Next-Token Distribution

Follow this topic Ask about this topic

Momentum

4 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Jul 6Week of Sep 21

Latest papers 19

Sep 29, 2026cs.LG

Interpolated Policy Distillation: A Controllable Continuum Between Off-Policy and On-Policy Distillation

Off-policy and on-policy distillation have traditionally been formulated as separate paradigms, each favoring a different property of distillation trajectories. Teacher-generated (off-policy) traces are typically high-quality but lie far from the student's distribution, whereas student-generated (on-policy) rollouts are more learnable but often contain erroneous reasoning. We view these paradigms as the endpoints of a policy continuum and posit that a more effective rollout policy may lie in between. We introduce \textbf{Interpolated Policy Distillation (IPD)}, which defines the next-token distribution at every decoding step as an explicit linear interpolation between the student and teacher distributions. The interpolation operates at the distribution level, token by token, and its coefficient provides direct control over the balance between trajectory quality and student learnability. Naively sampling from this policy would require sequentially querying the teacher at every token and is thus expensive. To make IPD practical, we accelerate it with a new speculative-decoding rule while exactly preserving the interpolated next-token distribution.At the trajectory level, the resulting rollouts naturally interleave student- and teacher-generated segments. Unlike recent heuristic segment-interleaving methods, however, this interleaving is induced by an exactly realized token-level interpolated policy rather than by hand-designed switching rules. Across text-only and multimodal reasoning benchmarks, IPD consistently outperforms both endpoint policies (SFT and OPD), their conventional two-stage combination (SFT-then-OPD), and recent heuristic segment-interleaving methods, demonstrating that token-level policy interpolation better balances trajectory quality and student learnability.

Youxu Shi, Yifan Sun, Dacheng Yin +5

University of Science and Technology of China · WeChat Vision, Tencent Inc.

Off-Policy Learning Next-Token Distribution Token-Level Uncertainty

Sep 27, 2026cs.CL

CertMark: Distortion-Free Multi-Bit Watermarking with Certified Decoding

Leading multi-bit watermarking methods for language models encode messages by biasing the model's next-token probabilities, creating a trade-off between message recovery and text quality. Their decoders typically return the highest-scoring candidate from accumulated token-level evidence, without a certified abstention rule that bounds the probability of outputting an incorrect message. We introduce CertMark, a distribution-preserving multi-bit watermark with certified decoding. Rather than modifying probabilities, CertMark uses the embedded message to seed an exact Gumbel-max sampler, thereby preserving the model's original sampling distribution. We propose two scalable decoders: a model-agnostic, text-only decoder and a model-aware variant that leverages the original next-token distributions for stronger recovery. Both support certified abstention with mathematical bounds on the probability of returning an incorrect message. Across text completion, summarization, and story generation, CertMark matches the perplexity of unwatermarked text while reliably recovering multi-bit messages. The model-aware decoder further achieves higher bit accuracy than probability-biasing baselines. Our code is publicly available at https://github.com/Batorskq/CertMark.

Paweł Batorski, Przemysław Spurek, Paul Swoboda

Heinrich Heine University Düsseldorf · Jagiellonian University · IDEAS Research Institute

Watermarks Decoding Next-Token Distribution

Sep 24, 2026cs.CL

Your Transformer Can Hold Two Thoughts at Once: Evidence of Linear Superposition in LLMs

While Large Language Models (LLMs) rely on highly non-linear components, in this work we demonstrate that they exhibit fundamental linearity: when inputs from distinct text streams are linearly combined, the model outputs a superposition of the individual next-token distributions. We term this the \textit{Superposition Linearity Hypothesis}. We provide evidence that superposition is an intrinsic property of the Transformer architecture rather than an emergent consequence of training; in fact, we observe that it tends to diminish as pretraining progresses. However, we demonstrate that linearity can be substantially restored through lightweight fine-tuning, significantly reducing the divergence between the predicted next-token distribution and the average of the individual next-token distributions. Finally, we introduce a guided decoding procedure that disentangles superposed outputs, enabling the simultaneous generation of two coherent continuations from a single forward pass.

