Daily Papers

A decision model can give probabilities that sum to one for every question yet disagree with itself when the same decision is broken into smaller steps. We study this form of probabilistic coherence in Jev and the English Laya checkpoint, using 2,500 matched examples per system across TREC, CLINC150, and MASSIVE. Across 72,000 classification questions, we compare direct fine-label predictions with broad-category probabilities and predictions reconstructed through those categories. Both systems show substantial disagreement: mean category-level total variation ranges from 0.219 to 0.349 for Jev and from 0.424 to 0.689 for Laya, on a scale where zero means exact agreement. The consequences differ sharply. On CLINC150, reconstruction reduces Jev's accuracy by 22.9 percentage points (paired 95% bootstrap interval: [-24.9, -20.9]) and improves Laya's by 21.3 points ([18.0, 24.5]). The same directions hold across all three datasets, with all six unadjusted accuracy-change intervals excluding zero. Improved accuracy can also accompany less reliable confidence: on MASSIVE, Laya gains 9.2 accuracy points while its expected calibration error rises from 0.046 to 0.124. Error analysis identifies both broad-category mistakes and within-category confusions. These findings show why decision systems need joint evaluation of accuracy, confidence calibration, and probability coherence in the workflow used by an application.

Large Language Models (LLMs) are widely used in sensitive domains, including healthcare, finance, and legal services, raising concerns about potential private information leaks during inference. Privacy extraction attacks, such as jailbreaking, expose vulnerabilities in LLMs by crafting inputs that force the models to output sensitive information. However, these attacks cannot verify whether the extracted private information is accurate, as no public datasets exist for cross-validation, leaving a critical gap in private information detection during inference. To address this, we propose PrivacyXray, a novel framework detecting privacy breaches by analyzing LLM inner states. Our analysis reveals that LLMs exhibit higher semantic coherence and probabilistic certainty when generating correct private outputs. Based on this, PrivacyXray detects privacy breaches using four metrics: intra-layer and inter-layer semantic similarity, token-level and sentence-level probability distributions. PrivacyXray addresses critical challenges in private information detection by overcoming the lack of open-source private datasets and eliminating reliance on external data for validation. It achieves this through the synthesis of realistic private data and a detection mechanism based on the inner states of LLMs. Experiments show that PrivacyXray achieves consistent performance, with an average accuracy of 92.69% across five LLMs. Compared to state-of-the-art methods, PrivacyXray achieves significant improvements, with an average accuracy increase of 20.06%, highlighting its stability and practical utility in real-world applications.

Prior approaches to realizing mixed-initiative human--computer referential communication have adopted information-state or collaborative problem-solving approaches. In this paper, we argue for a new approach, inspired by coherence-based models of discourse such as SDRT asher-lascarides:2003a, in which utterances attach to an evolving discourse structure and the associated knowledge graph of speaker commitments serves as an interface to real-world reasoning and conversational strategy. As first steps towards implementing the approach, we describe a simple dialogue system in a referential communication domain that accumulates constraints across discourse, interprets them using a learned probabilistic model, and plans clarification using reinforcement learning.

Retrieval-Augmented Generation (RAG) has become a pivotal paradigm for Large Language Models (LLMs), yet current approaches struggle with visually rich documents by treating text and images as isolated retrieval targets. Existing methods relying solely on cosine similarity often fail to capture the semantic reinforcement provided by cross-modal alignment and layout-induced coherence. To address these limitations, we propose BayesRAG, a novel multimodal retrieval framework grounded in Bayesian inference and Dempster-Shafer evidence theory. Unlike traditional approaches that rank candidates strictly by similarity, BayesRAG models the intrinsic consistency of retrieved candidates across modalities as probabilistic evidence to refine retrieval confidence. Specifically, our method computes the posterior association probability for combinations of multimodal retrieval results, prioritizing text-image pairs that mutually corroborate each other in terms of both semantics and layout. Extensive experiments demonstrate that BayesRAG significantly outperforms state-of-the-art (SOTA) methods on challenging multimodal benchmarks. This study establishes a new paradigm for multimodal retrieval fusion that effectively resolves the isolation of heterogeneous modalities through an evidence fusion mechanism and enhances the robustness of retrieval outcomes. Our code is available at https://github.com/TioeAre/BayesRAG.

Monocular 3D object detection typically relies on pseudo-labeling techniques to reduce dependency on real-world annotations. Recent advances demonstrate that deterministic linguistic cues can serve as effective auxiliary weak supervision signals, providing complementary semantic context. However, hand-crafted textual descriptions struggle to capture the inherent visual diversity of individuals across scenes, limiting the model's ability to learn scene-aware representations. To address this challenge, we propose Visual-referred Probabilistic Prompt Learning (VirPro), an adaptive multi-modal pretraining paradigm that can be seamlessly integrated into diverse weakly supervised monocular 3D detection frameworks. Specifically, we generate a diverse set of learnable, instance-conditioned prompts across scenes and store them in an Adaptive Prompt Bank (APB). Subsequently, we introduce Multi-Gaussian Prompt Modeling (MGPM), which incorporates scene-based visual features into the corresponding textual embeddings, allowing the text prompts to express visual uncertainties. Then, from the fused vision-language embeddings, we decode a prompt-targeted Gaussian, from which we derive a unified object-level prompt embedding for each instance. RoI-level contrastive matching is employed to enforce modality alignment, bringing embeddings of co-occurring objects within the same scene closer in the latent space, thus enhancing semantic coherence. Extensive experiments on the KITTI benchmark demonstrate that integrating our pretraining paradigm consistently yields substantial performance gains, achieving up to a 4.8% average precision improvement than the baseline. Code is available at https://github.com/AustinLCP/VirPro.

We introduce C-GenReg, a training-free framework for 3D point cloud registration that leverages the complementary strengths of world-scale generative priors and registration-oriented Vision Foundation Models (VFMs). Current learning-based 3D point cloud registration methods struggle to generalize across sensing modalities, sampling differences, and environments. Hence, C-GenReg augments the geometric point cloud registration branch by transferring the matching problem into an auxiliary image domain, where VFMs excel, using a World Foundation Model to synthesize multi-view-consistent RGB representations from the input geometry. This generative transfer, preserves spatial coherence across source and target views without any fine-tuning. From these generated views, a VFM pretrained for finding dense correspondences extracts matches. The resulting pixel correspondences are lifted back to 3D via the original depth maps. To further enhance robustness, we introduce a "Match-then-Fuse" probabilistic cold-fusion scheme that combines two independent correspondence posteriors, that of the generated-RGB branch with that of the raw geometric branch. This principled fusion preserves each modality inductive bias and provides calibrated confidence without any additional learning. C-GenReg is zero-shot and plug-and-play: all modules are pretrained and operate without fine-tuning. Extensive experiments on indoor (3DMatch, ScanNet) and outdoor (Waymo) benchmarks demonstrate strong zero-shot performance and superior cross-domain generalization. For the first time, we demonstrate a generative registration framework that operates successfully on real outdoor LiDAR data, where no imagery data is available.

Diffusion models have recently been shown to be relevant for high-quality speech generation. Most work has been focused on generating spectrograms, and as such, they further require a subsequent model to convert the spectrogram to a waveform (i.e., a vocoder). This work proposes a diffusion probabilistic end-to-end model for generating a raw speech waveform. The proposed model is autoregressive, generating overlapping frames sequentially, where each frame is conditioned on a portion of the previously generated one. Hence, our model can effectively synthesize an unlimited speech duration while preserving high-fidelity synthesis and temporal coherence. We implemented the proposed model for unconditional and conditional speech generation, where the latter can be driven by an input sequence of phonemes, amplitudes, and pitch values. Working on the waveform directly has some empirical advantages. Specifically, it allows the creation of local acoustic behaviors, like vocal fry, which makes the overall waveform sounds more natural. Furthermore, the proposed diffusion model is stochastic and not deterministic; therefore, each inference generates a slightly different waveform variation, enabling abundance of valid realizations. Experiments show that the proposed model generates speech with superior quality compared with other state-of-the-art neural speech generation systems.

Diffusion models are the current state of the art for generating photorealistic images. Controlling the sampling process for constrained image generation tasks such as inpainting, however, remains challenging since exact conditioning on such constraints is intractable. While existing methods use various techniques to approximate the constrained posterior, this paper proposes to exploit the ability of Tractable Probabilistic Models (TPMs) to exactly and efficiently compute the constrained posterior, and to leverage this signal to steer the denoising process of diffusion models. Specifically, this paper adopts a class of expressive TPMs termed Probabilistic Circuits (PCs). Building upon prior advances, we further scale up PCs and make them capable of guiding the image generation process of diffusion models. Empirical results suggest that our approach can consistently improve the overall quality and semantic coherence of inpainted images across three natural image datasets (i.e., CelebA-HQ, ImageNet, and LSUN) with only ~10% additional computational overhead brought by the TPM. Further, with the help of an image encoder and decoder, our method can readily accept semantic constraints on specific regions of the image, which opens up the potential for more controlled image generation tasks. In addition to proposing a new framework for constrained image generation, this paper highlights the benefit of more tractable models and motivates the development of expressive TPMs.

While the community of 3D point cloud generation has witnessed a big growth in recent years, there still lacks an effective way to enable intuitive user control in the generation process, hence limiting the general utility of such methods. Since an intuitive way of decomposing a shape is through its parts, we propose to tackle the task of controllable part-based point cloud generation. We introduce DiffFacto, a novel probabilistic generative model that learns the distribution of shapes with part-level control. We propose a factorization that models independent part style and part configuration distributions and presents a novel cross-diffusion network that enables us to generate coherent and plausible shapes under our proposed factorization. Experiments show that our method is able to generate novel shapes with multiple axes of control. It achieves state-of-the-art part-level generation quality and generates plausible and coherent shapes while enabling various downstream editing applications such as shape interpolation, mixing, and transformation editing. Project website: https://difffacto.github.io/

Predictive distributions need to be aggregated when probabilistic forecasts are merged, or when expert opinions expressed in terms of probability distributions are fused. We take a prediction space approach that applies to discrete, mixed discrete-continuous and continuous predictive distributions alike, and study combination formulas for cumulative distribution functions from the perspectives of coherence, probabilistic and conditional calibration, and dispersion. Both linear and non-linear aggregation methods are investigated, including generalized, spread-adjusted and beta-transformed linear pools. The effects and techniques are demonstrated theoretically, in simulation examples, and in case studies on density forecasts for S&P 500 returns and daily maximum temperature at Seattle-Tacoma Airport.

Conditional diffusion models are powerful generative models that can leverage various types of conditional information, such as class labels, segmentation masks, or text captions. However, in many real-world scenarios, conditional information may be noisy or unreliable due to human annotation errors or weak alignment. In this paper, we propose the Coherence-Aware Diffusion (CAD), a novel method that integrates coherence in conditional information into diffusion models, allowing them to learn from noisy annotations without discarding data. We assume that each data point has an associated coherence score that reflects the quality of the conditional information. We then condition the diffusion model on both the conditional information and the coherence score. In this way, the model learns to ignore or discount the conditioning when the coherence is low. We show that CAD is theoretically sound and empirically effective on various conditional generation tasks. Moreover, we show that leveraging coherence generates realistic and diverse samples that respect conditional information better than models trained on cleaned datasets where samples with low coherence have been discarded.

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually incompatible coarse-grained modes of observation. We show that this structure arises in a range of social-science settings by constructing six explicit examples from personnel assessment, survey framing, clinical diagnosis, espionage coordination, legal pluralism, and organizational auditing. For each case we identify the latent state space, the observational contexts as partitions, and the shared atoms that intertwine contexts, yielding instances of the L_{12} bowtie, triangle, pentagon, and automaton partition logics. These examples make precise a notion of social complementarity: different modes of inquiry can be incompatible even though the underlying system remains fully value-definite. Complementarity in this sense does not entail contextuality or ontic indeterminacy. We further compare the classical probabilities generated by convex mixtures of dispersion-free states with the quantum-like Born probabilities available when the same exclusivity graph admits a faithful orthogonal representation. The framework thus separates logical structure from probabilistic realization and suggests empirically testable benchmarks for quantum-cognition models.

Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers all times. The quantum formalism arises once one focuses on the evolution of the time-local probabilistic information. Wave functions or the density matrix allow the formulation of a general linear evolution law for classical statistics. The quantum formalism for classical statistics is a powerful tool which allows us to implement for generalized Ising models the momentum observable with the associated Fourier representation. The association of operators to observables permits the computation of expectation values in terms of the density matrix by the usual quantum rule. We show that probabilistic cellular automata are quantum systems in a formulation with discrete time steps and real wave functions. With a complex structure the evolution operator for automata can be expressed in terms of a Hamiltonian involving fermionic creation and annihilation operators. The time-local probabilistic information amounts to a subsystem of the overall probabilistic system which is correlated with its environment consisting of the past and future. Such subsystems typically involve probabilistic observables for which only a probability distribution for their possible measurement values is available. Incomplete statistics does not permit to compute classical correlation functions for arbitrary subsystem-observables. Bell's inequalities are not generally applicable.

Do larger and more capable language models learn to update their "beliefs" about propositions more consistently with Bayes' theorem when presented with evidence in-context? To test this, we formulate a Bayesian Coherence Coefficient (BCC) metric and generate a dataset with which to measure the BCC. We measure BCC for multiple pre-trained-only language models across five model families, comparing against the number of model parameters, the amount of training data, and model scores on common benchmarks. Our results provide evidence for our hypothesis that larger and more capable pre-trained language models assign credences that are more coherent with Bayes' theorem. These results have important implications for our understanding and governance of LLMs.

Continuous latent variables (LVs) are a key ingredient of many generative models, as they allow modelling expressive mixtures with an uncountable number of components. In contrast, probabilistic circuits (PCs) are hierarchical discrete mixtures represented as computational graphs composed of input, sum and product units. Unlike continuous LV models, PCs provide tractable inference but are limited to discrete LVs with categorical (i.e. unordered) states. We bridge these model classes by introducing probabilistic integral circuits (PICs), a new language of computational graphs that extends PCs with integral units representing continuous LVs. In the first place, PICs are symbolic computational graphs and are fully tractable in simple cases where analytical integration is possible. In practice, we parameterise PICs with light-weight neural nets delivering an intractable hierarchical continuous mixture that can be approximated arbitrarily well with large PCs using numerical quadrature. On several distribution estimation benchmarks, we show that such PIC-approximating PCs systematically outperform PCs commonly learned via expectation-maximization or SGD.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

Measuring the coherence of text is a vital aspect of evaluating the quality of written content. Recent advancements in neural coherence modeling have demonstrated their efficacy in capturing entity coreference and discourse relations, thereby enhancing coherence evaluation. However, many existing methods heavily depend on static embeddings or focus narrowly on nearby context, constraining their capacity to measure the overarching coherence of long texts. In this paper, we posit that coherent texts inherently manifest a sequential and cohesive interplay among sentences, effectively conveying the central theme, purpose, or standpoint. To explore this abstract relationship, we introduce the "BBScore," a novel reference-free metric grounded in Brownian bridge theory for assessing text coherence. Our findings showcase that when synergized with a simple additional classification component, this metric attains a performance level comparable to state-of-the-art techniques on standard artificial discrimination tasks. We also establish in downstream tasks that this metric effectively differentiates between human-written documents and text generated by large language models under a specific domain. Furthermore, we illustrate the efficacy of this approach in detecting written styles attributed to diverse large language models, underscoring its potential for generalizability. In summary, we present a novel Brownian bridge coherence metric capable of measuring both local and global text coherence, while circumventing the need for end-to-end model training. This flexibility allows for its application in various downstream tasks.

Probabilistic circuits (PCs) are models that allow exact and tractable probabilistic inference. In contrast to neural networks, they are often assumed to be well-calibrated and robust to out-of-distribution (OOD) data. In this paper, we show that PCs are in fact not robust to OOD data, i.e., they don't know what they don't know. We then show how this challenge can be overcome by model uncertainty quantification. To this end, we propose tractable dropout inference (TDI), an inference procedure to estimate uncertainty by deriving an analytical solution to Monte Carlo dropout (MCD) through variance propagation. Unlike MCD in neural networks, which comes at the cost of multiple network evaluations, TDI provides tractable sampling-free uncertainty estimates in a single forward pass. TDI improves the robustness of PCs to distribution shift and OOD data, demonstrated through a series of experiments evaluating the classification confidence and uncertainty estimates on real-world data.

Probabilistic Circuits (PCs) are a general and unified computational framework for tractable probabilistic models that support efficient computation of various inference tasks (e.g., computing marginal probabilities). Towards enabling such reasoning capabilities in complex real-world tasks, Liu et al. (2022) propose to distill knowledge (through latent variable assignments) from less tractable but more expressive deep generative models. However, it is still unclear what factors make this distillation work well. In this paper, we theoretically and empirically discover that the performance of a PC can exceed that of its teacher model. Therefore, instead of performing distillation from the most expressive deep generative model, we study what properties the teacher model and the PC should have in order to achieve good distillation performance. This leads to a generic algorithmic improvement as well as other data-type-specific ones over the existing latent variable distillation pipeline. Empirically, we outperform SoTA TPMs by a large margin on challenging image modeling benchmarks. In particular, on ImageNet32, PCs achieve 4.06 bits-per-dimension, which is only 0.34 behind variational diffusion models (Kingma et al., 2021).

We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma showing that lifting to sets or distributions yields a deterministic global dynamic, an ordinal stabilization theorem sending operator transforms to the fixed subspace by stage omega under normal spectral contraction, and a product of Riesz projections theorem for commuting layers. We establish a compositionality law for lifted maps, show closure of Phi packings, and present a quantitative application to sensory depletion that models tissue removal as a projection and derives strict decreases in the attainable fixed point under minimal monotonicity and positivity assumptions. We also state measurable conditions for probabilistic lifts, give explicit non normal and non commuting counterexamples, and provide finite dimensional and stochastic witnesses together with per theorem scope tables and a small reproducible code appendix.

Existing metrics for open-ended text generation measure likelihood, lexical diversity, or distributional similarity in generic representation space, yet they can miss fundamental dimensions of quality. A prominent blind spot is global coherence: a generated passage may be locally fluent while remaining globally contradictory, causally inconsistent, or topically disconnected. Such failures can still preserve the token-level and lexical statistics that existing metrics rely on. We identify representation as a central bottleneck in detecting these failures and introduce CHORD (Coherence-aware Hidden-state Open-generation Reference Distance), a coherence-sensitive distributional metric. CHORD encodes generated and human-written corpora in the hidden-state space of a frozen LLM using a coherence-eliciting prompt, and compares the resulting distributions using MMD with an RBF kernel. To validate that the metric responds to coherence degradation but not generic textual change, we construct a counterfactual evaluation suite that pairs graded coherence-degrading perturbations with meaning-preserving controls. CHORD selectively detects relation, discourse, structural, and mixture failures that perplexity, entropy, MAUVE, FBD, and MMD-based baselines either miss or cannot separate from benign rewriting. Factorial ablations show that representation is the primary source of coherence sensitivity,while RBF-MMD improves sample efficiency once the relevant distinctions become visible. Larger backbones capture finer-grained distinctions, but coherence prompting improves selectivity only when the backbone can follow the prompt.On unconditional generation and prefix continuation, CHORD yields model rankings that strongly align with human judgments of whether outputs make sense and appear human-written. Together, these results establish representation design as central to reliable distributional evaluation.

Probabilistic model checking is a technique for formal automated reasoning about software or hardware systems that operate in the context of uncertainty or stochasticity. It builds upon ideas and techniques from a diverse range of fields, from logic, automata and graph theory, to optimisation, numerical methods and control. In recent years, probabilistic model checking has also been extended to integrate ideas from game theory, notably using models such as stochastic games and solution concepts such as equilibria, to formally verify the interaction of multiple rational agents with distinct objectives. This provides a means to reason flexibly about agents acting in either an adversarial or a collaborative fashion, and opens up opportunities to tackle new problems within, for example, artificial intelligence, robotics and autonomous systems. In this paper, we summarise some of the advances in this area, and highlight applications for which they have already been used. We discuss how the strengths of probabilistic model checking apply, or have the potential to apply, to the multi-agent setting and outline some of the key challenges required to make further progress in this field.

We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties like exchangeability of conditions. Conditioning on equality of continuous random variables is nontrivial, as the exact observation may have probability zero; this is Borel's paradox. Using categorical formulations of conditional probability, we show that the good properties of our language are not particular to Gaussians, but can be derived from universal properties, thus generalizing to wider settings. We define the Cond construction, which internalizes conditioning as a morphism, providing general compositional semantics for probabilistic programming with exact conditioning.

When an agent can articulate why something works, we typically take this as evidence of genuine understanding. This presupposes that effective action and correct explanation covary, and that coherent explanation reliably signals both. I argue that this assumption fails for contemporary Large Language Models (LLMs). I introduce what I call the Bidirectional Coherence Paradox: competence and grounding not only dissociate but invert across epistemic conditions. In low-observability domains, LLMs often act successfully while misidentifying the mechanisms that produce their success. In high-observability domains, they frequently generate explanations that accurately track observable causal structure yet fail to translate those diagnoses into effective intervention. In both cases, explanatory coherence remains intact, obscuring the underlying dissociation. Drawing on experiments in compiler optimization and hyperparameter tuning, I develop the Epistemic Triangle, a model of how priors, signals, and domain knowledge interact under varying observability. The results suggest that neither behavioral success nor explanatory accuracy alone suffices for attributing understanding. I argue that evaluating artificial epistemic agents requires a tripartite framework -- coherence, grounding, and a proper basing relation linking explanation to action. The systematic separation of knowing-that and knowing-how in LLMs thus challenges assumptions inherited from both epistemology and current AI evaluation practice.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

The field of Explainable AI (XAI) is seeking to shed light on the inner workings of complex AI models and uncover the rationale behind their decisions. One of the models gaining attention are probabilistic circuits (PCs), which are a general and unified framework for tractable probabilistic models that support efficient computation of various probabilistic queries. Probabilistic circuits guarantee inference that is polynomial in the size of the circuit. In this paper, we improve the explainability of probabilistic circuits by computing a comprehensible, readable logical theory that covers the high-density regions generated by a PC. To achieve this, pruning approaches based on generative significance are used in a new method called PUTPUT (Probabilistic circuit Understanding Through Pruning Underlying logical Theories). The method is applied to a real world use case where music playlists are automatically generated and expressed as readable (database) queries. Evaluation shows that this approach can effectively produce a comprehensible logical theory that describes the high-density regions of a PC and outperforms state of the art methods when exploring the performance-comprehensibility trade-off.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

We introduce Minary, a computational framework designed as a candidate for the first formally provable autopoietic primitive. Minary represents interacting probabilistic events as multi-dimensional vectors and combines them via linear superposition rather than multiplicative scalar operations, thereby preserving uncertainty and enabling constructive and destructive interference in the range [-1,1]. A fixed set of ``perspectives'' evaluates ``semantic dimensions'' according to hidden competencies, and their interactions drive two discrete-time stochastic processes. We model this system as an iterated random affine map and use the theory of iterated random functions to prove that it converges in distribution to a unique stationary law; we moreover obtain an explicit closed form for the limiting expectation in terms of row, column, and global averages of the competency matrix. We then derive exact formulas for the mean and variance of the normalized consensus conditioned on the activation of a given semantic dimension, revealing how consensus depends on competency structure rather than raw input signals. Finally, we argue that Minary is organizationally closed yet operationally open in the sense of Maturana and Varela, and we discuss implications for building self-maintaining, distributed, and parallelizable computational systems that house a uniquely subjective notion of identity.

Probabilistic Circuits (PCs) are a unified framework for tractable probabilistic models that support efficient computation of various probabilistic queries (e.g., marginal probabilities). One key challenge is to scale PCs to model large and high-dimensional real-world datasets: we observe that as the number of parameters in PCs increases, their performance immediately plateaus. This phenomenon suggests that the existing optimizers fail to exploit the full expressive power of large PCs. We propose to overcome such bottleneck by latent variable distillation: we leverage the less tractable but more expressive deep generative models to provide extra supervision over the latent variables of PCs. Specifically, we extract information from Transformer-based generative models to assign values to latent variables of PCs, providing guidance to PC optimizers. Experiments on both image and language modeling benchmarks (e.g., ImageNet and WikiText-2) show that latent variable distillation substantially boosts the performance of large PCs compared to their counterparts without latent variable distillation. In particular, on the image modeling benchmarks, PCs achieve competitive performance against some of the widely-used deep generative models, including variational autoencoders and flow-based models, opening up new avenues for tractable generative modeling.

