Stephan Mandt

Ruihan Yang, Stephan Mandt

This paper outlines an end-to-end optimized lossy image compression framework using diffusion generative models. The approach relies on the transform coding paradigm, where an image is mapped into a latent space for entropy coding and, from there, mapped back to the data space for reconstruction. In contrast to VAE-based neural compression, where the (mean) decoder is a deterministic neural network, our decoder is a conditional diffusion model. Our approach thus introduces an additional ``content'' latent variable on which the reverse diffusion process is conditioned and uses this variable to store information about the image. The remaining ``texture'' variables characterizing the diffusion process are synthesized at decoding time. We show that the model's performance can be tuned toward perceptual metrics of interest. Our extensive experiments involving multiple datasets and image quality assessment metrics show that our approach yields stronger reported FID scores than the GAN-based model, while also yielding competitive performance with VAE-based models in several distortion metrics. Furthermore, training the diffusion with $\mathcal{X}$-parameterization enables high-quality reconstructions in only a handful of decoding steps, greatly affecting the model's practicality. Our code is available at: \url{https://github.com/buggyyang/CDC_compression}

Yibo Yang, Stephan Mandt

Neural image compression methods have seen increasingly strong performance in recent years. However, they suffer orders of magnitude higher computational complexity compared to traditional codecs, which hinders their real-world deployment. This paper takes a step forward towards closing this gap in decoding complexity by using a shallow or even linear decoding transform resembling that of JPEG. To compensate for the resulting drop in compression performance, we exploit the often asymmetrical computation budget between encoding and decoding, by adopting more powerful encoder networks and iterative encoding. We theoretically formalize the intuition behind, and our experimental results establish a new frontier in the trade-off between rate-distortion and decoding complexity for neural image compression. Specifically, we achieve rate-distortion performance competitive with the established mean-scale hyperprior architecture of Minnen et al. (2018) at less than 50K decoding FLOPs/pixel, reducing the baseline's overall decoding complexity by 80%, or over 90% for the synthesis transform alone. Our code can be found at https://github.com/mandt-lab/shallow-ntc.

Thomas Specht, Mayank Nagda, Sophie Fellenz et al.

We present the first hard-constraint neural network for predicting activity coefficients (HANNA), a thermodynamic mixture property that is the basis for many applications in science and engineering. Unlike traditional neural networks, which ignore physical laws and result in inconsistent predictions, our model is designed to strictly adhere to all thermodynamic consistency criteria. By leveraging deep-set neural networks, HANNA maintains symmetry under the permutation of the components. Furthermore, by hard-coding physical constraints in the network architecture, we ensure consistency with the Gibbs-Duhem equation and in modeling the pure components. The model was trained and evaluated on 317,421 data points for activity coefficients in binary mixtures from the Dortmund Data Bank, achieving significantly higher prediction accuracies than the current state-of-the-art model UNIFAC. Moreover, HANNA only requires the SMILES of the components as input, making it applicable to any binary mixture of interest. HANNA is fully open-source and available for free use.

Aodong Li, Chen Qiu, Marius Kloft et al.

Anomaly detection (AD) plays a crucial role in many safety-critical application domains. The challenge of adapting an anomaly detector to drift in the normal data distribution, especially when no training data is available for the "new normal," has led to the development of zero-shot AD techniques. In this paper, we propose a simple yet effective method called Adaptive Centered Representations (ACR) for zero-shot batch-level AD. Our approach trains off-the-shelf deep anomaly detectors (such as deep SVDD) to adapt to a set of inter-related training data distributions in combination with batch normalization, enabling automatic zero-shot generalization for unseen AD tasks. This simple recipe, batch normalization plus meta-training, is a highly effective and versatile tool. Our theoretical results guarantee the zero-shot generalization for unseen AD tasks; our empirical results demonstrate the first zero-shot AD results for tabular data and outperform existing methods in zero-shot anomaly detection and segmentation on image data from specialized domains. Code is at https://github.com/aodongli/zero-shot-ad-via-batch-norm

Chen Qiu, Marius Kloft, Stephan Mandt et al.

Graph-level anomaly detection has become a critical topic in diverse areas, such as financial fraud detection and detecting anomalous activities in social networks. While most research has focused on anomaly detection for visual data such as images, where high detection accuracies have been obtained, existing deep learning approaches for graphs currently show considerably worse performance. This paper raises the bar on graph-level anomaly detection, i.e., the task of detecting abnormal graphs in a set of graphs. By drawing on ideas from self-supervised learning and transformation learning, we present a new deep learning approach that significantly improves existing deep one-class approaches by fixing some of their known problems, including hypersphere collapse and performance flip. Experiments on nine real-world data sets involving nine techniques reveal that our method achieves an average performance improvement of 11.8% AUC compared to the best existing approach.

