLM safety.

Large Language Models (LLMs) are increasingly used as automated judges, yet decoding temperature is often set by intuition rather than evidence. We run over one million large scale evaluations, multiple open-source models, prompting strategies, and judging paradigms to examine how temperature affects judge reliability. Low temperatures yield consistent outputs with few errors, especially in smaller models, while higher temperatures reduce consistency and increase errors. Yet consistency alone does not guarantee sound judgments: low temperatures can narrow the range of reasoning explored. We characterize judge behavior through four reasoning personas and find that temperature shifts their distributions in model-dependent ways, most visibly in ambiguous cases where competing answers are hard to distinguish. Repeated high-temperature sampling reveals this hidden uncertainty, and combining it with majority voting or using high temperature for reasoning and low temperature for the final decision, improves agreement on ambiguous cases without hurting clear ones, at the cost of extra inference. Our findings suggest a simple rule: keep temperature low for stable outputs, but explore more when the judgment is hard.

We present ATLAS-RTC, a runtime control system for autoregressive language models that enforces structured output during decoding. ATLAS-RTC monitors generation at each step, detects drift from output contracts using lightweight signals, and applies targeted interventions such as biasing, masking, and rollback. Unlike post-hoc validation or static constrained decoding, it operates in a closed loop, enabling correction before errors materialize. Across structured generation and tool-calling tasks, ATLAS-RTC improves first-attempt success rates by 20 to 37.8 percentage points, with up to 88% latency reduction in failure-dominated settings. Results show that many failures arise from decoding artifacts rather than task misunderstanding, motivating runtime control as a distinct layer in LLM systems.

Multimodal Diffusion Large Language Models (MDLLMs) achieve high-concurrency generation through parallel masked decoding, yet the architectures remain prone to multimodal hallucinations. This structural vulnerability stems from an algorithmic flaw: the decoder ranks candidate tokens based on textual likelihood without verifying localized visual support. We establish that this language-only ranking induces an objective mismatch, where language probability mass acts as a misspecified proxy for the intended multimodal task. Consequently, we reinterpret hallucination as a localized optimization error, a phenomenon where the decoder exploits language shortcuts to maximize a proxy score at the expense of visual grounding. To address this objective mismatch, we introduce VISAGE, a training-free decoding framework that calibrates the objective at inference time. VISAGE estimates the proxy discrepancy by quantifying the spatial entropy of cross-attention distributions. By enforcing a localization consensus across attention heads, the method penalizes spatially uniform distributions and re-ranks token commitments to favor visually grounded outcomes. We provide an analytical stability guarantee establishing that VISAGE maintains a bounded objective loss under estimation error. Evaluations across hallucination-sensitive and general-purpose benchmarks demonstrate the robustness of the framework, yielding relative gains of 8.59% on MMMU-val and 7.75% on HallusionBench.

Poetry generation in Sanskrit typically requires the verse to be semantically coherent and adhere to strict prosodic rules. In Sanskrit prosody, every line of a verse is typically a fixed length sequence of syllables adhering to prescribed binary patterns of syllable weights. We observe that instead of treating a verse as a monolithic sequence, segmenting them as grouped-lines leads to significant improvement in semantic coherence by 10% with comparable metrical adherence. Specifically, Pingala, our proposed decoding approach is designed to encourage every line to have well-formed words and our token selection biases the model towards it by preferring longer tokens. Writing in Sanskrit follows phonemic orthography, hence using a phonetically aware transliteration scheme, SLP1, increased the metrical alignment by 46% with comparable semantic similarity, for a instruction fine-tuned large language models like Phi-4. We also introduce a new approach for reference-free evaluation using cross-encoders which achieved better alignment with true poetry instances.

We address a not-widely-recognized subset of exploratory search, where a user sets out on a typically long "search quest" for the perfect wedding dress, overlooked research topic, killer company idea, etc. The first few outputs of current large language models (LLMs) may be helpful but only as a start, since the quest requires learning the search space and evaluating many diverse and creative alternatives along the way. Although LLMs encode an impressive fraction of the world's knowledge, common decoding methods are narrowly optimized for prompts with correct answers and thus return mostly homogeneous and conventional results. Other approaches, including those designed to increase diversity across a small set of answers, start to repeat themselves long before search quest users learn enough to make final choices, or offer a uniform type of "creativity" to every user asking similar questions. We develop a novel, easy-to-implement decoding scheme that induces sustained creativity and diversity in LLMs, producing as many conceptually unique results as desired, even without access to the inner workings of an LLM's vector space. The algorithm unlocks an LLM's vast knowledge, both orthodox and heterodox, well beyond modal decoding paths. With this approach, search quest users can more quickly explore the search space and find satisfying answers.