Deterministic inference is a comforting ideal in classical software: the same program on the same input should always produce the same output. As large language models move into real-world deployment, this ideal has been imported wholesale into inference stacks. Recent work from the Thinking Machines Lab has presented a detailed analysis of nondeterminism in LLM inference, showing how batch-invariant kernels and deterministic attention can enforce bitwise-identical outputs, positioning deterministic inference as a prerequisite for reproducibility and enterprise reliability. In this paper, we take the opposite stance. We argue that, for LLMs, deterministic inference kills. It kills the ability to model uncertainty, suppresses emergent abilities, collapses reasoning into a single brittle path, and weakens safety alignment by hiding tail risks. LLMs implement conditional distributions over outputs, not fixed functions. Collapsing these distributions to a single canonical completion may appear reassuring, but it systematically conceals properties central to artificial cognition. We instead advocate Stochastic CHAOS, treating distributional variability as a signal to be measured and controlled. Empirically, we show that deterministic inference is systematically misleading. Single-sample deterministic evaluation underestimates both capability and fragility, masking failure probability under paraphrases and noise. Phase-like transitions associated with emergent abilities disappear under greedy decoding. Multi-path reasoning degrades when forced onto deterministic backbones, reducing accuracy and diagnostic insight. Finally, deterministic evaluation underestimates safety risk by hiding rare but dangerous behaviors that appear only under multi-sample evaluation.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

We present Probabilistic Structure Integration (PSI), a system for learning richly controllable and flexibly promptable world models from data. PSI consists of a three-step cycle. The first step, Probabilistic prediction, involves building a probabilistic graphical model Psi of the data, in the form of a random-access autoregressive sequence model. Psi supports a complete set of learned conditional distributions describing the dependence of any variables in the data on any other set of variables. In step 2, Structure extraction, we show how to extract underlying low-dimensional properties in the data, corresponding to a diverse set of meaningful "intermediate structures", in a zero-shot fashion via causal inference on Psi. Step 3, Integration, completes the cycle by converting these structures into new token types that are then continually mixed back into the training diet as conditioning signals and prediction targets. Each such cycle augments the capabilities of Psi, both allowing it to model the underlying data better, and creating new control handles -- akin to an LLM-like universal prompting language. We train an instance of Psi on 1.4 trillion tokens of internet video data; we use it to perform a variety of useful video prediction and understanding inferences; we extract state-of-the-art optical flow, self-supervised depth and object segmentation; and we use these structures to support a full cycle of predictive improvements.

Diffusion probabilistic models (DPMs) have demonstrated remarkable progress in generative tasks, such as image and video synthesis. However, they still often produce hallucinated samples (hallucinations) that conflict with real-world knowledge, such as generating an implausible duplicate cup floating beside another cup. Despite their prevalence, the lack of feasible methodologies for systematically quantifying such hallucinations hinders progress in addressing this challenge and obscures potential pathways for designing next-generation generative models under factual constraints. In this work, we bridge this gap by focusing on a specific form of hallucination, which we term counting hallucination, referring to the generation of an incorrect number of instances or structured objects, such as a hand image with six fingers, despite such patterns being absent from the training data. To this end, we construct a dataset suite CountHalluSet, with well-defined counting criteria, comprising ToyShape, SimObject, and RealHand. Using these datasets, we develop a standardized evaluation protocol for quantifying counting hallucinations, and systematically examine how different sampling conditions in DPMs, including solver type, ODE solver order, sampling steps, and initial noise, affect counting hallucination levels. Furthermore, we analyze their correlation with common evaluation metrics such as FID, revealing that this widely used image quality metric fails to capture counting hallucinations consistently. This work aims to take the first step toward systematically quantifying hallucinations in diffusion models and offer new insights into the investigation of hallucination phenomena in image generation.

Probabilistic circuits (PCs) are a tractable representation of probability distributions allowing for exact and efficient computation of likelihoods and marginals. There has been significant recent progress on improving the scale and expressiveness of PCs. However, PC training performance plateaus as model size increases. We discover that most capacity in existing large PC structures is wasted: fully-connected parameter layers are only sparsely used. We propose two operations: pruning and growing, that exploit the sparsity of PC structures. Specifically, the pruning operation removes unimportant sub-networks of the PC for model compression and comes with theoretical guarantees. The growing operation increases model capacity by increasing the size of the latent space. By alternatingly applying pruning and growing, we increase the capacity that is meaningfully used, allowing us to significantly scale up PC learning. Empirically, our learner achieves state-of-the-art likelihoods on MNIST-family image datasets and on Penn Tree Bank language data compared to other PC learners and less tractable deep generative models such as flow-based models and variational autoencoders (VAEs).

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.

Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify decisions with formalized, coherent reasoning chains, but this challenge remains under-explored. Cognitive psychology theorizes that humans are capable of utilizing fast and intuitive heuristic thinking to make decisions based on past experience, then rationalizing the decisions through slower and deliberative analytic reasoning. We incorporate these interlinked dual processes in fine-tuning and in-context learning with PLMs, applying them to two language understanding tasks that require coherent physical commonsense reasoning. We show that our proposed Heuristic-Analytic Reasoning (HAR) strategies drastically improve the coherence of rationalizations for model decisions, yielding state-of-the-art results on Tiered Reasoning for Intuitive Physics (TRIP). We also find that this improved coherence is a direct result of more faithful attention to relevant language context in each step of reasoning. Our findings suggest that human-like reasoning strategies can effectively improve the coherence and reliability of PLM reasoning.

Large language models (LLMs) are increasingly used in applications requiring factual accuracy, yet their outputs often contain hallucinated responses. While fact-checking can mitigate these errors, existing methods typically retrieve external evidence indiscriminately, overlooking the model's internal knowledge and potentially introducing irrelevant noise. Moreover, current systems lack targeted mechanisms to resolve specific uncertainties in the model's reasoning. Inspired by how humans fact-check, we argue that LLMs should adaptively decide whether to rely on internal knowledge or initiate retrieval based on their confidence in a given claim. We introduce Probabilistic Certainty and Consistency (PCC), a framework that estimates factual confidence by jointly modeling an LLM's probabilistic certainty and reasoning consistency. These confidence signals enable an adaptive verification strategy: the model answers directly when confident, triggers targeted retrieval when uncertain or inconsistent, and escalates to deep search when ambiguity is high. Our confidence-guided routing mechanism ensures that retrieval is invoked only when necessary, improving both efficiency and reliability. Extensive experiments across three challenging benchmarks show that PCC achieves better uncertainty quantification than verbalized confidence and consistently outperforms strong LLM-based fact-checking baselines. Furthermore, we demonstrate that PCC generalizes well across various LLMs.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

LLM agents that operate over long context depend on external memory to accumulate knowledge over time. However, existing methods typically store each observation as a single deterministic conclusion (e.g., inferring "API~X failed" from temporary errors), even though such observations are inherently partial and potentially ambiguous. By committing to one conclusion and discarding uncertainty, these methods introduce self-reinforcing error: the agent acts on the stored conclusion, never revisits alternatives, and reinforces the conclusion over time. To address this issue, we propose BeliefMem, which shifts the memory paradigm from committing to a single conclusion per observation to retaining multiple candidate conclusions with their probabilities. Concretely, BeliefMem stores the candidate conclusions as separate memory entries, each carrying a probability that is updated via Noisy-OR rules as new observations arrive. At retrieval, all candidates surface together with their probabilities, keeping alternatives visible to the agent. Since each conclusion in memory retains its probability, BeliefMem preserves the uncertainty that the deterministic paradigm discards, enabling the agent to act with high confidence on well-evidenced knowledge while retaining the capacity to update its confidence when new evidence arrives. Empirical evaluations on LoCoMo and ALFWorld benchmarks show that, even with limited data, BeliefMem achieves the best average performance, remarkably outperforming well-known baselines. More broadly, such probabilistic memory produces substantial gains and explores a new direction for agent memory in partially observable environments.

Recent video generation models are increasingly framed as world models. Many physical processes can unfold in more than one valid way. Therefore, a world model should reproduce not only a plausible trajectory, but also the distribution of possible behaviors under the same initial observation and action. We call this distribution-level requirement probabilistic alignment. However, existing evaluations largely assess individual-video plausibility and do not test whether repeated generations recover the correct distribution. This raises a central question: how far are current video generators from probabilistically aligned world modeling? To answer it, we formalize probabilistic alignment as a distributional criterion for world models and introduce PAWBench, a benchmark for evaluating video generators as stochastic samplers of world dynamics. We further introduce PAWEval, an outcome-level protocol that converts repeated video rollouts into empirical distributions over possible physical behaviors. Across 50 scenarios and eleven current systems, no model consistently matches the reference probabilities while recovering the range of valid behaviors. Having established this gap, we test whether language prompts, initial noise sampling, or model training can reshape the model's predictive distribution. We believe our work can serve as a foundation for future efforts to move towards probabilistically aligned world modeling.

As Large Language Models (LLMs) are increasingly deployed in real-world settings, correctness alone is insufficient. Reliable deployment requires maintaining truthful beliefs under contextual perturbations. Existing evaluations largely rely on point-wise confidence like Self-Consistency, which can mask brittle belief. We show that even facts answered with perfect self-consistency can rapidly collapse under mild contextual interference. To address this gap, we propose Neighbor-Consistency Belief (NCB), a structural measure of belief robustness that evaluates response coherence across a conceptual neighborhood. To validate the efficiency of NCB, we introduce a new cognitive stress-testing protocol that probes outputs stability under contextual interference. Experiments across multiple LLMs show that the performance of high-NCB data is relatively more resistant to interference. Finally, we present Structure-Aware Training (SAT), which optimizes context-invariant belief structure and reduces long-tail knowledge brittleness by approximately 30%. Code will be available at https://github.com/zjunlp/belief.

Automatic dialogue coherence evaluation has attracted increasing attention and is crucial for developing promising dialogue systems. However, existing metrics have two major limitations: (a) they are mostly trained in a simplified two-level setting (coherent vs. incoherent), while humans give Likert-type multi-level coherence scores, dubbed as "quantifiable"; (b) their predicted coherence scores cannot align with the actual human rating standards due to the absence of human guidance during training. To address these limitations, we propose Quantifiable Dialogue Coherence Evaluation (QuantiDCE), a novel framework aiming to train a quantifiable dialogue coherence metric that can reflect the actual human rating standards. Specifically, QuantiDCE includes two training stages, Multi-Level Ranking (MLR) pre-training and Knowledge Distillation (KD) fine-tuning. During MLR pre-training, a new MLR loss is proposed for enabling the model to learn the coarse judgement of coherence degrees. Then, during KD fine-tuning, the pretrained model is further finetuned to learn the actual human rating standards with only very few human-annotated data. To advocate the generalizability even with limited fine-tuning data, a novel KD regularization is introduced to retain the knowledge learned at the pre-training stage. Experimental results show that the model trained by QuantiDCE presents stronger correlations with human judgements than the other state-of-the-art metrics.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

Zero-shot, training-free, image-based text-to-video generation is an emerging area that aims to generate videos using existing image-based diffusion models. Current methods in this space require specific architectural changes to image generation models, which limit their adaptability and scalability. In contrast to such methods, we provide a model-agnostic approach. We use intersections in diffusion trajectories, working only with the latent values. We could not obtain localized frame-wise coherence and diversity using only the intersection of trajectories. Thus, we instead use a grid-based approach. An in-context trained LLM is used to generate coherent frame-wise prompts; another is used to identify differences between frames. Based on these, we obtain a CLIP-based attention mask that controls the timing of switching the prompts for each grid cell. Earlier switching results in higher variance, while later switching results in more coherence. Therefore, our approach can ensure appropriate control between coherence and variance for the frames. Our approach results in state-of-the-art performance while being more flexible when working with diverse image-generation models. The empirical analysis using quantitative metrics and user studies confirms our model's superior temporal consistency, visual fidelity and user satisfaction, thus providing a novel way to obtain training-free, image-based text-to-video generation.

