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Probabilistic Methods · Bayesian Models and Methods

Laurence Davies, Daniel MacKinlay, Rafael Oliveira, Scott SIsson

The expressiveness of flow-based models combined with stochastic variational inference (SVI) has expanded the application of optimization-based Bayesian inference to highly complex problems. However, despite the importance of multi-model Bayesian inference, defined over a transdimensional joint model and parameter space, flow-based SVI has been limited to problems defined over a fixed-dimensional parameter space. We introduce CoSMIC normalizing flows (COntextually-Specified Masking for Identity-mapped Components), an extension to neural autoregressive conditional normalizing flow architectures that enables use of a single amortized variational density for inference over a transdimensional (multi-model) conditional target distribution. We propose a combined stochastic variational transdimensional inference (VTI) approach to training CoSMIC flows using ideas from Bayesian optimization and Monte Carlo gradient estimation. Numerical experiments show the performance of VTI on challenging problems that scale to high-cardinality model spaces.

Antonio Orvieto, Robert Gower

Understanding the remarkable efficacy of Adam when training transformer-based language models has become a central research topic within the optimization community. To gain deeper insights, several simplifications of Adam have been proposed, such as the signed gradient and signed momentum methods. In this work, we conduct an extensive empirical study — training over 1,500 language models across different data configurations and scales — comparing Adam to several known simplified variants. We find that signed momentum methods are faster than SGD, but consistently underperform relative to Adam, even after careful tuning of momentum, clipping setting and learning rates. However, our analysis reveals a compelling option that preserves near-optimal performance while allowing for new insightful reformulations: constraining the Adam momentum parameters to be equal, $\beta_1=\beta_2$. Beyond robust performance, this choice affords new theoretical insights, highlights the "secret sauce" on top of signed momentum, and grants a precise statistical interpretation: we show that Adam in this setting implements a natural online algorithm for estimating the mean and variance of gradients—one that arises from a mean-field Gaussian variational inference perspective.

Jiayi Yuan, Hao Li, Xinheng Ding, Wenya Xie, Yu-Jhe Li, Wentian Zhao, Kun Wan, Jing Shi, Xia Hu, Zirui Liu

Large Language Models (LLMs) are now integral across various domains and have demonstrated impressive performance. Progress, however, rests on the premise that benchmark scores are both accurate and reproducible. We demonstrate that the reproducibility of LLM performance is fragile: changing system configuration, such as evaluation batch size, GPU count, and GPU version, can introduce significant differences in the generated responses. This issue is especially pronounced in reasoning models, where minor rounding differences in early tokens can cascade into divergent chains of thought, ultimately affecting accuracy. For instance, under bfloat16 precision with greedy decoding, a reasoning model like DeepSeek-R1-Distill-Qwen-7B can exhibit up to 9\% variation in accuracy and 9,000 tokens difference in response length due to differences in GPU count, type, and evaluation batch size. We trace the root cause of this variability to the non-associative nature of floating-point arithmetic under limited numerical precision. This work presents the first systematic investigation into how numerical precision affects reproducibility in LLM inference. Through carefully controlled experiments across various hardware, software, and precision settings, we quantify when and how model outputs diverge. Our analysis reveals that floating-point precision—while critical for reproducibility—is often neglected in evaluation practices. Inspired by this, we develop a lightweight inference pipeline, dubbed LayerCast, that stores weights in 16-bit precision but performs all computations in FP32, balancing memory efficiency with numerical stability. Code is available at https://github.com/nanomaoli/llm_reproducibility.

Applications · Chemistry and Drug Discovery

Shayan Shekarforoush, David Lindell, Marcus Brubaker, David Fleet

Cryo-EM is a transformational paradigm in molecular biology where computational methods are used to infer 3D molecular structure at atomic resolution from extremely noisy 2D electron microscope images. At the forefront of research is how to model the structure when the imaged particles exhibit non-rigid conformational flexibility and compositional variation where parts are sometimes missing. We introduce a novel 3D reconstruction framework with a hierarchical Gaussian mixture model, inspired in part by Gaussian Splatting for 4D scene reconstruction. In particular, the structure of the model is grounded in an initial process that infers a part-based segmentation of the particle, providing essential inductive bias in order to handle both conformational and compositional variability. The framework, called \methodName, is shown to reveal biologically meaningful structures on complex experimental datasets, and establishes a new state-of-the-art on CryoBench, a benchmark for cryo-EM heterogeneity methods.