Discrete diffusion models are promising alternatives to autoregressive approaches for text generation, yet their decoding methods remain under-studied. Standard autoregressive search procedures, such as beam search, do not directly apply to iterative denoising, where hypotheses are complete intermediate sequences rather than left-to-right prefixes. Furthermore, existing diffusion decoding procedures only provide limited control over the diversity and coverage of retained hypotheses. In this work, we introduce D5P4, a beam-style decoding method tailored to discrete diffusion models, which casts intermediate beam selection as MAP inference under a partitioned Determinantal Point Process. This yields a model-internal batch objective that balances quality and diversity without external verifiers. Experiments on open-ended generation, question answering, and mathematical reasoning show that D5P4 improves diversity and pass@$k$ coverage while matching or surpassing baseline quality and fidelity

Why does machine-generated text remain detectable? We investigate a mechanistic explanation at the decoding stage: standard strategies such as top-$k$ and nucleus sampling restrict generation to high-probability tokens, while human writers routinely choose contextually appropriate words from deeper in the model's probability distribution. Truncation makes a measurable share of these choices unreachable; we call this the truncation blind spot. Across five open models and three domains, 8--18% of human-selected tokens fall outside common truncation boundaries. Linguistic analysis further reveals disproportionate exclusion of content-word tokens. In a benchmark comprising 1.8 million machine generations, classifiers using only predictability and lexical diversity achieve mean AUC-ROC near 0.97, with substantial variation across decoding settings and strong transfer across generators. Probability-floor samplers substantially narrow the blind spot, demonstrating that the choice of truncation criterion matters for retaining human-used tokens. Together, these findings characterize a source of human--machine distributional mismatch and motivate decoding methods that preserve contextually appropriate low-probability choices while maintaining generation quality. Code and data are available at https://github.com/EstebanGarces/human_vs_machine.

Decoding strategies largely determine the quality of Large Language Model (LLM) outputs, yet widely used heuristics such as greedy or fixed temperature/top-p decoding are static and often task-agnostic, leading to suboptimal or inconsistent generation quality across domains that demand stylistic or structural flexibility. We introduce a reinforcement learning-based decoder sampler that treats decoding as sequential decision-making and learns a lightweight policy to adjust sampling parameters at test-time while keeping LLM weights frozen. We evaluated summarization datasets including BookSum, arXiv, and WikiHow using Granite-3.3-2B and Qwen-2.5-0.5B. Our policy sampler consistently outperforms greedy and static baselines, achieving relative gains of up to +88% (BookSum, Granite) and +79% (WikiHow, Qwen). Reward ablations show that overlap-only objectives underperform compared to composite rewards, while structured shaping terms (length, coverage, repetition, completeness) enable stable and sustained improvements. These findings highlight reinforcement learning as a practical mechanism for test-time adaptation in decoding, enabling domain-aware and user-controllable generation without retraining large models.

Extended reasoning models represent a transformative shift in Large Language Model (LLM) capabilities by enabling explicit test-time computation for complex problem solving. However, the optimal configuration of sampling temperature and prompting strategy for these systems remains largely underexplored. We systematically evaluate chain-of-thought and zero-shot prompting across four temperature settings (0.0, 0.4, 0.7, and 1.0) using Grok-4.1 with extended reasoning on 39 mathematical problems from AMO-Bench, a challenging International Mathematical Olympiad-level benchmark. We find that zero-shot prompting achieves peak performance at moderate temperatures, reaching 59% accuracy at T=0.4 and T=0.7, while chain-of-thought prompting performs best at the temperature extremes. Most notably, the benefit of extended reasoning increases from 6x at T=0.0 to 14.3x at T=1.0. These results suggest that temperature should be optimized jointly with prompting strategy, challenging the common practice of using T=0 for reasoning tasks.

Sampling from a categorical distribution is mathematically simple, but in large-vocabulary decoding, it often triggers extra memory traffic and extra kernels after the LM head. We present FlashSampling, an exact sampling primitive that fuses sampling into the LM-head matmul and never materializes the logits tensor in HBM. The method is simple: compute logits tile-by-tile on chip, add Gumbel noise, keep only one maximizer per row and per vocabulary tile, and finish with a small reduction over tiles. In tensor-parallel decoding, FlashSampling replaces the all-gather of logits with streaming peer-to-peer writes: This overlaps GPU-to-GPU communication with computation and HBM loads across up to 8 GPUs, with near-ideal scaling at large batch sizes. Our kernel is exact because $\text{argmax}$ decomposes over partitions; grouped variants for online and tensor-parallel settings are exact by hierarchical factorization of the categorical distribution. FlashSampling demonstrates kernel-level speedups on decode workloads across 4 different datacenter GPUs (H100, H200, B200, B300), and in end-to-end vLLM experiments, it reduces time per output token by up to $10$ on the models we test. These results show that exact sampling, with no approximation, can be integrated into the matmul itself, consolidating the bandwidth-bound sampling step in an efficient epilogue.