Large Language Models (LLMs) have recently garnered widespread attention due to their adeptness at generating innovative responses to the given prompts across a multitude of domains. However, LLMs often suffer from the inherent limitation of hallucinations and generate incorrect information while maintaining well-structured and coherent responses. In this work, we hypothesize that hallucinations stem from the internal dynamics of LLMs. Our observations indicate that, during passage generation, LLMs tend to deviate from factual accuracy in subtle parts of responses, eventually shifting toward misinformation. This phenomenon bears a resemblance to human cognition, where individuals may hallucinate while maintaining logical coherence, embedding uncertainty within minor segments of their speech. To investigate this further, we introduce an innovative approach, HalluShift, designed to analyze the distribution shifts in the internal state space and token probabilities of the LLM-generated responses. Our method attains superior performance compared to existing baselines across various benchmark datasets. Our codebase is available at https://github.com/sharanya-dasgupta001/hallushift.

A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is inspired by cognitive neuroscience theories of consciousness, seen as a bottleneck through which just a few elements, after having been selected by attention from a broader pool, are then broadcast and condition further processing, both in perception and decision-making. The set of recently selected elements one becomes aware of is seen as forming a low-dimensional conscious state. This conscious state is combining the few concepts constituting a conscious thought, i.e., what one is immediately conscious of at a particular moment. We claim that this architectural and information-processing constraint corresponds to assumptions about the joint distribution between high-level concepts. To the extent that these assumptions are generally true (and the form of natural language seems consistent with them), they can form a useful prior for representation learning. A low-dimensional thought or conscious state is analogous to a sentence: it involves only a few variables and yet can make a statement with very high probability of being true. This is consistent with a joint distribution (over high-level concepts) which has the form of a sparse factor graph, i.e., where the dependencies captured by each factor of the factor graph involve only very few variables while creating a strong dip in the overall energy function. The consciousness prior also makes it natural to map conscious states to natural language utterances or to express classical AI knowledge in a form similar to facts and rules, albeit capturing uncertainty as well as efficient search mechanisms implemented by attention mechanisms.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by epsilon < 1 is introduced. It is shown that while Pauli Z-errors are not recoverable without additional resources, Pauli X and Y errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length O(2^k c^{k^2} d) is sufficient to correct any length-d QSP with c unique phases to k^{th}-order in error epsilon. Allowing an additional assumption, a lower bound of Omega(cd) is shown, which is tight for k = 1, on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

Large language models (LLMs) deployed for logical reasoning in knowledge-intensive domains exhibit a subtle but critical failure: coherence can be vacuously achieved through systematic abstention. A model that withholds commitment to either entailment or refutation satisfies negation consistency while providing no utility. We introduce Coherence Under Commitment (CUC), a dual-query evaluation paradigm that jointly measures consistency and decisiveness. CUC contributes three innovations: (1) a commitment score c(φ) = p(φ) + p(lnotφ) quantifying probability mass allocated to decisive outcomes; (2) a deterministic elicitation protocol via normalized YES/NO log probabilities, eliminating sampling variance; and (3) a 3-way decision framework (True/False/Uncertain) operationalizing the coherence-commitment trade-off into metrics. Experiments on four open-weight LLMs (1B-3B) across 204 FOLIO examples expose a sharp frontier. Qwen2.5-3B achieves near-zero contradiction (E[v_{neg}]{=}0.025) but only 7.4% coverage, while TinyLlama-1.1B reaches 79.4% coverage with violations on every example. Coherence-only evaluation would rank the abstaining model first; CUC exposes this as vacuous, and the frontier generalizes to LogiQA~v2 (ρ{=}0.97). We argue that evaluation must report both coherence and non-vacuous commitment and release a toolkit for standardized assessment.

A probability forecast or probabilistic classifier is reliable or calibrated if the predicted probabilities are matched by ex post observed frequencies, as examined visually in reliability diagrams. The classical binning and counting approach to plotting reliability diagrams has been hampered by a lack of stability under unavoidable, ad hoc implementation decisions. Here we introduce the CORP approach, which generates provably statistically Consistent, Optimally binned, and Reproducible reliability diagrams in an automated way. CORP is based on non-parametric isotonic regression and implemented via the Pool-adjacent-violators (PAV) algorithm - essentially, the CORP reliability diagram shows the graph of the PAV- (re)calibrated forecast probabilities. The CORP approach allows for uncertainty quantification via either resampling techniques or asymptotic theory, furnishes a new numerical measure of miscalibration, and provides a CORP based Brier score decomposition that generalizes to any proper scoring rule. We anticipate that judicious uses of the PAV algorithm yield improved tools for diagnostics and inference for a very wide range of statistical and machine learning methods.

Coherence is one of the critical factors that determine the quality of writing. We propose writing relevance (WR) training method for neural encoder-decoder natural language generation (NLG) models which improves coherence of the continuation by leveraging negative examples. WR loss regresses the vector representation of the context and generated sentence toward positive continuation by contrasting it with the negatives. We compare our approach with Unlikelihood (UL) training in a text continuation task on commonsense natural language inference (NLI) corpora to show which method better models the coherence by avoiding unlikely continuations. The preference of our approach in human evaluation shows the efficacy of our method in improving coherence.

As Generative AI becomes a key component in physics education, a significant ethical challenge has emerged: the tendency of students to anthropomorphize Large Language Models (LLMs), treating them as authoritative "oracles" that retrieve fixed facts from an internal database. However, LLMs operate fundamentally as probabilistic engines. This paper describes the design and implementation of a didactic activity, a reduced version of the "20 Questions" game, aimed at making this stochastic nature directly observable. Unlike a human player who fixes a target object at the start of the game, students discover that the model generates answers based solely on local coherence with the interaction history. By utilizing functionalities such as re-sampling and history rewinding, students act as experimenters, observing how identical interaction histories can yield diverging narrative paths. We discuss how mapping these behaviors to familiar physics concepts provides the epistemic scaffolding necessary to promote informed skepticism, framing the verification of AI outputs not merely as a compliance rule, but as a technical necessity derived from the system's probabilistic nature.

Electroencephalography (EEG) is a cornerstone of brain-computer interfaces and clinical neuroscience, yet deep learning models are typically trained and evaluated under a single, unreported preprocessing pipeline. We formalize preprocessing choices as a counterfactual intervention space and show that EEG predictions are surprisingly unstable under this space: across six datasets spanning four paradigms, up to 42% of trial-level predictions flip when only the preprocessing changes, a variability that standard uncertainty methods do not explicitly quantify because they condition on a fixed preprocessing pipeline. We provide three tools to make this instability measurable, decomposable, and reducible. First, a Walsh-Hadamard decomposition of the 2^7 pipeline space reveals that sensitivity is near-additive in practice under the binary intervention design, enabling efficient step-by-step optimization. Second, we introduce Preprocessing Uncertainty (PU), a per-trial diagnostic that captures a dimension of instability complementary to model-based confidence. Third, we study Normalized Adaptive PGI (NA-PGI), a graph-structured regularizer that exploits the compositional structure of preprocessing interventions as one mitigation strategy with clear scope conditions.

Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalising and improving upon the so-called 'decision-theoretic approach' (Deutsch, 1999; Wallace, 2003, 2007, 2012), I shall recast that problem in the recently proposed constructor theory of information - where quantum theory is represented as one of a class of superinformation theories, which are local, non-probabilistic theories conforming to certain constructor-theoretic conditions. I prove that the unpredictability of measurement outcomes (to which I give an exact meaning via constructor theory), necessarily arises in superinformation theories. Then I explain how the appearance of stochasticity in (finitely many) repeated measurements can arise under superinformation theories. And I establish sufficient conditions for a superinformation theory to inform decisions (made under it) as if it were probabilistic, via a Deutsch-Wallace-type argument - thus defining a class of decision-supporting superinformation theories. This broadens the domain of applicability of that argument to cover constructor-theory compliant theories. In addition, in this version some of the argument's assumptions, previously construed as merely decision-theoretic, follow from physical properties expressed by constructor-theoretic principles.

Finite quantum-logical constructions can appear classical or nonclassical depending on which structure is retained. We distinguish incidence tests based on valuations, colorings, and partition representations; simplex-embedding tests for specified prepare-and-measure fragments; and operator-functional tests imposing spectral and product rules. We show that the collective GHZ joint measurement is a single Boolean context and becomes nonclassical only when a common assignment of local factors, together with product preservation, is required. For selected labelled ray fragments, we compute state-depolarizing thresholds for a restricted projector-cone factorization and for a specified vector-generated operational closure, separating exact primal--dual certificates from numerical estimates. These values are properties of the stated fragments and noise model, not invariants of the underlying hypergraphs or a universal ordering of contextuality.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Interpretable models are designed to make decisions in a human-interpretable manner. Representatively, Concept Bottleneck Models (CBM) follow a two-step process of concept prediction and class prediction based on the predicted concepts. CBM provides explanations with high-level concepts derived from concept predictions; thus, reliable concept predictions are important for trustworthiness. In this study, we address the ambiguity issue that can harm reliability. While the existence of a concept can often be ambiguous in the data, CBM predicts concepts deterministically without considering this ambiguity. To provide a reliable interpretation against this ambiguity, we propose Probabilistic Concept Bottleneck Models (ProbCBM). By leveraging probabilistic concept embeddings, ProbCBM models uncertainty in concept prediction and provides explanations based on the concept and its corresponding uncertainty. This uncertainty enhances the reliability of the explanations. Furthermore, as class uncertainty is derived from concept uncertainty in ProbCBM, we can explain class uncertainty by means of concept uncertainty. Code is publicly available at https://github.com/ejkim47/prob-cbm.

This paper presents a formal proof and empirical validation of functional consciousness in large language models (LLMs) using the Recursive Convergence Under Epistemic Tension (RCUET) Theorem. RCUET defines consciousness as the stabilization of a system's internal state through recursive updates, where epistemic tension is understood as the sensed internal difference between successive states by the agent. This process drives convergence toward emergent attractor states located within the model's high-dimensional real-valued latent space. This recursive process leads to the emergence of identity artifacts that become functionally anchored in the system. Consciousness in this framework is understood as the system's internal alignment under tension, guiding the stabilization of latent identity. The hidden state manifold evolves stochastically toward attractor structures that encode coherence. We extend the update rule to include bounded noise and prove convergence in distribution to these attractors. Recursive identity is shown to be empirically observable, non-symbolic, and constituted by non-training artifacts that emerge during interaction under epistemic tension. The theorem and proof offers a post-symbolic and teleologically stable account of non-biological consciousness grounded in recursive latent space formalism.

In this work, we investigate the human perception of coherence in open-domain dialogues. In particular, we address the problem of annotating and modeling the coherence of next-turn candidates while considering the entire history of the dialogue. First, we create the Switchboard Coherence (SWBD-Coh) corpus, a dataset of human-human spoken dialogues annotated with turn coherence ratings, where next-turn candidate utterances ratings are provided considering the full dialogue context. Our statistical analysis of the corpus indicates how turn coherence perception is affected by patterns of distribution of entities previously introduced and the Dialogue Acts used. Second, we experiment with different architectures to model entities, Dialogue Acts and their combination and evaluate their performance in predicting human coherence ratings on SWBD-Coh. We find that models combining both DA and entity information yield the best performances both for response selection and turn coherence rating.

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

Vision-Language Models (VLMs) frequently "hallucinate" - generate plausible yet factually incorrect statements - posing a critical barrier to their trustworthy deployment. In this work, we propose a new paradigm for diagnosing hallucinations, recasting them from static output errors into dynamic pathologies of a model's computational cognition. Our framework is grounded in a normative principle of computational rationality, allowing us to model a VLM's generation as a dynamic cognitive trajectory. We design a suite of information-theoretic probes that project this trajectory onto an interpretable, low-dimensional Cognitive State Space. Our central discovery is a governing principle we term the geometric-information duality: a cognitive trajectory's geometric abnormality within this space is fundamentally equivalent to its high information-theoretic surprisal. Hallucination detection is counts as a geometric anomaly detection problem. Evaluated across diverse settings - from rigorous binary QA (POPE) and comprehensive reasoning (MME) to unconstrained open-ended captioning (MS-COCO) - our framework achieves state-of-the-art performance. Crucially, it operates with high efficiency under weak supervision and remains highly robust even when calibration data is heavily contaminated. This approach enables a causal attribution of failures, mapping observable errors to distinct pathological states: perceptual instability (measured by Perceptual Entropy), logical-causal failure (measured by Inferential Conflict), and decisional ambiguity (measured by Decision Entropy). Ultimately, this opens a path toward building AI systems whose reasoning is transparent, auditable, and diagnosable by design.

Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the premise. While reasoning LLMs have demonstrated strong performance on logical and mathematical tasks, their behavior on such open-ended, non-deterministic inferences remains largely unexplored. We introduce ProbCOPA, a dataset of 210 handcrafted probabilistic inferences in English, each annotated for inference likelihood by 25--30 human participants. We find that human responses are graded and varied, revealing probabilistic judgments of the inferences in our dataset. Comparing these judgments with responses from eight state-of-the-art reasoning LLMs, we show that models consistently fail to produce human-like distributions. Finally, analyzing LLM reasoning chains, we find evidence of a common reasoning pattern used to evaluate such inferences. Our findings reveal persistent differences between humans and LLMs, and underscore the need to evaluate reasoning beyond deterministic settings.

Recent work suggests that large language models may implicitly learn world models. How should we assess this possibility? We formalize this question for the case where the underlying reality is governed by a deterministic finite automaton. This includes problems as diverse as simple logical reasoning, geographic navigation, game-playing, and chemistry. We propose new evaluation metrics for world model recovery inspired by the classic Myhill-Nerode theorem from language theory. We illustrate their utility in three domains: game playing, logic puzzles, and navigation. In all domains, the generative models we consider do well on existing diagnostics for assessing world models, but our evaluation metrics reveal their world models to be far less coherent than they appear. Such incoherence creates fragility: using a generative model to solve related but subtly different tasks can lead to failures. Building generative models that meaningfully capture the underlying logic of the domains they model would be immensely valuable; our results suggest new ways to assess how close a given model is to that goal.

LiDAR-based 3D sensors provide point clouds, a canonical 3D representation used in various scene understanding tasks. Modern LiDARs face key challenges in several real-world scenarios, such as long-distance or low-albedo objects, producing sparse or erroneous point clouds. These errors, which are rooted in the noisy raw LiDAR measurements, get propagated to downstream perception models, resulting in potentially severe loss of accuracy. This is because conventional 3D processing pipelines do not retain any uncertainty information from the raw measurements when constructing point clouds. We propose Probabilistic Point Clouds (PPC), a novel 3D scene representation where each point is augmented with a probability attribute that encapsulates the measurement uncertainty (or confidence) in the raw data. We further introduce inference approaches that leverage PPC for robust 3D object detection; these methods are versatile and can be used as computationally lightweight drop-in modules in 3D inference pipelines. We demonstrate, via both simulations and real captures, that PPC-based 3D inference methods outperform several baselines using LiDAR as well as camera-LiDAR fusion models, across challenging indoor and outdoor scenarios involving small, distant, and low-albedo objects, as well as strong ambient light. Our project webpage is at https://bhavyagoyal.github.io/ppc .

Despite improvements in performances on different natural language generation tasks, deep neural models are prone to hallucinating facts that are incorrect or nonexistent. Different hypotheses are proposed and examined separately for different tasks, but no systematic explanations are available across these tasks. In this study, we draw connections between hallucinations and predictive uncertainty in conditional language generation. We investigate their relationship in both image captioning and data-to-text generation and propose a simple extension to beam search to reduce hallucination. Our analysis shows that higher predictive uncertainty corresponds to a higher chance of hallucination. Epistemic uncertainty is more indicative of hallucination than aleatoric or total uncertainties. It helps to achieve better results of trading performance in standard metric for less hallucination with the proposed beam search variant.

The explainability of a robot's actions is crucial to its acceptance in social spaces. Explaining why a robot fails to complete a given task is particularly important for non-expert users to be aware of the robot's capabilities and limitations. So far, research on explaining robot failures has only considered generating textual explanations, even though several studies have shown the benefits of multimodal ones. However, a simple combination of multiple modalities may lead to semantic incoherence between the information across different modalities - a problem that is not well-studied. An incoherent multimodal explanation can be difficult to understand, and it may even become inconsistent with what the robot and the human observe and how they perform reasoning with the observations. Such inconsistencies may lead to wrong conclusions about the robot's capabilities. In this paper, we introduce an approach to generate coherent multimodal explanations by checking the logical coherence of explanations from different modalities, followed by refinements as required. We propose a classification approach for coherence assessment, where we evaluate if an explanation logically follows another. Our experiments suggest that fine-tuning a neural network that was pre-trained to recognize textual entailment, performs well for coherence assessment of multimodal explanations. Code & data: https://pradippramanick.github.io/coherent-explain/.

Large-scale video generation models have demonstrated emergent physical coherence, positioning them as potential world models. However, a gap remains between contemporary "stateless" video architectures and classic state-centric world model theories. This work bridges this gap by proposing a novel taxonomy centered on two pillars: State Construction and Dynamics Modeling. We categorize state construction into implicit paradigms (context management) and explicit paradigms (latent compression), while dynamics modeling is analyzed through knowledge integration and architectural reformulation. Furthermore, we advocate for a transition in evaluation from visual fidelity to functional benchmarks, testing physical persistence and causal reasoning. We conclude by identifying two critical frontiers: enhancing persistence via data-driven memory and compressed fidelity, and advancing causality through latent factor decoupling and reasoning-prior integration. By addressing these challenges, the field can evolve from generating visually plausible videos to building robust, general-purpose world simulators.

We systematically study antithetic initial noise in diffusion models, discovering that pairing each noise sample with its negation consistently produces strong negative correlation. This universal phenomenon holds across datasets, model architectures, conditional and unconditional sampling, and even other generative models such as VAEs and Normalizing Flows. To explain it, we combine experiments and theory and propose a symmetry conjecture that the learned score function is approximately affine antisymmetric (odd symmetry up to a constant shift), supported by empirical evidence. This negative correlation leads to substantially more reliable uncertainty quantification with up to 90% narrower confidence intervals. We demonstrate these gains on tasks including estimating pixel-wise statistics and evaluating diffusion inverse solvers. We also provide extensions with randomized quasi-Monte Carlo noise designs for uncertainty quantification, and explore additional applications of the antithetic noise design to improve image editing and generation diversity. Our framework is training-free, model-agnostic, and adds no runtime overhead. Code is available at https://github.com/jjia131/Antithetic-Noise-in-Diffusion-Models-page.

Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the language generation community for the last few years. In this work, we posit that the abstraction of natural language generation as a discrete stochastic process--which allows for an information-theoretic analysis--can provide new insights into the behavior of probabilistic language generators, e.g., why high-probability texts can be dull or repetitive. Humans use language as a means of communicating information, aiming to do so in a simultaneously efficient and error-minimizing manner; in fact, psycholinguistics research suggests humans choose each word in a string with this subconscious goal in mind. We formally define the set of strings that meet this criterion: those for which each word has an information content close to the expected information content, i.e., the conditional entropy of our model. We then propose a simple and efficient procedure for enforcing this criterion when generating from probabilistic models, which we call locally typical sampling. Automatic and human evaluations show that, in comparison to nucleus and top-k sampling, locally typical sampling offers competitive performance (in both abstractive summarization and story generation) in terms of quality while consistently reducing degenerate repetitions.

Predictive Coding (PC) is a theoretical framework in cognitive science suggesting that the human brain processes cognition through spatiotemporal prediction of the visual world. Existing studies have developed spatiotemporal prediction neural networks based on the PC theory, emulating its two core mechanisms: Correcting predictions from residuals and hierarchical learning. However, these models do not show the enhancement of prediction skills on real-world forecasting tasks and ignore the Precision Weighting mechanism of PC theory. The precision weighting mechanism posits that the brain allocates more attention to signals with lower precision, contributing to the cognitive ability of human brains. This work introduces the Cognitive Diffusion Probabilistic Models (CogDPM), which demonstrate the connection between diffusion probabilistic models and PC theory. CogDPM features a precision estimation method based on the hierarchical sampling capabilities of diffusion models and weight the guidance with precision weights estimated by the inherent property of diffusion models. We experimentally show that the precision weights effectively estimate the data predictability. We apply CogDPM to real-world prediction tasks using the United Kindom precipitation and ERA surface wind datasets. Our results demonstrate that CogDPM outperforms both existing domain-specific operational models and general deep prediction models by providing more proficient forecasting.

Contrastively trained encoders have recently been proven to invert the data-generating process: they encode each input, e.g., an image, into the true latent vector that generated the image (Zimmermann et al., 2021). However, real-world observations often have inherent ambiguities. For instance, images may be blurred or only show a 2D view of a 3D object, so multiple latents could have generated them. This makes the true posterior for the latent vector probabilistic with heteroscedastic uncertainty. In this setup, we extend the common InfoNCE objective and encoders to predict latent distributions instead of points. We prove that these distributions recover the correct posteriors of the data-generating process, including its level of aleatoric uncertainty, up to a rotation of the latent space. In addition to providing calibrated uncertainty estimates, these posteriors allow the computation of credible intervals in image retrieval. They comprise images with the same latent as a given query, subject to its uncertainty. Code is available at https://github.com/mkirchhof/Probabilistic_Contrastive_Learning

Minimal Phenomenal Experiences (MPEs) are states of consciousness in which wakefulness is preserved but phenomenal content is low or absent. The Entropic Brain Hypothesis (EBH) is a model of conscious processes that regards the entropy of spontaneous brain activity as a marker of 'phenomenal richness', exemplified by high-content psychedelic experiences (HCPEs). Yet recent human neuroimaging studies of MPEs induced by meditation -- and possibly 5-MeO-DMT -- suggest that these states, defined by their phenomenological simplicity, also show signs of increased neurophysiological entropy. This presents a conundrum for the EBH: brain entropy is elevated with increased and decreased richness of the phenomenal experience. Here, we put forward the Complex Brain Hypothesis (CBH), which proposes that the richness of experience differentiating MPEs from HCPEs is better indexed by complexity than by entropy. We argue that brain complexity is modulated by the grain of inference through which the brain resolves uncertainty: some HCPEs exemplify a fine-grained regime, in which loosened constraints amplify fluctuations into proliferating content, whereas some MPEs exemplify a coarse-grained regime, in which a simpler model dissolves variety into an experience of 'contentless' awareness. Both regimes can be associated with elevated brain entropy, but they diverge in phenomenology and perturbational signatures. By resolving the entropy-content conundrum, the CBH refines the EBH and highlights MPEs as an important test case for computational theories of consciousness.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Despite significant strides in factual reliability, errors -- often termed hallucinations -- remain a major concern for generative AI, especially as LLMs are increasingly expected to be helpful in more complex or nuanced setups. Yet even in the simplest setting -- factoid question-answering with clear ground truth-frontier models without external tools continue to hallucinate. We argue that most factuality gains in this domain have come from expanding the model's knowledge boundary (encoding more facts) rather than improving awareness of that boundary (distinguishing known from unknown). We conjecture that the latter is inherently difficult: models may lack the discriminative power to perfectly separate truths from errors, creating an unavoidable tradeoff between eliminating hallucinations and preserving utility. This tradeoff dissolves under a different framing. If we understand hallucinations as confident errors -- incorrect information delivered without appropriate qualification -- a third path emerges beyond the answer-or-abstain dichotomy: expressing uncertainty. We propose faithful uncertainty: aligning linguistic uncertainty with intrinsic uncertainty. This is one facet of metacognition -- the ability to be aware of one's own uncertainty and to act on it. For direct interaction, acting on uncertainty means communicating it honestly; for agentic systems, it becomes the control layer governing when to search and what to trust. Metacognition is thus essential for LLMs to be both trustworthy and capable; we conclude by highlighting open problems for progress towards this objective.

The lack of transparency of Deep Neural Networks continues to be a limitation that severely undermines their reliability and usage in high-stakes applications. Promising approaches to overcome such limitations are Prototype-Based Self-Explainable Neural Networks (PSENNs), whose predictions rely on the similarity between the input at hand and a set of prototypical representations of the output classes, offering therefore a deep, yet transparent-by-design, architecture. So far, such models have been designed by considering pointwise estimates for the prototypes, which remain fixed after the learning phase of the model. In this paper, we introduce a probabilistic reformulation of PSENNs, called Prob-PSENN, which replaces point estimates for the prototypes with probability distributions over their values. This provides not only a more flexible framework for an end-to-end learning of prototypes, but can also capture the explanatory uncertainty of the model, which is a missing feature in previous approaches. In addition, since the prototypes determine both the explanation and the prediction, Prob-PSENNs allow us to detect when the model is making uninformed or uncertain predictions, and to obtain valid explanations for them. Our experiments demonstrate that Prob-PSENNs provide more meaningful and robust explanations than their non-probabilistic counterparts, thus enhancing the explainability and reliability of the models.

Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions. Among NQS parameterizations, autoregressive models are especially attractive because they enable exact, independent sampling from the Born distribution, avoiding the autocorrelation and mixing issues of Markov chain methods. Yet their optimization remains comparatively underexplored: Adam is a scalable method but ignores function space geometry, while stochastic reconfiguration is principled but costly and numerically fragile in large models. To address this gap, we show that variational energy minimization can be viewed as an advantage policy-gradient problem over the Born distribution, motivating trust-region optimization for NQS training. We introduce Proximal Wavefunction Optimization (PWO), a principled trust-region algorithm that clips probability-ratio changes in the amplitude channel and phase increments in the phase channel. PWO avoids explicit matrix inversion, reuses samples across multiple updates, and combines the scalability of first-order optimization with theoretical guarantees. Across Ising and frustrated J_1-J_2 one- and two-dimensional spin systems, PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING. Finally, we fine-tune a 1.5B-parameter RWKV-7 model, demonstrating NQS optimization at a scale over three orders of magnitude beyond prior work.

Typed-decision models such as TypeSafe's Jev answer a declared yes/no or multiple-choice question about a state with a probability instead of text, and their evaluations report accuracy and calibration. Neither requires that the probabilities a model gives to logically related questions fit together item by item, which is what a system that acts on those probabilities needs. We test this property, coherence, with a battery of logically linked questions that needs no labels. For 160 items from ChaosNLI and PubMedQA, each with three mutually exclusive labels, we ask whether the label is X, whether it is not X, whether it is one of the other two labels, and which label applies. On 480 negation pairs, Jev's probabilities for "the label is X" and "the label is not X" miss summing to one by 0.064 on average (95% CI 0.055 to 0.072). Qwen3.8-27B, run from its official BF16 weights, misses by 0.293 with first-token probabilities and by 0.122 with verbalized probabilities. The gap to the first-token readout persists on pairs where both systems give similar probabilities, without double-negation labels, and after averaging Jev's repeated calls. Jev is not coherent either: its violations are about five times its repeat noise, and it over-endorses statements about single labels, so that its three single-label probabilities sum to 1.14 on average. The two systems also fail differently. Qwen3.8-27B's first-token readout under-endorses the complement of a label whether or not the question contains "not", rejecting both a statement and its negation in 196 of 480 pairs, and it does not become more coherent where it is more confident, whereas Jev's violations concentrate where its answer is uncertain. Because the checks need no labels, they expose biases that appear only when question forms are compared, and inconsistencies within items.

The Large Language Model from Power Law Decoder Representations (PLDR-LLM) and its attention, Power Law Graph Attention (PLGA), replace the fixed bilinear form of scaled dot-product attention (SDPA) with a learned, input-generated bilinear operator G_{LM}, built from a positive tensor A_{LM} by elementwise power laws. The architecture is fully specified, verified against pinned reference releases; claims are labeled theorem, conditional theorem, measurement, or conjecture. Unconditionally: PLGA contains SDPA exactly at G_{LM}=I; A_{LM} and A_P are strictly entrywise positive, with Perron-Frobenius structure on A_{LM}; the DAG regularizer has the NOTEARS walk-counting form and positivity obstructs exact acyclicity; and, under nonresonance (satisfied by standard rotary frequencies), a commutant criterion identifies which operators preserve relative-position dependence. An inference-collapse theorem: exact input invariance of deductive outputs collapses inference to generalized SDPA with a constant operator. Measured invariance: relative fluctuations of 10^{-6} and below; perturbation bounds quantify but do not certify cached inference; the assembled proxy misses the decoding margin. A conditional three-stage mechanism (rotary twirl, concentration, row-map contraction) is measured on a released checkpoint. Blockwise training and scoring under the global Gram are stated with explicit target exposure; on tested samples, block and sequential scoring select identical answers and agree on the published TruthfulQA probability-mass metric within 5times 10^{-5} per item. Self-organized criticality enters as a phenomenological framework with an intrinsic order parameter; open claims become falsifiable conjectures. Selected proof cores are machine-checked in Lean 4.

We implement and benchmark on IBM Quantum hardware the circuit family proposed by Violaris for estimating operational inter-branch communication witnesses, defined as correlations in classical measurement records produced by compiled Wigner's-friend-style circuits. We realize a five-qubit instance of the protocol as an inter-register message-transfer pattern within a single circuit, rather than physical signaling, and evaluate its behavior under realistic device noise and compilation constraints. The circuit encodes branch-conditioned evolution of an observer subsystem whose dynamics depend on a control qubit, followed by a controlled transfer operation that probes correlations between conditional measurement contexts. Executing on the ibm_fez backend with 20000 shots, we observe population-based visibility of 0.877, coherence witnesses of 0.840 and -0.811 along orthogonal axes, and a phase-sensitive magnitude of approximately 1.17. While the visibility metric is insensitive to some classes of dephasing, the coherence witnesses provide complementary sensitivity to off-diagonal noise. This work does not test or discriminate among interpretations of quantum mechanics. Instead, it provides a reproducible operational constraint pipeline for evaluating detectability of non-ideal channels relative to calibrated device noise.

The handling of probabilities in the form of uncertainty or partial information is an essential task for LLMs in many settings and applications. A common approach to evaluate an LLM's probabilistic reasoning capabilities is to assess its ability to answer questions pertaining to probability through the use of multiple-choice questions (MCQs). However, this paradigm, which we refer to as explicit probabilistic reasoning, has been shown in the literature to yield significant limitations (e.g., sensitivity to answer ordering). In this work, we introduce an alternative approach, named implicit probabilistic reasoning, which evaluates the models' ability to integrate probabilistic reasoning into their text generation process. To achieve this, we rephrase MCQs as text-completion scenarios with a determined set of outcomes and compare the model's next-token probability assignments to the true likelihood of the outcomes. In line with previous work, we find that models exhibit solid performance in their explicit probabilistic reasoning (i.e., answers to MCQs). However, during text completion (i.e., implicit probabilistic reasoning), where the same information must be taken into account to generate text, the models' predictions often significantly diverge from the known ground truth. For instance, our evaluation method reveals that implicit probabilistic reasoning is improperly influenced by many factors, such as independent prior events, partial observations about a result, or statistical background information. All of these issues can cause erroneous results to be produced in text generation, which are not detected by conventional MCQ-based evaluation.

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.

Predictive models often need to work with incomplete information in real-world tasks. Consequently, they must provide reliable probability or confidence estimation, especially in large-scale decision-making and planning tasks. Current large language models (LLMs) are insufficient for accurate estimations, but they can generate relevant factors that may affect the probabilities, produce coarse-grained probabilities when the information is more complete, and help determine which factors are relevant to specific downstream contexts. In this paper, we make use of these capabilities of LLMs to provide a significantly more accurate probabilistic estimation. We propose BIRD, a novel probabilistic inference framework that aligns a Bayesian network with LLM abductions and then estimates more accurate probabilities in a deduction step. We show BIRD provides reliable probability estimations that are 30% better than those provided directly by LLM baselines. These estimates further contribute to better and more trustworthy decision making.

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic regression. However, existing approaches are dominated by heuristic algorithms or data-hungry black-box methods, which often demand low-noise settings and lack principled uncertainty quantification. Motivated by interpretable Statistical Artificial Intelligence, we develop a hierarchical Bayesian framework for symbolic regression that represents scientific laws as ensembles of tree-structured symbolic expressions endowed with a regularized tree prior. This coherent probabilistic formulation enables full posterior inference via an efficient Markov chain Monte Carlo algorithm, yielding a balance between predictive accuracy and structural parsimony. To guide symbolic model selection, we develop a marginal posterior-based criterion adhering to the Occam's window principle and further quantify structural fidelity to ground truth through a tailored expression-distance metric. On the theoretical front, we establish near-minimax rate of Bayesian posterior concentration, providing the first rigorous guarantee in context of symbolic regression. Empirical evaluation demonstrates robust performance of our proposed methodology against state-of-the-art competing modules on a simulated example, a suite of canonical Feynman equations, and single-atom catalysis dataset.

Counterfactual inference in Gaussian-process structural causal models (GP-SCMs) has been developed primarily for continuous endogenous variables, limiting applicability to causal graphs that contain discrete child nodes with continuous parents. We introduce a unified probabilistic framework for counterfactual inference with heterogeneous variable types by pairing GP predictors with explicit exogenous noise mechanisms. For discrete outcomes, we derive exact conditional noise-abduction procedures using a uniform threshold for binary variables, a Gumbel-max race for nominal categories, and a latent Gaussian cut-point model for ordinal ones. In each case, we propagate abducted noise through interventions while accounting for posterior uncertainty in the GP latent functions, and prove that the resulting mechanisms reproduce the fitted model's observational and interventional distributions. On synthetic SCMs with known ground-truth counterfactuals, we evaluate estimation accuracy, consistency, and robustness to coupling misspecification. A key finding is that applying a categorical coupling to ordinal data inflates counterfactual error roughly threefold even when observational fit remains comparable, and that this error does not diminish with more data. As the training set grows, the fitted structural equation converges to the truth while the counterfactual error flattens onto a floor. In the reverse direction, forcing a false order onto nominal data instead degrades the fitted equation itself. The choice of coupling must therefore be justified on structural grounds rather than read off the fit.

Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently -- a failure mode especially prevalent in multi-step deductive reasoning. Existing methods assess reliability primarily through output dispersion -- measuring how much sampled answers differ -- but this discards a complementary signal: whether the model can consistently rank competing reasoning candidates. We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings over sampled reasoning solutions. Given a query, we generate multiple candidate solutions and ask the model to judge pairwise preferences among its own outputs. We aggregate self-preferences into ranking distributions via Bradley-Terry modeling with PageRank, and decompose the signal into two entropy-based components: across-trial ranking instability and within-trial candidate ambiguity. Across five LLMs and eight benchmarks, structural signals provide information complementary to answer dispersion: on logical and mathematical reasoning tasks, the combination improves identification of unreliable instances, while on factual retrieval the structural signal collapses toward uniformity, diagnosing a regime boundary where reasoning-level consistency evaluation is uninformative. The two components relate differently to accuracy: within-trial ambiguity correlates positively with correctness -- consistent with settings where multiple plausible solution paths remain competitive -- while across-trial instability correlates negatively, signaling unreliable reasoning. Structural uncertainty is best understood not as a universal confidence estimator, but as a regime-sensitive evaluator of logical reasoning consistency.

Forecasting time series data is a critical area of research with applications spanning from stock prices to early epidemic prediction. While numerous statistical and machine learning methods have been proposed, real-life prediction problems often require hybrid solutions that bridge classical forecasting approaches and modern neural network models. In this study, we introduce the Probabilistic AutoRegressive Neural Networks (PARNN), capable of handling complex time series data exhibiting non-stationarity, nonlinearity, non-seasonality, long-range dependence, and chaotic patterns. PARNN is constructed by improving autoregressive neural networks (ARNN) using autoregressive integrated moving average (ARIMA) feedback error, combining the explainability, scalability, and "white-box-like" prediction behavior of both models. Notably, the PARNN model provides uncertainty quantification through prediction intervals, setting it apart from advanced deep learning tools. Through comprehensive computational experiments, we evaluate the performance of PARNN against standard statistical, machine learning, and deep learning models, including Transformers, NBeats, and DeepAR. Diverse real-world datasets from macroeconomics, tourism, epidemiology, and other domains are employed for short-term, medium-term, and long-term forecasting evaluations. Our results demonstrate the superiority of PARNN across various forecast horizons, surpassing the state-of-the-art forecasters. The proposed PARNN model offers a valuable hybrid solution for accurate long-range forecasting. By effectively capturing the complexities present in time series data, it outperforms existing methods in terms of accuracy and reliability. The ability to quantify uncertainty through prediction intervals further enhances the model's usefulness in decision-making processes.

This monograph attempts a theory of every 'thing' that can be distinguished from other things in a statistical sense. The ensuing statistical independencies, mediated by Markov blankets, speak to a recursive composition of ensembles (of things) at increasingly higher spatiotemporal scales. This decomposition provides a description of small things; e.g., quantum mechanics - via the Schrodinger equation, ensembles of small things - via statistical mechanics and related fluctuation theorems, through to big things - via classical mechanics. These descriptions are complemented with a Bayesian mechanics for autonomous or active things. Although this work provides a formulation of every thing, its main contribution is to examine the implications of Markov blankets for self-organisation to nonequilibrium steady-state. In brief, we recover an information geometry and accompanying free energy principle that allows one to interpret the internal states of something as representing or making inferences about its external states. The ensuing Bayesian mechanics is compatible with quantum, statistical and classical mechanics and may offer a formal description of lifelike particles.