Pavel Tikhonov, Anton Korznikov, Matvey Mikhalchuk +6

Transformer Architectures Next-Token Distribution Thoughts Nonlinearity

Sep 17, 2026stat.ML

Next-token functional estimation

Suppose we observe the first

n

points of a sequence of random variables having length

n+1

, and wish to estimate a functional of the unobserved final point and the empirical measure of the

n

observed training points. Such next-token functionals include the probability that the next token is novel (also known as the surprise probability), the tail probability of the minimum distance between the next token and training points, and the test error of a classifier trained on the observed points. All of these quantities are classically estimated by the leave-one-out method, which is inconsistent under temporal dependence. We propose a leave-a-window-out estimator, which deletes a window of length

τ

after each index before forming the empirical measure and reduces to leave-one-out at

τ= 1

. Under natural assumptions, we show that the error of our estimator decays at a parametric rate for any stationary

β

-mixing process that also admits a Marton coupling. Our results thus cover several natural functionals on a large class of stochastic processes. We complement these upper bounds with a sharp minimax lower bound for estimating the surprise probability on mixing Markov chains. Simulations on Markov chains, moving-average processes, and autoregressive processes show that our estimator succeeds in many scenarios where leave-one-out and add-constant baselines fail.

Milind Nakul, Vidya Muthukumar, Ashwin Pananjady

Schools of Industrial and Systems Engineering and Electrical and Computer Engineering Georgia Institute of Technology

Next-Token Distribution Surprisal Autoregressive Model

Sep 14, 2026cs.IR

Recommendation Retrievers Need Verifiers: Universal Generative Reranking for Sequential Recommendations

First-stage recommenders in multi-stage systems produce a ranked candidate list from which a limited prefix is forwarded to downstream rankers. Because each forwarded item must be processed by more expensive ranking stages, this shortlist cannot be arbitrarily large. The first-stage objective is therefore high coverage of relevant items within the forwarded prefix, commonly measured by Recall@

k

. A relevant item may be available deeper in the retrieved list but absent from the shorter prefix that is actually consumed. This paper studies post-hoc verification for promoting such candidates into the consumed shortlist without retraining or replacing the retriever. We introduce a lightweight generative verifier for retrieval models. Given a retriever state and a candidate item, the verifier scores the item through the likelihood of its identifier tokens. It is trained post hoc with next-token cross entropy, requires no sampled negatives or candidate pool during training, and scores only the retriever's top-

K

candidates at inference. The interface is minimal: the retriever supplies a query state and candidate items, and the item representation can use any fixed tokenization. Across Amazon product recommendation and YaMBDa music recommendation, the same verifier training recipe improves Recall@10 for SASRec, GRU4Rec, NextItNet, and MiniOneRec. Ablations show that the improvements are not explained solely by injecting item-content features into the retriever, supporting verification as a post-hoc output-side adaptation mechanism.

Benyu Zhang, Qiang Zhang, Rui Li +3

Meta MRS

Sequential Recommendation Cross-Encoder Reranking Reranking Recommendation Next-Token Distribution

Jul 31, 2026cs.CV

Attention-Steered Vision-Language Models for Sign Language Translation

Vision-language models (VLMs) have emerged as a powerful framework for multimodal video understanding. However, they remain limited in the sign language translation task, where we identify a key failure mode of existing VLMbased translators: poor spatial-temporal visual grounding. In particular, we find that standard next-token cross-entropy does not directly provide signal for where and when the model should attend, causing models to overlook sign-relevant regions and frames. To address this challenge, we propose AttnSign, a VLM-based spatial-temporal attention steering framework for sign language translation. AttnSign first introduces spatial attention supervision for sign-relevant regions, such as face and hands, in each frame; then develops an RL-based motion-cadence steering method that encourages the model to explore and focus on sign-level keyframes. Experimental results on How2Sign and OpenASL benchmarks show that our proposed AttnSign consistently outperforms existing methods.

Meibo Hu, Guohao Sun, Annemarie D. Ross +2

Rochester Institute of Technology · National Technical Institute for the Deaf / Rochester Institute of Technology · University of Virginia

Gloss-Free Sign Language Translation Sign Language Translation Recent Vision-Language Models Spatio-Temporal Attention Keyframe Selection Next-Token Distribution

Jul 22, 2026cs.CR

Geometric Configurations of Perturbed Jailbreak Prompts

Perturbation techniques that turn unsuccessful jailbreak prompts into successful ones are continuously evolving, constituting a major security threat to LLM safety. In this paper, we investigate the internal representations of such string-level perturbed jailbreak inputs in the small weight models of the Qwen-2.5-1.5B/-3B/-7B-Instruct and Llama-3.2-1B/-3B/-3.1-8B-Instruct families. We select two representation spaces: the last-layer-last-token embedding space and the top-50 next-token probability space. The former space separates prompts based on their spelling and format, while the latter space is effectively one-dimensional but appears more complex to cluster. Within our refusal-dominated answer set we find no behavioral hyperplane in either space. Only the next token "Sure" in the 1.5B Qwen model, and both tokens "," and "ĊĊ" in the 1$ Llama model, display a significant association with a compliant-labeled answer.