Ruihan Yang, Prakhar Srivastava, Stephan Mandt

Denoising diffusion probabilistic models are a promising new class of generative models that mark a milestone in high-quality image generation. This paper showcases their ability to sequentially generate video, surpassing prior methods in perceptual and probabilistic forecasting metrics. We propose an autoregressive, end-to-end optimized video diffusion model inspired by recent advances in neural video compression. The model successively generates future frames by correcting a deterministic next-frame prediction using a stochastic residual generated by an inverse diffusion process. We compare this approach against five baselines on four datasets involving natural and simulation-based videos. We find significant improvements in terms of perceptual quality for all datasets. Furthermore, by introducing a scalable version of the Continuous Ranked Probability Score (CRPS) applicable to video, we show that our model also outperforms existing approaches in their probabilistic frame forecasting ability.

Kushagra Pandey, Stephan Mandt

Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical heuristics or simplifying assumptions. Utilizing insights from the development of scalable Bayesian posterior samplers, we present a complete recipe for formulating forward processes in SGMs, ensuring convergence to the desired target distribution. Our approach reveals that several existing SGMs can be seen as specific manifestations of our framework. Building upon this method, we introduce Phase Space Langevin Diffusion (PSLD), which relies on score-based modeling within an augmented space enriched by auxiliary variables akin to physical phase space. Empirical results exhibit the superior sample quality and improved speed-quality trade-off of PSLD compared to various competing approaches on established image synthesis benchmarks. Remarkably, PSLD achieves sample quality akin to state-of-the-art SGMs (FID: 2.10 for unconditional CIFAR-10 generation). Lastly, we demonstrate the applicability of PSLD in conditional synthesis using pre-trained score networks, offering an appealing alternative as an SGM backbone for future advancements. Code and model checkpoints can be accessed at \url{https://github.com/mandt-lab/PSLD}.

Kushagra Pandey, Maja Rudolph, Stephan Mandt

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey & Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at \url{https://github.com/mandt-lab/PSLD}.

Alex Boyd, Sam Showalter, Stephan Mandt et al.

In reasoning about sequential events it is natural to pose probabilistic queries such as "when will event A occur next" or "what is the probability of A occurring before B", with applications in areas such as user modeling, medicine, and finance. However, with machine learning shifting towards neural autoregressive models such as RNNs and transformers, probabilistic querying has been largely restricted to simple cases such as next-event prediction. This is in part due to the fact that future querying involves marginalization over large path spaces, which is not straightforward to do efficiently in such models. In this paper we introduce a general typology for predictive queries in neural autoregressive sequence models and show that such queries can be systematically represented by sets of elementary building blocks. We leverage this typology to develop new query estimation methods based on beam search, importance sampling, and hybrids. Across four large-scale sequence datasets from different application domains, as well as for the GPT-2 language model, we demonstrate the ability to make query answering tractable for arbitrary queries in exponentially-large predictive path-spaces, and find clear differences in cost-accuracy tradeoffs between search and sampling methods.

Fabian Hartung, Billy Joe Franks, Tobias Michels et al.

This paper provides the first comprehensive evaluation and analysis of modern (deep-learning) unsupervised anomaly detection methods for chemical process data. We focus on the Tennessee Eastman process dataset, which has been a standard litmus test to benchmark anomaly detection methods for nearly three decades. Our extensive study will facilitate choosing appropriate anomaly detection methods in industrial applications.

Aodong Li, Chen Qiu, Marius Kloft et al.

Selecting informative data points for expert feedback can significantly improve the performance of anomaly detection (AD) in various contexts, such as medical diagnostics or fraud detection. In this paper, we determine a set of theoretical conditions under which anomaly scores generalize from labeled queries to unlabeled data. Motivated by these results, we propose a data labeling strategy with optimal data coverage under labeling budget constraints. In addition, we propose a new learning framework for semi-supervised AD. Extensive experiments on image, tabular, and video data sets show that our approach results in state-of-the-art semi-supervised AD performance under labeling budget constraints.

Felix Draxler, Justus Will, Farrin Marouf Sofian et al.