Masked diffusion language models (MDLMs) have recently emerged as a new paradigm in language modeling, offering flexible generation dynamics and enabling efficient parallel decoding. However, existing decoding strategies for pre-trained MDLMs predominantly rely on token-level uncertainty criteria, while largely overlooking sequence-level information and inter-token dependencies. To address this limitation, we propose Dependency-Oriented Sampler (DOS), a training-free decoding strategy that leverages inter-token dependencies to inform token updates during generation. Specifically, DOS exploits attention matrices from transformer blocks to approximate inter-token dependencies, emphasizing information from unmasked tokens when updating masked positions. Empirical results demonstrate that DOS consistently achieves superior performance on both code generation and mathematical reasoning tasks. Moreover, DOS can be seamlessly integrated with existing parallel sampling methods, leading to improved generation efficiency without sacrificing generation quality.

A promising pathway for restoring communication in patients with dysarthria and anarthria is speech neuroprostheses, which directly decode speech from cortical neural activity. Two benchmarks, Brain-to-Text '24 and '25, released intracranial recordings from patients with dysarthria along with a baseline algorithm trained with Connectionist Temporal Classification (CTC). Despite significant innovation on these benchmarks, all leading published prior work relies on a WFST-based CTC decoder that requires ${\sim}$320 GB of RAM. These memory requirements limit accessibility for both patients and researchers. Here, we propose LightBeam, a non-WFST based CTC decoder that requires only ${\sim}$10 GB of RAM and achieves state-of-the-art performance on both benchmarks. LightBeam achieves this by integrating an LLM into the beam-search process via delayed fusion, obviating the prior need for using a large N-gram LM. LightBeam is implemented in Python and is open-source.

Speech production and perception are the main ways humans communicate daily. Prior brain-to-text decoding studies have largely focused on a single modality and alphabetic languages. Here, we present a unified brain-to-sentence decoding framework for both speech production and perception in Mandarin Chinese. The framework exhibits strong generalization ability, enabling sentence-level decoding when trained only on single-character data and supporting characters and syllables unseen during training. In addition, it allows direct and controlled comparison of neural dynamics across modalities. Mandarin speech is decoded by first classifying syllable components in Hanyu Pinyin, namely initials and finals, from neural signals, followed by a post-trained large language model (LLM) that maps sequences of toneless Pinyin syllables to Chinese sentences. To enhance LLM decoding, we designed a three-stage post-training and two-stage inference framework based on a 7-billion-parameter LLM, achieving overall performance that exceeds larger commercial LLMs with hundreds of billions of parameters or more. In addition, several characteristics were observed in Mandarin speech production and perception: speech production involved neural responses across broader cortical regions than auditory perception; channels responsive to both modalities exhibited similar activity patterns, with speech perception showing a temporal delay relative to production; and decoding performance was broadly comparable across hemispheres. Our work not only establishes the feasibility of a unified decoding framework but also provides insights into the neural characteristics of Mandarin speech production and perception. These advances contribute to brain-to-text decoding in logosyllabic languages and pave the way toward neural language decoding systems supporting multiple modalities.

Three-way logical question answering (QA) assigns one of $\text{True}$, $\text{False}$, or $\text{Unknown}$ to a hypothesis $H$ given a premise set $S$. We study this task as a compact compositional inference problem: predictions for $H$ and for a mechanically negated hypothesis $\neg H$ should agree under a deterministic negation map. Despite this simple structure, large language models (LLMs) can exhibit two practical failure modes: (i) negation inconsistency, where answers to $H$ and $\neg H$ violate the required label mapping, and (ii) epistemic $\text{Unknown}$, where the model abstains even when one side is entailed. We introduce CGD-PD, a lightweight, training-free test-time layer that combines neural 3-way classification, symbolic negation-consistency projection, and targeted binary entailment probes. On one validation split of FOLIO's first-order logic fields, CGD-PD improves accuracy by 4.4 points on GPT-5.2 and 6.8 points on Claude Sonnet 4.5, while reducing $\text{Unknown}$ predictions and epistemic abstention. These results provide a controlled proof of concept that simple logical composition at inference time can help evaluate and improve LLM reasoning reliability; they do not, by themselves, establish robustness beyond this formal benchmark setting.