Lynn Delcon, Andres Algaba, Vincent Ginis

Department of Business Technology and Operations, Data Analytics Laboratory, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium · imec-SMIT, Vrije Universiteit Brussel, Pleinlaan 9, 1050 Brussels, Belgium · School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

Large Language Model Jailbreaks Jailbreak Attacks Jailbreaks Prompt Engineering Refusals Next-Token Distribution

Jul 15, 2026cs.AI

Tracing LLM Behavior to the Training Data with Empirical Next-Token Distributions

In this paper, we study the connection between an LLM's output distribution and the data used to train it. Specifically, we study the degree to which an LLM's next-token distribution agrees with the empirical next-token distribution (ENTD) given the context in the training data. The ENTD is an appealing target because it is the unrestricted global minimizer of the next-token cross entropy loss used for pretraining, as well as an easily interpretable function of the pretraining corpus. We find that for a significant fraction of inputs, the LLM's distribution agrees with the ENTD almost perfectly, and the average agreement increases with model scale and training compute. Nevertheless, there is a long tail of input sequences where the LLM and ENTD differ significantly, and we examine several possible sources of this discrepancy across the transformer architecture, training procedure, and finite-sample noise in the ENTD estimate itself. More broadly, we hope our findings will encourage more work on ``data-centric mechanistic interpretability,'' a complement to standard mechanistic interpretability that opens the black box of how model behaviors arise from the data, rather than how they are encoded in the learned weights.

Zachary Izzo

NEC Labs America

Next-Token Distribution Mechanistic Interpretability Training Data

Jun 9, 2026cs.LG

K-Forcing: Joint Next-K-Token Decoding via Push-Forward Language Modeling

Autoregressive (AR) language modeling is the dominant paradigm for text generation, yet its sequential token-by-token decoding makes inference memory-bound and inefficient. Existing acceleration approaches, such as speculative decoding and diffusion language models, can yield speedups under certain conditions but do not directly address high-load batch serving--the scenario most critical for industrial-scale deployment. We introduce K-Forcing, a push-forward language modeling paradigm for joint next-k-token decoding. K-Forcing distills an existing AR model into a conditional push-forward mapping--one that transforms independent uniform noise variables into a joint sample of multiple future tokens in a single forward pass. This design preserves fixed-length outputs, reuses the AR teacher backbone, and remains compatible with standard AR serving infrastructure. We train this mapping via progressive self-forcing distillation, which gradually expands the prediction window while enabling the student to closely match the sequence distribution of the AR teacher. We evaluate K-Forcing on LM1B and OpenWebText using a standard causal Transformer backbone. When aggressively configured to generate k = 4 tokens per forward pass, K-Forcing delivers approximately 2.4-3.5x speedup across different batch sizes, while incurring modest quality degradation relative to its AR teacher. As inference increasingly dominates the lifetime compute cost of modern LLMs, K-Forcing offers a promising route toward accelerating AR generation under real-world high-load deployment.

Zhiwei Tang, Yuanyu He, Yizheng Han +4

1DAMO Academy, Alibaba Group · 2Hupan Lab · 3Zhejiang University +1

Autoregressive Language Models Autoregressive Generation Next-Token Distribution Language Modeling

Jun 1, 2026cs.LG

Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete

Positional encoding (PE) is widely viewed as necessary for transformers to process ordered sequences: without them, the next-token map appears permutation-invariant in its context tokens. This intuition underlies all prior universality results, which rely on positional information to prove that transformers with chain-of-thought can perform arbitrary computation, i.e., they are Turing complete. We revisit this belief in the regime most relevant to long-form reasoning, where generation proceeds through a finite sliding context window. Our opening perception is that the window mechanism itself (mildly) breaks the permutation symmetry. To distill and precisely capture the degree of this added expressiveness, we introduce an abstract autoregressive model, the HIST model, in which each update depends only on constant-size internal state and the token-count histogram within the current window. We prove that this HIST model is Turing complete by showing that the evolution of the window can reveal the token that has just left the window, which suffices to simulate Turing-complete Post machines. We then construct a sliding-window transformer over a constant-size token alphabet, without PE, and show that it can simulate the HIST model. Our result demonstrates that positional encodings are not indispensable for transformers to perform universal computation: The window sliding itself already breaks permutation symmetry and captures sufficient positional information.