Jabez Magomere, Emanuele La Malfa, Manuel Tonneau, Ashkan Kazemi, Scott A. Hale

Online misinformation remains a critical challenge, and fact-checkers increasingly rely on claim matching systems that use sentence embedding models to retrieve relevant fact-checks. However, as users interact with claims online, they often introduce edits, and it remains unclear whether current embedding models used in retrieval are robust to such edits. To investigate this, we introduce a perturbation framework that generates valid and natural claim variations, enabling us to assess the robustness of a wide-range of sentence embedding models in a multi-stage retrieval pipeline and evaluate the effectiveness of various mitigation approaches. Our evaluation reveals that standard embedding models exhibit notable performance drops on edited claims, while LLM-distilled embedding models offer improved robustness at a higher computational cost. Although a strong reranker helps to reduce the performance drop, it cannot fully compensate for first-stage retrieval gaps. To address these retrieval gaps, we evaluate train- and inference-time mitigation approaches, demonstrating that they can improve in-domain robustness by up to 17 percentage points and boost out-of-domain generalization by 10 percentage points. Overall, our findings provide practical improvements to claim-matching systems, enabling more reliable fact-checking of evolving misinformation.

Raymond Li, Chuyuan Li, Gabriel Murray, Giuseppe Carenini

Large language models (LLMs) have demonstrated impressive generative capabilities, yet their inner mechanisms remain largely opaque. In this work, we introduce a novel approach to interpret LLMs generation process through the lens of an explicit Bayesian framework by inferring latent topic variables via variational inference. Specifically, we leverage a variational autoencoder-based neural topic model to dynamically approximate the posterior distribution over the high-level latent topic variables at each generation step. By reconstructing the LLM’s next-token predictions through these latent topics and maintaining a regularized latent space, our method yields interpretable and diverse topic representations but also has the ability to effectively captures semantic shifts throughout the text. We validate our approach on multiple datasets, showing that our latent topics outperform state-of-the-art topic models on intrinsic measures of coherence and diversity. Furthermore, we demonstrate the utility of our approach in downstream applications by using the inferred topic distributions to retrieve relevant demonstration examples for in-context learning, resulting in significant gains on classification and summarization tasks.

Chunyang Li, Weiqi Wang, Tianshi Zheng, Yangqiu Song

Inductive reasoning, a cornerstone of human cognition, enables generalization from limited data but hasn’t yet been fully achieved by large language models (LLMs). While modern LLMs excel at reasoning tasks, their ability to maintain stable and consistent rule abstraction under imperfect observations remains underexplored. To fill this gap, in this work, we introduce **Robust Rule Induction**, a task that evaluates LLMs’ capability in inferring rules from data that are fused with noisy examples. To address this task, we further propose Sample-steered Rule Refinement (SRR), a method enhancing reasoning stability via observation diversification and execution-guided feedback. Experiments across arithmetic, cryptography, and list functions reveal: (1) SRR outperforms other methods with minimal performance degradation under noise; (2) Despite slight accuracy variation, LLMs exhibit instability under noise (e.g., 0 accuracy change with only 70 consistent score);(3) Counterfactual task gaps highlight LLMs’ reliance on memorized patterns over genuine abstraction. Our findings challenge LLMs’ reasoning robustness, revealing susceptibility to hypothesis drift and pattern overfitting, while providing empirical evidence critical for developing human-like inductive systems.

Dallas Card

Legal scholars are increasingly using corpus based methods for assessing historical meaning. Among work focused on the so-called founding era (mid to late 18th century), the majority of such studies use the Corpus of Founding Era American English (COFEA) and rely on methods such as word counting and manual coding. Here, we demonstrate what can be inferred about meaning change and variation using more advanced NLP methods, focusing on terms in the U.S. Constitution. We also carry out a data quality assessment of COFEA, pointing out issues with OCR quality and metadata, compare diachronic change to synchronic variation, and discuss limitations when using NLP methods for studying historical meaning.