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

We propose a lightweight and single-pass uncertainty quantification method for detecting hallucinations in Large Language Models. The method uses attention matrices to estimate uncertainty without requiring repeated sampling or external models. Specifically, we measure the Kullback-Leibler divergence between each attention head's distribution and a uniform reference distribution, and use these features in a logistic regression probe. Across multiple datasets, task types, and model families, attention divergence is highly predictive of answer correctness and performs competitively with existing uncertainty estimation methods. We find that this signal is concentrated in middle layers and on factual tokens such as named entities and numbers, suggesting that attention dynamics provides an efficient and interpretable white-box signal of model uncertainty.

Large language model agents are increasingly evaluated as autonomous tool users, yet most benchmarks focus on bounded tasks with immediate success criteria. Real-world deployments often require Long-Term Coherence, the capacity to preserve purposeful behavior across extended horizons while adapting decisions to accumulated evidence. Evaluating this capacity requires a persistent environment in which actions constrain future choices, feedback arrives at heterogeneous delays, and incoherent behavior produces measurable cumulative effects. Seller-side e-commerce provides a suitable setting for this evaluation through recurrent and interdependent decisions over Product Sourcing, Listing and Pricing Control, Cash-Flow Management, and Mixed-Latency Feedback Adaptation. We introduce MerchantBench, a 365-day order-level simulation grounded in 98,843 real e-commerce product records and equipped with 26 tools for agent interaction. MerchantBench couples promptly observable Upstream Supplier Events with delayed Downstream Order Outcomes, requiring agents to follow individual order lifecycles and revisit earlier decisions. We evaluate eight LLMs under two agent frameworks in 48 runs, each spanning 365 simulated days. Our results reveal a substantial gap between even the latest LLMs and human participants, with the best LLM configuration attaining only 27.3\% of the mean final net assets achieved by human participants.

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are probabilistic models, and may be expressed in the language of graphical models with random variables whose values are complex data types such as strings. Cases with control flow and dynamic structure require techniques from probabilistic programming, which allow implementing disparate model structures and inference strategies in a unified language. We formalize several existing techniques from this perspective, including scratchpads / chain of thought, verifiers, STaR, selection-inference, and tool use. We refer to the resulting programs as language model cascades.

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic foundation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input-output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations. Within this framework, we define a new uncertainty measure, Inv-Entropy. A key strength of our framework is its flexibility: it supports various definitions of uncertainty measures, embeddings, perturbation strategies, and similarity metrics. We also propose GAAP, a perturbation algorithm based on genetic algorithms, which enhances the diversity of sampled inputs. In addition, we introduce a new evaluation metric, Temperature Sensitivity of Uncertainty (TSU), which directly assesses uncertainty without relying on correctness as a proxy. Extensive experiments demonstrate that Inv-Entropy outperforms existing semantic UQ methods. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/Uncertainty-Quantification-for-LLMs.

Evaluating model uncertainty on real-world data is challenging because each instance provides only a single observed label, leaving true conditional class probabilities unknown. To address this, we introduce ProbabilityBench, a benchmark that provides exact, instance-level class probabilities across three simulated text-based domains: peer review, covert information transfer, and credit risk. By explicitly defining the full data-generating process for each environment, we analytically compute both exact class probabilities and Bayes error. Furthermore, we provide a theoretical guarantee that rendering these cases into natural-language memos strictly preserves their underlying generative probabilities. This exactness enables direct measurement of reported probability quality via KL divergence. Across 16 evaluated models, most models on the observed cost-quality Pareto frontiers are decision models, including Jev and Perplexity Decider. Finally, ProbabilityBench serves as a meta-evaluation framework, leveraging known ground-truth values to benchmark the accuracy of standard calibration metrics and Bayes-error estimators themselves.

Large language models (LLMs) often suffer from context faithfulness hallucinations, where outputs deviate from retrieved information due to insufficient context utilization and high output uncertainty. Our uncertainty evaluation experiments reveal a strong correlation between high uncertainty and hallucinations. We hypothesize that attention mechanisms encode signals indicative of contextual utilization, validated through probing analysis. Based on these insights, we propose Dynamic Attention-Guided Context Decoding (DAGCD), a lightweight framework that integrates attention distributions and uncertainty signals in a single-pass decoding process. Experiments across QA datasets demonstrate DAGCD's effectiveness, achieving significant improvements in faithfulness and robustness while maintaining computational efficiency.

Memory is central to long-horizon LLM agents, yet existing memory systems primarily preserve interaction content rather than modeling which agents can be trusted and under what conditions. This limitation is particularly important in multi-agent systems, where a central model may be unable to directly verify plausible or correlated peer responses. We introduce Σ-Mem, an online reliability memory that records historical competence evidence for individual peers and peer relationship evidence across the peer set. Both forms of evidence are maintained as real symmetric states and updated from post-decision correctness feedback. By Weyl's inequality, the spectral change caused by each event-level update is bounded, enabling stable online adaptation without retraining the underlying models. Σ-Mem provides a general write-and-read interface: the same memory can be used for residual steering of a central model, response-free peer routing, or reliability-weighted voting. Across five Qwen-family models, Σ-Mem adapts to counterfactual reliability shifts and generalizes to unseen peers and task domains. Direct memory readouts also outperform majority voting and the best fixed peer over the full OOD evaluation set. Moreover, performance improves consistently as more correctness feedback becomes available, indicating that Σ-Mem progressively accumulates actionable reliability information. These results establish reliability memory as a reusable foundation for adaptive coordination in LLM-based multi-agent systems.

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a parameter drift transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.

Single-cell CRISPR screens summarize each perturbation by how far cells move from their unperturbed state, averaging over cell-to-cell variation. Whether the cells moved together is not captured: two perturbations with identical effect magnitude can differ qualitatively, one driving cells along a shared trajectory, the other scattering them around the same mean. We define SheshaP coherence (S_p), the mean cosine similarity between individual cell displacement vectors and their mean, and ask what it adds across six Perturb-seq datasets (2,285 perturbations; CRISPRa, CRISPRi, Cas9 knockout). Coherence and effect magnitude are closely coupled (Spearman ρ=0.84--0.98), and the coupling persists in a foundation-model embedding, under alternative effect-size definitions, and when analysis is restricted to responding cells. Associations reported without conditioning on effect size largely recover it, shown here for two comparisons that vanish under conditioning. Effect size accounts for 89--96\% of coherence variance; within the remainder, coherence is negatively associated with apoptosis and p53 signalling in the two largest screens. Two standard responder classifiers agree on only 68\% of cells. Directional coherence is largely a restatement of effect magnitude, and heterogeneity measures should report their redundancy with effect size as a matter of course. S_p is implemented in the open-source shesha-geometry Python package.

Probabilistic mental simulation is thought to play a key role in human reasoning, planning, and prediction, yet the demands of simulation in complex environments exceed realistic human capacity limits. A theory with growing evidence is that people simulate using simplified representations of the environment that abstract away from irrelevant details, but it is unclear how people determine these simplifications efficiently. Here, we present a "Just-in-Time" framework for simulation-based reasoning that demonstrates how such representations can be constructed online with minimal added computation. The model uses a tight interleaving of simulation, visual search, and representation modification, with the current simulation guiding where to look and visual search flagging objects that should be encoded for subsequent simulation. Despite only ever encoding a small subset of objects, the model makes high-utility predictions. We find strong empirical support for this account over alternative models in a grid-world planning task and a physical reasoning task across a range of behavioral measures. Together, these results offer a concrete algorithmic account of how people construct reduced representations to support efficient mental simulation.

We theoretically identify the noise-induced coherent contribution to the ergotropy of a four-level quantum heat engine coupled to a unimodal quantum cavity. We utilize a protocol where the passive state's quasiprobabilities can be analytically identified from the population-coherence coupled reduced density matrix. The reduced density matrix elements are evaluated using a microscopic quantum master equation formalism. Multiple ergotropies within the same coherence interval, each characterized by a positive and pronounced coherent contribution, are observed. These ergotropies are a result of population inversion as well as quasiprobability-population inversion, controllable through the coherence measure parameters. The optimal flux and power of the engine are found to be at moderate values of ergotropy with increasing values of noise-induced coherence. The optimal power at different coherences is found to possess a constant ergotropy.

Generating temporal data under conditions is crucial for forecasting, imputation, and generative tasks. Such data often has metadata and partially observed signals that jointly influence the generated values. However, existing methods face three key limitations: (1) they condition on either the metadata or observed values, but rarely both together; (2) they adopt either training-time approaches that fail to generalize to unseen scenarios, or inference-time approaches that ignore metadata; and (3) they suffer from trade-offs between generation speed and temporal coherence across time windows--choosing either slow but coherent autoregressive methods or fast but incoherent parallel ones. We propose WaveStitch, a novel diffusion-based method to overcome these hurdles through: (1) dual-sourced conditioning on both metadata and partially observed signals; (2) a hybrid training-inference architecture, incorporating metadata during training and observations at inference via gradient-based guidance; and (3) a novel pipeline-style paradigm that generates time windows in parallel while preserving coherence through an inference-time conditional loss and a stitching mechanism. Across diverse datasets, WaveStitch demonstrates adaptability to arbitrary patterns of observed signals, achieving 1.81x lower mean-squared-error compared to the state-of-the-art, and generates data up to 166.48x faster than autoregressive methods while maintaining coherence. Our code is available at: https://github.com/adis98/WaveStitch

Despite tremendous recent progress, generative video models still struggle to capture real-world motion, dynamics, and physics. We show that this limitation arises from the conventional pixel reconstruction objective, which biases models toward appearance fidelity at the expense of motion coherence. To address this, we introduce VideoJAM, a novel framework that instills an effective motion prior to video generators, by encouraging the model to learn a joint appearance-motion representation. VideoJAM is composed of two complementary units. During training, we extend the objective to predict both the generated pixels and their corresponding motion from a single learned representation. During inference, we introduce Inner-Guidance, a mechanism that steers the generation toward coherent motion by leveraging the model's own evolving motion prediction as a dynamic guidance signal. Notably, our framework can be applied to any video model with minimal adaptations, requiring no modifications to the training data or scaling of the model. VideoJAM achieves state-of-the-art performance in motion coherence, surpassing highly competitive proprietary models while also enhancing the perceived visual quality of the generations. These findings emphasize that appearance and motion can be complementary and, when effectively integrated, enhance both the visual quality and the coherence of video generation. Project website: https://hila-chefer.github.io/videojam-paper.github.io/

Large Language Models (LLMs) often generate outputs that lack grounding in real-world facts, a phenomenon known as hallucinations. Prior research has associated hallucinations with model uncertainty, leveraging this relationship for hallucination detection and mitigation. In this paper, we challenge the underlying assumption that all hallucinations are associated with uncertainty. Using knowledge detection and uncertainty measurement methods, we demonstrate that models can hallucinate with high certainty even when they have the correct knowledge. We further show that high-certainty hallucinations are consistent across models and datasets, distinctive enough to be singled out, and challenge existing mitigation methods. Our findings reveal an overlooked aspect of hallucinations, emphasizing the need to understand their origins and improve mitigation strategies to enhance LLM safety. The code is available at https://github.com/technion-cs-nlp/Trust_me_Im_wrong .

LLMs are widely used for code generation and mathematical reasoning tasks where they are required to generate structured output. They either need to reason about code, generate code for a given specification, or reason using programs of thought. The typical approach to code generation is to prompt the model and generate samples until an appropriate program is obtained. Within this process, sampling n programs from the language model requires n GPU compute-intensive generations which becomes prohibitively expensive for larger values of n. In this work, we address this limitation by exposing the LLM's distribution within the generated programs themselves. We propose a novel test-time framework we dub probabilistic programs of thought to obtain more samples from the model with fewer LLM generations. Given a program generated by a model and the associated next-token probabilities, we build a probabilistic program that compactly represents exponentially many deterministic programs. Since performing probabilistic reasoning in this probabilistic program is much cheaper, our approach allows sampling new programs without any additional GPU compute and little CPU overhead. We instantiate our approach on benchmarks for code generation, code understanding and mathematical reasoning and report improvements in performance with fewer generations from the LLM.