Qian Li, Xinyu Mao, Shang-Hua Teng

Shenzhen Research Institute of Big Data · University of Southern California

Positional Encoding Transformer Architectures Next-Token Distribution Tractability Role Completion

May 28, 2026cs.LG

Bastion: Budget-Aware Speculative Decoding with Tree-structured Block Diffusion Drafting

Block-diffusion drafters have recently emerged as a powerful alternative for speculative decoding by predicting multiple future-token distributions in a single parallel step. However, since these parallel predictions are sampled from position-wise marginals rather than fully conditioned sequences, committing to a single greedy path often fails to capture the target model's preferred trajectory. To address this, we propose BASTION, a budget-aware speculative decoding framework with tree-based diffusion drafting. Unlike existing methods that rely on static tree topologies, BASTION dynamically constructs query-dependent trees by balancing draft quality against hardware constraints. Our framework integrates three synergistic components: (1) an acceptance surrogate that estimates expected accepted length via path confidence, (2) an online latency estimator that calibrates a hardware-aware roofline model, and (3) an adaptive best-first expansion that grows the tree until marginal gains no longer justify incremental verification costs. BASTION is training-free, preserves the target model's distribution, and requires no per-setting tuning. Across diverse benchmarks and GPU architectures, BASTION achieves up to a 6.61x speedup over standard autoregressive decoding, outperforming state-of-the-art block-diffusion baselines by 39%.

Soowon Oh, Nam Cao, Yujin Kim +4

KAIST AI · Samsung Advanced Institute of Technology

Block-Diffusion Drafter Speculative Decoding Next-Token Distribution Token Budget Allocation

May 25, 2026cs.LG

The Bridge-Garden Dilemma in LLM Distillation: Why Mixing Hard and Soft Labels Works

Knowledge distillation (KD) transfers knowledge from a large teacher model to a smaller student. In language modeling, the student is trained either on tokens sampled from the teacher (hard labels) or the teacher's full next-token distribution (soft labels). Despite soft labels appear strictly richer, we find that mixing hard and soft labels consistently yields better results. Crucially, we show that this gain cannot be explained by closer teacher matching during training. Instead, it comes from reduced exposure bias, the mismatch between training and inference distributions. To explain this phenomenon, we introduce the Bridge-Garden Decomposition theory, which categorizes generation steps into two types: Bridges, where the next token must be exact, and Gardens, where it can be flexible. We show that hard-only KD excels in Bridges by avoiding risky deviations, while soft-only KD preserves diversity in Gardens. A hybrid strategy handles both cases and, as a result, reduces exposure bias across the sequence. Guided by this theory, we develop a family of Bridge-Garden hybrid supervision methods that adaptively balance hard and soft labels. Across a primary suite of seven teacher-student pairs (including Qwen, Llama, Gemma, and DeepSeek) and benchmarks in reasoning and coding, our approach outperforms divergence-based and on-policy KD baselines while reducing training cost by 9.7x, enabling efficient model compression. Code is available at https://github.com/ghwang-s/bridge_garden_hybrid_kd_release.

Guanghui Wang, Kaiwen Lv Kacuila, Zhiyong Yang +5

School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China · Alibaba Group, Hangzhou, China · State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China +2

Knowledge Distillation Dataset Distillation Next-Token Distribution Efficient Sequence Mixers

May 13, 2026cs.LG

N-vium: Mixture-of-Exits Transformer for Accelerated Exact Generation

Improving the inference efficiency of autoregressive transformers typically means reducing FLOPs per token, usually through approximations that degrade model quality. We introduce N-vium, a mixture-of-exits transformer that partially parallelizes computation across depth on standard hardware, increasing effective FLOPs per second rather than minimizing compute per token. N-vium attaches prediction heads at multiple depths and defines the next-token distribution as a learned mixture over these exits, with token-adaptive routing. This formulation strictly generalizes the standard transformer, which is recovered exactly when routing assigns zero mass to all intermediate heads. Sampling from the mixture is exact, and complete KV caches are recovered by deferring the upper-layer computation and batching it with later tokens. We pretrain N-vium at scales up to 1.5B parameters. Our largest model reaches 57.9% wall-clock speedup over a parameter- and data-matched standard transformer at no perplexity cost.