Jared Fernandez, Clara Na, Vashisth Tiwari, Yonatan Bisk, Sasha Luccioni, Emma Strubell

As large language models (LLMs) scale in size and adoption, their computational and environmental costs continue to rise. Prior benchmarking efforts have primarily focused on latency reduction in idealized settings, often overlooking the diverse real-world inference workloads that shape energy use. In this work, we systematically analyze the energy implications of common inference efficiency optimizations across diverse Natural Language Processing (NLP) and generative Artificial Intelligence (AI) workloads, including conversational AI and code generation. We introduce a modeling approach that approximates real-world LLM workflows through a binning strategy for input-output token distributions and batch size variations. Our empirical analysis spans software frameworks, decoding strategies, GPU architectures, online and offline serving settings, and model parallelism configurations. We show that the effectiveness of inference optimizations is *highly sensitive to workload geometry, software stack, and hardware accelerators*, demonstrating that naive energy estimates based on FLOPs or theoretical GPU utilization significantly underestimate real-world energy consumption.Our findings reveal that the proper application of relevant inference efficiency optimizations can reduce total energy use by up to **73%** from unoptimized baselines. These insights provide a foundation for sustainable LLM deployment and inform energy-efficient design strategies for future AI infrastructure.

Niyati Bafna, Emily Chang, Nathaniel Romney Robinson, David R. Mortensen, Kenton Murray, David Yarowsky, Hale Sirin

Most of the world’s languages and dialects are low-resource, and lack support in mainstream machine translation (MT) models. However, many of them have a closely-related high-resource language (HRL) neighbor, and differ in linguistically regular ways from it. This underscores the importance of model robustness to dialectal variation and cross-lingual generalization to the HRL dialect continuum. We present DialUp, consisting of a training-time technique for adapting a pretrained model to dialectal data (M–>D), and an inference-time intervention adapting dialectal data to the model expertise (D–>M). M–>D induces model robustness to potentially unseen and unknown dialects by exposure to synthetic data exemplifying linguistic mechanisms of dialectal variation, whereas D–>M treats dialectal divergence for known target dialects. These methods show considerable performance gains for several dialects from four language families, and modest gains for two other language families. We also conduct feature and error analyses, which show that language varieties with low baseline MT performance are more likely to benefit from these approaches.

Leonardo Ranaldi, Marco Valentino, Andre Freitas

Chain-of-Though (CoT) represents a common strategy for reasoning in Large Language Models (LLMs) by decomposing complex tasks into intermediate inference steps. However, explanations generated via CoT are susceptible to content biases that negatively affect their robustness and faithfulness. To mitigate existing limitations, recent work has proposed using logical formalisms coupled with external symbolic solvers. However, fully symbolic approaches possess the bottleneck of requiring a complete translation from natural language to formal languages, a process that affects efficiency and flexibility. To achieve a trade-off, this paper investigates methods to disentangle content from logical reasoning without a complete formalisation. In particular, we present QuaSAR (for Quasi-Symbolic Abstract Reasoning), a variation of CoT that guides LLMs to operate at a higher level of abstraction via quasi-symbolic explanations. Our framework leverages the capability of LLMs to formalise only relevant variables and predicates, enabling the coexistence of symbolic elements with natural language. We show the impact of QuaSAR for in-context learning and for constructing demonstrations to improve the reasoning capabilities of smaller models. Our experiments show that quasi-symbolic abstractions can improve CoT-based methods by up to 8% accuracy, enhancing robustness and consistency on challenging adversarial variations on both natural language (i.e. MMLU-Redux) and symbolic reasoning tasks (i.e., GSM-Symbolic).