Abstractive summarization requires models to generate summaries that convey information in the source document. While large language models can generate summaries without fine-tuning, they often miss key details and include extraneous information. We propose BLooP (Bigram Lookahead Promotion), a simple training-free decoding intervention that encourages large language models (LLMs) to generate tokens that form bigrams from the source document. BLooP operates through a hash table lookup at each decoding step, requiring no training, fine-tuning, or model modification. We demonstrate improvements in ROUGE and BARTScore for Llama-3.1-8B-Instruct, Mistral-Nemo-Instruct-2407, and Gemma-2-9b-it on CNN/DM, CCSum, Multi-News, and SciTLDR. Human evaluation shows that BLooP significantly improves faithfulness without reducing readability. We make the code available at https://github.com/varuniyer/BLooP

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.

Decoding from large language models (LLMs) typically relies on fixed sampling hyperparameters (e.g., temperature, top-p), despite substantial variation in task difficulty and uncertainty across prompts and individual decoding steps. We propose to learn adaptive decoding policies that dynamically select sampling strategies at inference time, conditioned on available compute resources. Rather than fine-tuning the language model itself, we introduce lightweight decoding adapters trained with reinforcement learning and verifiable terminal rewards (e.g. correctness on math and coding tasks). At the sequence level, we frame decoding as a contextual bandit problem: a policy selects a decoding strategy (e.g. greedy, top-k, min-p) for each prompt, conditioned on the prompt embedding and a parallel sampling budget. At the token level, we model decoding as a partially observable Markov decision process (POMDP), where a policy selects sampling actions at each token step based on internal model features and the remaining token budget. Experiments on the MATH and CodeContests benchmarks show that the learned adapters improve the accuracy-budget tradeoff: on MATH, the token-level adapter improves Pass@1 accuracy by up to 10.2% over the best static baseline under a fixed token budget, while the sequence-level adapter yields 2-3% gains under fixed parallel sampling. Ablation analyses support the contribution of both sequence- and token-level adaptation.

How much do large language models actually hallucinate when answering questions grounded in provided documents? Despite the critical importance of this question for enterprise AI deployments, reliable measurement has been hampered by benchmarks that rely on static datasets vulnerable to contamination, LLM-based judges with documented biases, or evaluation scales too small for statistical confidence. We address this gap using RIKER, a ground-truth-first evaluation methodology that enables deterministic scoring without human annotation. Across 35 open-weight models, three context lengths (32K, 128K, and 200K tokens), four temperature settings, and three hardware platforms (NVIDIA H200, AMD MI300X, and Intel Gaudi 3), we conducted over 172 billion tokens of evaluation - an order of magnitude beyond prior work. Our findings reveal that: (1) even the best-performing models fabricate answers at a non-trivial rate - 1.19% at best at 32K, with top-tier models at 5 - 7% - and fabrication rises steeply with context length, nearly tripling at 128K and exceeding 10% for all models at 200K; (2) model selection dominates all other factors, with overall accuracy spanning a 72-percentage-point range and model family predicting fabrication resistance better than model size; (3) temperature effects are nuanced - T=0.0 yields the best overall accuracy in roughly 60% of cases, but higher temperatures reduce fabrication for the majority of models and dramatically reduce coherence loss (infinite generation loops), which can reach 48x higher rates at T=0.0 versus T=1.0; (4) grounding ability and fabrication resistance are distinct capabilities - models that excel at finding facts may still fabricate facts that do not exist; and (5) results are consistent across hardware platforms, confirming that deployment decisions need not be hardware-dependent.

Preference-based alignment methods (e.g., RLHF, DPO) typically optimize a single scalar objective, implicitly averaging over heterogeneous human preferences. In practice, systematic annotator and user-group disagreement makes mean-reward maximization brittle and susceptible to proxy over-optimization. We propose Disagreement-Aware Alignment via Risk-Constrained Decoding (DARC), a retraining-free inference-time method that frames response selection as distributionally robust, risk-sensitive decision making. Given multiple preference samples or scalable disagreement proxies, DARC reranks candidates by maximizing a KL-robust (entropic) satisfaction objective, and provides simple deployment controls that cap or penalize the corresponding entropic risk premium relative to the mean, enabling explicit risk budgets without retraining. We provide theoretical characterization linking this decoding rule to principled pessimism and KL-based distributionally robust optimization. Experiments on alignment benchmarks show that DARC reduces disagreement and tail risk while maintaining competitive average quality under noisy, heterogeneous feedback.