Aleksander Lorenc, Frédéric Berdoz, Joël Mathys +1

ETH Zurich

Autoregressive Transformers Transformer Architectures Next-Token Distribution

May 8, 2026cs.LG

Future Validity is the Missing Statistic: From Impossibility to $Φ$ -Estimation for Grammar-Faithful Speculative Decoding

Grammar-constrained generation is often combined with local vocabulary masking and speculative decoding, but the resulting sampling law is not the grammar-conditional distribution users usually intend. We show that any speculative decoder with local mask access, Leviathan rejection, and rollback soundness samples from the locally projected distribution

μ^{\mathrm{proj}}

rather than the grammar-conditional distribution

μ^\star

. This extends the GAD impossibility result to speculative decoding; on Dyck grammars with Qwen3-8B, the total-variation gap can reach 0.996. We identify the future-validity function

Φ_t(y)=\Pr_p[\mathrm{valid\ completion}\mid y]

as the missing correction statistic. The target distribution is a Doob transform of the base model with

h=Φ

, while local masking corresponds to setting

h

to one. With exact

Φ

, our oracle decoder FVO-Spec samples exactly from

μ^\star

; with approximate

Φ

, we bound the resulting total-variation error. Because exact future validity is hard for general context-free grammars, we evaluate estimator hierarchies on tractable Dyck and finite JSON languages. OneStep reduces Dyck TV by 14% with under 1% throughput overhead, exact dynamic programming reduces it by 97%, and finite-language correction closes JSON gaps to numerical precision. All fidelity claims are scoped to enumerable grammars and token tries.

Wenhua Nie, Zijie Meng, Kun Zou +5

National Taiwan University

Speculative Decoding Context-Free Grammars Next-Token Distribution Grammatical Error Correction Uncertainty Score Impossibility+2

May 8, 2026cs.LG

The Convergence Gap: Instruction-Tuned Language Models Stabilize Later in the Forward Pass

Final outputs hide when a checkpoint commits to its next-token prediction. We introduce the convergence gap, a model-diffing diagnostic that decodes each layer's next-token distribution and measures its distance to the model's own final distribution. Across six paired pretrained and instruction-tuned checkpoints in native prompting regimes, instruction-tuned checkpoints remain farther from their final predictions later into the stack. The effect persists under endpoint-matched raw and tuned readouts, endpoint-free same-history checks, and fixed-history template replay. Matched-prefix interventions identify late MLP windows as the largest tested leverage point: late IT grafts into PT hosts increase late KL by +0.34 nats, while PT-late swaps into IT hosts reduce it by -0.51 nats; matched random late perturbations give only +0.003 versus +0.327 for the true late graft. A preselected Gemma case study provides behavior-facing plausibility for the same late swap, without serving as a benchmark claim. These results identify a robust predictiondynamics signature of post-training: released instruction-following checkpoints tend to settle later, and late MLP computation is the strongest tested bidirectional handle on that delay under matched histories.

Yifan Zhou

University of California, Los Angeles

Instruction-Tuned Models Training-Inference Mismatch Intermediate Checkpoints Next-Token Distribution Forward Propagation Multilayer Perceptrons+2

Apr 21, 2026cs.AI

OLLM: Options-based Large Language Models

We introduce Options LLM (OLLM), a simple, general method that replaces the single next-token prediction of standard LLMs with a \textit{set of learned options} for the next token, indexed by a discrete latent variable. Instead of relying on temperature or sampling heuristics to induce diversity, OLLM models variation explicitly: a small latent space parametrizes multiple plausible next-token options which can be selected or searched by a downstream policy. Architecturally, OLLM is a lightweight "plug-in" that inserts two layers: an encoder and a decoder, before the output head, allowing almost any pretrained LLM to be converted with minimal additional parameters. We apply OLLM to a 1.7B-parameter backbone (only

1.56\%

of parameters trainable) trained on OpenMathReasoning and evaluated on OmniMath. The SOTA LoRA-adapted baselines peak at

51\%

final answer correctness, while OLLM's option set allows up to

\sim 70\%

under optimal latent selection. We then train a compact policy in the latent space that emits latents to control generation. Operating in a low-dimensional option space makes reward optimization far more sample-efficient and substantially reduces common misalignments (e.g., language switching or degenerate reasoning), as the policy is constrained to options learned during SFT. Crucially, this alignment arises from model structure rather than additional KL or handcrafted alignment losses. Our results demonstrate that optionized next-token modeling enhances controllability, robustness, and efficiency in math reasoning, and highlight latent-space policy learning as a promising direction for reinforcement learning in LLMs.