Jiaxu Zhao, Meng Fang, Kun Zhang, Mykola Pechenizkiy

Natural language processing applications are increasingly prevalent, but social biases in their outputs remain a critical challenge. While various bias evaluation methods have been proposed, these assessments show unexpected instability when input texts undergo minor stylistic changes. This paper conducts a comprehensive analysis of how different style transformations impact bias evaluation results across multiple language models and bias types using causal inference techniques. Our findings reveal that formality transformations significantly affect bias scores, with informal style showing substantial bias reductions (up to 8.33% in LLaMA-2-13B). We identify appearance bias, sexual orientation bias, and religious bias as most susceptible to style changes, with variations exceeding 20%. Larger models demonstrate greater sensitivity to stylistic variations, with bias measurements fluctuating up to 3.1% more than in smaller models. These results highlight critical limitations in current bias evaluation methods and emphasize the need for reliable and fair assessments of language models.

Lingwei Meng, Long Zhou, Shujie Liu, Sanyuan Chen, Bing Han, Shujie Hu, Yanqing Liu, Jinyu Li, Sheng Zhao, Xixin Wu 等

We present MELLE, a novel continuous-valued token based language modeling approach for text-to-speech synthesis (TTS). MELLE autoregressively generates continuous mel-spectrogram frames directly from text condition, bypassing the need for vector quantization, which is typically designed for audio compression and sacrifices fidelity compared to continuous representations. Specifically, (i) instead of cross-entropy loss, we apply regression loss with a proposed spectrogram flux loss function to model the probability distribution of the continuous-valued tokens; (ii) we have incorporated variational inference into MELLE to facilitate sampling mechanisms, thereby enhancing the output diversity and model robustness. Experiments demonstrate that, compared to the two-stage codec language model VALL-E and its variants, the single-stage MELLE mitigates robustness issues by avoiding the inherent flaws of sampling vector-quantized codes, achieves superior performance across multiple metrics, and, most importantly, offers a more streamlined paradigm. The demos of our work are provided at https://aka.ms/melle.

Deep Learning · Generative Models and Autoencoders

Hao Chen, Yujin Han, Fangyi Chen, Xiang Li, Yidong Wang, Jindong Wang, Ze Wang, Zicheng Liu, Difan Zou, Bhiksha Raj

Recent advances in latent diffusion models have demonstrated their effectiveness for high-resolution image synthesis. However, the properties of the latent space from tokenizer for better learning and generation of diffusion models remain under-explored. Theoretically and empirically, we find that improved generation quality is closely tied to the latent distributions with better structure, such as the ones with fewer Gaussian Mixture modes and more discriminative features. Motivated by these insights, we propose MAETok, an autoencoder (AE) leveraging mask modeling to learn semantically rich latent space while maintaining reconstruction fidelity. Extensive experiments validate our analysis, demonstrating that the variational form of autoencoders is not necessary, and a discriminative latent space from AE alone enables state-of-the-art performance on ImageNet generation using only 128 tokens. MAETok achieves significant practical improvements, enabling a gFID of 1.69 with 76× faster training and 31× higher inference throughput for 512×512 generation. Our findings show that the structure of the latent space, rather than variational constraints, is crucial for effective diffusion models. Code and trained models will be released.

Probabilistic Methods · Variational Inference

Evan Sidrow, Alexandre Bouchard-Côté, Lloyd Elliott

Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric phylogenetic trees. We present a novel variational family based on coalescent times of a single-linkage clustering and derive a closed-form density for the resulting distribution over trees. Unlike existing methods for ultrametric trees, our method performs inference over all of tree space, it does not require any Markov chain Monte Carlo subroutines, and our variational family is differentiable. Through experiments on benchmark genomic datasets and an application to the viral RNA of SARS-CoV-2, we demonstrate that our method achieves competitive accuracy while requiring significantly fewer gradient evaluations than existing state-of-the-art techniques.

Probabilistic Methods · Everything Else

Tennessee Hickling, Dennis Prangle

Normalizing flows are a flexible class of probability distributions, expressed as transformations of a simple base distribution. A limitation of standard normalizing flows is representing distributions with heavy tails, which arise in applications to both density estimation and variational inference. A popular current solution to this problem is to use a heavy tailed base distribution. We argue this can lead to poor performance due to the difficulty of optimising neural networks, such as normalizing flows, under heavy tailed input. We propose an alternative, "tail transform flow'' (TTF), which uses a Gaussian base distribution and a final transformation layer which can produce heavy tails. Experimental results show this approach outperforms current methods, especially when the target distribution has large dimension or tail weight.