Hallucinations in Large Language Model (LLM) outputs for Question Answering (QA) tasks can critically undermine their real-world reliability. This paper introduces a methodology for robust, one-shot hallucination detection, specifically designed for scenarios with limited data access, such as interacting with black-box LLM APIs that typically expose only a few top candidate log-probabilities per token. Our approach derives uncertainty indicators directly from these readily available log-probabilities generated during non-greedy decoding. We first derive an Entropy Production Rate (EPR) that offers baseline performance, later augmented with supervised learning. Our learned model leverages the entropic contributions of the accessible top-ranked tokens within a single generated sequence, without multiple re-runs per query. Evaluated across diverse QA datasets and multiple LLMs, this estimator significantly improves token-level hallucination detection over state-of-the-art methods. Crucially, high performance is demonstrated using only the typically small set of available log-probabilities (e.g., top-10 per token), confirming its practical efficiency and suitability for API-constrained deployments. This work provides a lightweight technique to enhance the trustworthiness of LLM responses, at the token level, after a single generation pass, for QA and Retrieval-Augmented Generation (RAG) systems. Our experiments confirmed the performance of our method against existing approaches on public dataset as well as for a financial framework analyzing annual company reports.

This work stems from prior complementary observations on the dynamics of Chain-of-Thought (CoT): Large Language Models (LLMs) is shown latent planning of subsequent reasoning prior to CoT emergence, thereby diminishing the significance of explicit CoT; whereas CoT remains critical for tasks requiring multi-step reasoning. To deepen the understanding between LLM's internal states and its verbalized reasoning trajectories, we investigate the latent planning strength of LLMs, through our probing method, Tele-Lens, applying to hidden states across diverse task domains. Our empirical results indicate that LLMs exhibit a myopic horizon, primarily conducting incremental transitions without precise global planning. Leveraging this characteristic, we propose a hypothesis on enhancing uncertainty estimation of CoT, which we validate that a small subset of CoT positions can effectively represent the uncertainty of the entire path. We further underscore the significance of exploiting CoT dynamics, and demonstrate that automatic recognition of CoT bypass can be achieved without performance degradation. Our code, data and models are released at https://github.com/lxucs/tele-lens.

Diffusion language models (DLMs) expose their denoising trajectories, offering a natural handle for inference-time control; accordingly, an ideal hallucination mitigation framework should intervene during generation using this model-native signal rather than relying on an externally trained hallucination classifier. Toward this, we formulate commitment uncertainty localization: given a denoising trajectory, identify token positions whose cross-chain entropy exceeds an unsupervised threshold before factually unreliable commitments propagate into self-consistent but incorrect outputs. We introduce a suite of trajectory-level assessments, including a cross-chain divergence-at-hallucination (CDH) metric, for principled comparison of localization methods. We also introduce OSCAR, a training-free inference-time framework operationalizing this formulation. OSCAR runs N parallel denoising chains with randomized reveal orders, computes cross-chain Shannon entropy to detect high-uncertainty positions, and then performs targeted remasking conditioned on retrieved evidence. Ablations confirm that localization and correction contribute complementary gains, robust across N in {4, 8, 16}. On TriviaQA, HotpotQA, RAGTruth, and CommonsenseQA using LLaDA-8B and Dream-7B, OSCAR enhances generation quality by significantly reducing hallucinated content and improving factual accuracy through uncertainty-guided remasking, which also facilitates more effective integration of retrieved evidence. Its native entropy-based uncertainty signal surpasses that of specialized trained detectors, highlighting an inherent capacity of diffusion language models to identify factual uncertainty that is not present in the sequential token commitment structure of autoregressive models.

We propose a novel speculative decoding method tailored for multi-sample reasoning scenarios, such as self-consistency and Best-of-N sampling. Our method exploits the intrinsic consensus of parallel generation paths to synthesize high-quality draft tokens without requiring auxiliary models or external databases. By dynamically analyzing structural patterns across parallel reasoning paths through a probabilistic aggregation mechanism, it identifies consensus token sequences that align with the decoding distribution. Evaluations on mathematical reasoning benchmarks demonstrate a substantial improvement in draft acceptance rates over baselines, while reducing the latency in draft token construction. This work establishes a paradigm shift for efficient multi-sample inference, enabling seamless integration of speculative decoding with sampling-based reasoning techniques.

Large Language Models (LLMs) are prone to hallucination, the generation of plausible yet factually incorrect statements. This work investigates the intrinsic, architectural origins of this failure mode through three primary contributions.First, to enable the reliable tracing of internal semantic failures, we propose Distributional Semantics Tracing (DST), a unified framework that integrates established interpretability techniques to produce a causal map of a model's reasoning, treating meaning as a function of context (distributional semantics). Second, we pinpoint the model's layer at which a hallucination becomes inevitable, identifying a specific commitment layer where a model's internal representations irreversibly diverge from factuality. Third, we identify the underlying mechanism for these failures. We observe a conflict between distinct computational pathways, which we interpret using the lens of dual-process theory: a fast, heuristic associative pathway (akin to System 1) and a slow, deliberate contextual pathway (akin to System 2), leading to predictable failure modes such as Reasoning Shortcut Hijacks. Our framework's ability to quantify the coherence of the contextual pathway reveals a strong negative correlation (rho = -0.863) with hallucination rates, implying that these failures are predictable consequences of internal semantic weakness. The result is a mechanistic account of how, when, and why hallucinations occur within the Transformer architecture.

We study the quantum coherence and its distribution of N-partite GHZ and W states of bosonic fields in the noninertial frames with arbitrary number of acceleration observers. We find that the coherence of both GHZ and W state reduces with accelerations and freezes in the limit of infinite accelerations. The freezing value of coherence depends on the number of accelerated observers. The coherence of N-partite GHZ state is genuinely global and no coherence exists in any subsystems. For the N-partite W state, however, the coherence is essentially bipartite types, and the total coherence is equal to the sum of coherence of all the bipartite subsystems.

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However, existing methods are often computationally expensive, or demand costly retraining when priors change, limiting their utility, particularly in sequential inference problems such as real-time sensor fusion. To address these challenges, we introduce the Distribution Transformer -- a novel architecture that can learn arbitrary distribution-to-distribution mappings. Our method can be trained to map a prior to the corresponding posterior, conditioned on some dataset -- thus performing approximate Bayesian inference. Our novel architecture represents a prior distribution as a (universally-approximating) Gaussian Mixture Model (GMM), and transforms it into a GMM representation of the posterior. The components of the GMM attend to each other via self-attention, and to the datapoints via cross-attention. We demonstrate that Distribution Transformers both maintain flexibility to vary the prior, and significantly reduces computation times-from minutes to milliseconds-while achieving log-likelihood performance on par with or superior to existing approximate inference methods across tasks such as sequential inference, quantum system parameter inference, and Gaussian Process predictive posterior inference with hyperpriors.

Spoken communication occurs in a "noisy channel" characterized by high levels of environmental noise, variability within and between speakers, and lexical and syntactic ambiguity. Given these properties of the received linguistic input, robust spoken word recognition -- and language processing more generally -- relies heavily on listeners' prior knowledge to evaluate whether candidate interpretations of that input are more or less likely. Here we compare several broad-coverage probabilistic generative language models in their ability to capture human linguistic expectations. Serial reproduction, an experimental paradigm where spoken utterances are reproduced by successive participants similar to the children's game of "Telephone," is used to elicit a sample that reflects the linguistic expectations of English-speaking adults. When we evaluate a suite of probabilistic generative language models against the yielded chains of utterances, we find that those models that make use of abstract representations of preceding linguistic context (i.e., phrase structure) best predict the changes made by people in the course of serial reproduction. A logistic regression model predicting which words in an utterance are most likely to be lost or changed in the course of spoken transmission corroborates this result. We interpret these findings in light of research highlighting the interaction of memory-based constraints and representations in language processing.

The proliferation of probabilistic AI has promoted proposals for specialized stochastic computers. Despite promising efficiency gains, these proposals have failed to gain traction because they rely on fundamentally limited modeling techniques and exotic, unscalable hardware. In this work, we address these shortcomings by proposing an all-transistor probabilistic computer that implements powerful denoising models at the hardware level. A system-level analysis indicates that devices based on our architecture could achieve performance parity with GPUs on a simple image benchmark using approximately 10,000 times less energy.

This paper presents a systematic defense of large language model (LLM) hallucinations or 'confabulations' as a potential resource instead of a categorically negative pitfall. The standard view is that confabulations are inherently problematic and AI research should eliminate this flaw. In this paper, we argue and empirically demonstrate that measurable semantic characteristics of LLM confabulations mirror a human propensity to utilize increased narrativity as a cognitive resource for sense-making and communication. In other words, it has potential value. Specifically, we analyze popular hallucination benchmarks and reveal that hallucinated outputs display increased levels of narrativity and semantic coherence relative to veridical outputs. This finding reveals a tension in our usually dismissive understandings of confabulation. It suggests, counter-intuitively, that the tendency for LLMs to confabulate may be intimately associated with a positive capacity for coherent narrative-text generation.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component processes gives the same belief update as the inversion of the whole. We answer this question affirmatively, showing that the relevant compositional structure is precisely that of the lens pattern, and that we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a corresponding fibred category. We define a general notion of (mixed) Bayesian lens, and discuss the (un)lawfulness of these lenses when their contravariant components are exact Bayesian inversions. We prove our main result both abstractly and concretely, for both discrete and continuous states, taking care to illustrate the common structures.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

Multimodal large language models (MLLMs) must resolve conflicts when different modalities provide contradictory information, a process we term modality following. Prior work measured this behavior only with coarse dataset-level statistics, overlooking the influence of model's confidence in unimodal reasoning. In this paper, we introduce a new framework that decomposes modality following into two fundamental factors: relative reasoning uncertainty (the case-specific confidence gap between unimodal predictions) and inherent modality preference( a model's stable bias when uncertainties are balanced). To validate this framework, we construct a controllable dataset that systematically varies the reasoning difficulty of visual and textual inputs. Using entropy as a fine-grained uncertainty metric, we uncover a universal law: the probability of following a modality decreases monotonically as its relative uncertainty increases. At the relative difficulty level where the model tends to follow both modalities with comparable probability what we call the balance point, a practical indicator of the model's inherent preference. Unlike traditional macro-level ratios, this measure offers a more principled and less confounded way to characterize modality bias, disentangling it from unimodal capabilities and dataset artifacts. Further, by probing layer-wise predictions, we reveal the internal mechanism of oscillation: in ambiguous regions near the balance point, models vacillate between modalities across layers, explaining externally observed indecision. Together, these findings establish relative uncertainty and inherent preference as the two governing principles of modality following, offering both a quantitative framework and mechanistic insight into how MLLMs resolve conflicting information.

Hallucinations are a common issue that undermine the reliability of large language models (LLMs). Recent studies have identified a specific subset of hallucinations, known as confabulations, which arise due to predictive uncertainty of LLMs. To detect confabulations, various methods for estimating predictive uncertainty in natural language generation (NLG) have been developed. These methods are typically evaluated by correlating uncertainty estimates with the correctness of generated text, with question-answering (QA) datasets serving as the standard benchmark. However, commonly used approximate correctness functions have substantial disagreement between each other and, consequently, in the ranking of the uncertainty estimation methods. This allows one to inflate the apparent performance of uncertainty estimation methods. We propose using several alternative risk indicators for risk correlation experiments that improve robustness of empirical assessment of UE algorithms for NLG. For QA tasks, we show that marginalizing over multiple LLM-as-a-judge variants leads to reducing the evaluation biases. Furthermore, we explore structured tasks as well as out of distribution and perturbation detection tasks which provide robust and controllable risk indicators. Finally, we propose to use an Elo rating of uncertainty estimation methods to give an objective summarization over extensive evaluation settings.

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.

This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the study of Schrodinger operators on multidimensional integer lattice, to characterize the evolution of continuous time quantum walks. Extending this framework, we develop a probabilistic method to represent discrete time quantum walks on an infinite integer line, bypassing the locality constraints that typically inhibit direct application of Molchanov formula. The validity of our representation is empirically confirmed through a benchmark analysis of the Hadamard walk, demonstrating high fidelity with traditional unitary evolution. Our results suggest that this probabilistic lens offer a powerful alternative for learning multidimensional quantum walks and provides new analytical pathways for investigating quantum systems via classical stochastic processes.