Shashank Sharma, Janina Hoffmann, Vinay Namboodiri

Department of Computer Science University of Bath · Department of Psychology University of Bath

LLM Reasoning Strategies Large Language Models(Llms Large Language Model Tool Use Next-Token Distribution

Apr 21, 2026cs.LG

Self-Improving Tabular Language Models via Iterative Reward-Guided Post-Training

Tabular language models can generate synthetic tables by modeling rows as token sequences, but they are typically trained once with supervised fine-tuning and then used as static synthesizers. This is limiting because next-token likelihood does not directly optimize the distributional, utility, and indistinguishability properties used to evaluate synthetic data. We study iterative reward-guided post-training for tabular language models through a generate--score--align protocol, where a generator samples synthetic rows, a task-specified reward ranks them, and the model is updated relative to a fixed supervised reference. Within this protocol, we propose \textbf{TabGRAA} (\textbf{Tab}ular \textbf{G}roup-\textbf{R}elative \textbf{A}dvantage \textbf{A}lignment), a group-relative alignment method that compares high- and low-reward generated groups using group-averaged policy/reference log-ratios rather than one-to-one preference pairs. Across five mixed-type benchmarks, TabGRAA improves a GReaT backbone beyond additional supervised fine-tuning and achieves the strongest average trade-off among adapted DPO, KTO, and NPO baselines on fidelity and downstream utility, while maintaining empirical privacy diagnostics near the supervised baseline. Ablations show that the gains depend on meaningful reward ranking and stable group-level updates rather than extra training alone. Reward-substitution and scorer-separation studies further show that the post-training loop can use both classifier-based and classifier-free rewards, and that proper scorer separation is important for preserving the fidelity--utility--privacy trade-off. These results position TabGRAA as a self-improving post-training method for tabular language-model generators, complementary to strong static tabular synthesizers.

Yunbo Long, Tejumade Afonja, Guangya Hao +2

Department of Engineering, University of Cambridge · CISPA Helmholtz Center for Information Security, Saarbrücken, Germany · The Alan Turing Institute, London

Post-Training Next-Token Distribution Synthetic Data Large Language Model Generation Iterative

Feb 7, 2026cs.LG

Deriving Neural Scaling Laws from the statistics of natural language

Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset. We provide the first such theory in the case of data-limited scaling laws. We isolate two key statistical properties of language that alone can predict neural scaling exponents: (i) the decay of pairwise token correlations with time separation between token pairs, and (ii) the decay of the next-token conditional entropy with the length of the conditioning context. We further derive a simple formula in terms of these statistics that predicts data-limited neural scaling exponents from first principles without any free parameters or synthetic data models. Our theory exhibits a remarkable match with experimentally measured neural scaling laws obtained from training GPT-2 and LLaMA style models from scratch on two qualitatively different benchmarks, TinyStories and WikiText.

Francesco Cagnetta, Allan Raventós, Surya Ganguli +1

Theoretical and Scientific Data Science, International School for Advanced Studies (SISSA), Trieste, Italy · Department of Applied Physics, Stanford University, Stanford, California · Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland +1

Scaling Laws Next-Token Distribution Natural Language Datasets Scaling Natural Language Statistical Inference

May 21, 2025cs.CL

Extracting Probabilistic Knowledge from Large Language Models for Bayesian Network Parameterization

In this work, we evaluate the potential of Large Language Models (LLMs) in building Bayesian Networks (BNs) by approximating domain expert priors. LLMs have demonstrated potential as factual knowledge bases; however, their capability to generate probabilistic knowledge about real-world events remains understudied. We explore utilizing the probabilistic knowledge inherent in LLMs to derive probability estimates for statements regarding events and their relationships within a BN. Using LLMs in this context allows for the parameterization of BNs, enabling probabilistic modeling within specific domains. Our experiments on eighty publicly available Bayesian Networks, from healthcare to finance, demonstrate that querying LLMs about the conditional probabilities of events provides meaningful results when compared to baselines, including random and uniform distributions, as well as approaches based on next-token generation probabilities. We explore how these LLM-derived distributions can serve as expert priors to refine distributions extracted from data, especially when data is scarce. Overall, this work introduces a promising strategy for automatically constructing Bayesian Networks by combining probabilistic knowledge extracted from LLMs with real-world data. Additionally, we establish the first comprehensive baseline for assessing LLM performance in extracting probabilistic knowledge.

Aliakbar Nafar, Kristen Brent Venable, Zijun Cui +1

Michigan State University · Florida Institute for Human and Machine Cognition (IHMC) University of West Florida

Bayesian Networks Prior Knowledge Integration Next-Token Distribution