Deep Learning · Generative Models and Autoencoders

Xinyu Peng, Ziyang Zheng, Yaoming Wang, Han Li, Nuowen Kan, Wenrui Dai, Chenglin Li, Junni Zou, Hongkai Xiong

We propose Noise Conditional Variational Score Distillation (NCVSD), a novel method for distilling pretrained diffusion models into generative denoisers. We achieve this by revealing that the unconditional score function implicitly characterizes the score function of denoising posterior distributions. By integrating this insight into the Variational Score Distillation (VSD) framework, we enable scalable learning of generative denoisers capable of approximating samples from the denoising posterior distribution across a wide range of noise levels. The proposed generative denoisers exhibit desirable properties that allow fast generation while preserve the benefit of iterative refinement: (1) fast one-step generation through sampling from pure Gaussian noise at high noise levels; (2) improved sample quality by scaling the test-time compute with multi-step sampling; and (3) zero-shot probabilistic inference for flexible and controllable sampling. We evaluate NCVSD through extensive experiments, including class-conditional image generation and inverse problem solving. By scaling the test-time compute, our method outperforms teacher diffusion models and is on par with consistency models of larger sizes. Additionally, with significantly fewer NFEs than diffusion-based methods, we achieve record-breaking LPIPS on inverse problems.

Deep Learning · Generative Models and Autoencoders

Pengsheng Guo, Alex Schwing

We study Variational Rectified Flow Matching, a framework that enhances classic rectified flow matching by modeling multi-modal velocity vector-fields. At inference time, classic rectified flow matching 'moves' samples from a source distribution to the target distribution by solving an ordinary differential equation via integration along a velocity vector-field. At training time, the velocity vector-field is learnt by linearly interpolating between coupled samples one drawn from the source and one drawn from the target distribution randomly. This leads to ''ground-truth'' velocity vector-fields that point in different directions at the same location, i.e., the velocity vector-fields are multi-modal/ambiguous. However, since training uses a standard mean-squared-error loss, the learnt velocity vector-field averages ''ground-truth'' directions and isn't multi-modal. In contrast, variational rectified flow matching learns and samples from multi-modal flow directions. We show on synthetic data, MNIST, CIFAR-10, and ImageNet that variational rectified flow matching leads to compelling results.

Probabilistic Methods · Variational Inference

Kian Ming Chai, Edwin V. Bonilla

We introduce a novel one-parameter variational objective that lower bounds the data evidence and enables the estimation of approximate fractional posteriors. We extend this framework to hierarchical construction and Bayes posteriors, offering a versatile tool for probabilistic modelling. We demonstrate two cases where gradients can be obtained analytically and a simulation study on mixture models showing that our fractional posteriors can be used to achieve better calibration compared to posteriors from the conventional variational bound. When applied to variational autoencoders (VAEs), our approach attains higher evidence bounds and enables learning of high-performing approximate Bayes posteriors jointly with fractional posteriors. We show that VAEs trained with fractional posteriors produce decoders that are better aligned for generation from the prior.

Probabilistic Methods · Variational Inference

Tuan Truong, Quyen Tran, Ngoc Quan Pham, Nhat Ho, Dinh Phung, Trung Le

We introduce Flat Hilbert Bayesian Inference (FHBI), an algorithm designed to enhance generalization in Bayesian inference. Our approach involves an iterative two-step procedure with an adversarial functional perturbation step and a functional descent step within the reproducing kernel Hilbert spaces. This methodology is supported by a theoretical analysis that extends previous findings on generalization ability from finite-dimensional Euclidean spaces to infinite-dimensional functional spaces. To evaluate the effectiveness of FHBI, we conduct comprehensive comparisons against nine baseline methods on the VTAB-1K benchmark, which encompasses 19 diverse datasets across various domains with diverse semantics. Empirical results demonstrate that FHBI consistently outperforms the baselines by notable margins, highlighting its practical efficacy.