Autoregressive decoding in language models is inherently slow, generating only one token per forward pass. We propose Parallel Token Prediction (PTP), a general-purpose framework for predicting multiple tokens in a single model call. PTP moves the source of randomness from post-hoc sampling to random input variables, making future tokens deterministic functions of those inputs and thus jointly predictable in a single forward pass. We prove that a single PTP call can represent arbitrary dependencies between tokens. PTP is trained by distilling an existing model or through inverse autoregressive training without a teacher. Experimentally, PTP achieves a 2.4x speedup on a diverse-task speculative decoding benchmark. We provide code and checkpoints at https://github.com/mandt-lab/ptp.

Yoshitomo Matsubara, Ruihan Yang, Marco Levorato et al.

With the increasing demand for deep learning models on mobile devices, splitting neural network computation between the device and a more powerful edge server has become an attractive solution. However, existing split computing approaches often underperform compared to a naive baseline of remote computation on compressed data. Recent studies propose learning compressed representations that contain more relevant information for supervised downstream tasks, showing improved tradeoffs between compressed data size and supervised performance. However, existing evaluation metrics only provide an incomplete picture of split computing. This study introduces supervised compression for split computing (SC2) and proposes new evaluation criteria: minimizing computation on the mobile device, minimizing transmitted data size, and maximizing model accuracy. We conduct a comprehensive benchmark study using 10 baseline methods, three computer vision tasks, and over 180 trained models, and discuss various aspects of SC2. We also release sc2bench, a Python package for future research on SC2. Our proposed metrics and package will help researchers better understand the tradeoffs of supervised compression in split computing.

Yibo Yang, Stephan Eckstein, Marcel Nutz et al.

In the theory of lossy compression, the rate-distortion (R-D) function $R(D)$ describes how much a data source can be compressed (in bit-rate) at any given level of fidelity (distortion). Obtaining $R(D)$ for a given data source establishes the fundamental performance limit for all compression algorithms. We propose a new method to estimate $R(D)$ from the perspective of optimal transport. Unlike the classic Blahut--Arimoto algorithm which fixes the support of the reproduction distribution in advance, our Wasserstein gradient descent algorithm learns the support of the optimal reproduction distribution by moving particles. We prove its local convergence and analyze the sample complexity of our R-D estimator based on a connection to entropic optimal transport. Experimentally, we obtain comparable or tighter bounds than state-of-the-art neural network methods on low-rate sources while requiring considerably less tuning and computation effort. We also highlight a connection to maximum-likelihood deconvolution and introduce a new class of sources that can be used as test cases with known solutions to the R-D problem.

Ba-Hien Tran, Babak Shahbaba, Stephan Mandt et al.

Autoencoders and their variants are among the most widely used models in representation learning and generative modeling. However, autoencoder-based models usually assume that the learned representations are i.i.d. and fail to capture the correlations between the data samples. To address this issue, we propose a novel Sparse Gaussian Process Bayesian Autoencoder (SGPBAE) model in which we impose fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder. We perform posterior estimation for this model via stochastic gradient Hamiltonian Monte Carlo. We evaluate our approach qualitatively and quantitatively on a wide range of representation learning and generative modeling tasks and show that our approach consistently outperforms multiple alternatives relying on Variational Autoencoders.

Nicolas Hayer, Thorsten Wendel, Stephan Mandt et al.

Accurate prediction of thermodynamic properties is pivotal in chemical engineering for optimizing process efficiency and sustainability. Physical group-contribution (GC) methods are widely employed for this purpose but suffer from historically grown, incomplete parameterizations, limiting their applicability and accuracy. In this work, we overcome these limitations by combining GC with matrix completion methods (MCM) from machine learning. We use the novel approach to predict a complete set of pair-interaction parameters for the most successful GC method: UNIFAC, the workhorse for predicting activity coefficients in liquid mixtures. The resulting new method, UNIFAC 2.0, is trained and validated on more than 224,000 experimental data points, showcasing significantly enhanced prediction accuracy (e.g., nearly halving the mean squared error) and increased scope by eliminating gaps in the original model's parameter table. Moreover, the generic nature of the approach facilitates updating the method with new data or tailoring it to specific applications.

Eliot Wong-Toi, Alex Boyd, Vincent Fortuin et al.

Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit all training data perfectly, eliminating residual noise entirely; at the other, they overfit the residual noise while predicting a constant, uninformative mean. We observe a lack of middle ground, suggesting a phase transition dependent on model regularization strength. Empirical verification supports this conjecture by fitting numerous models with varying mean and variance regularization. To explain the transition, we develop a theoretical framework based on a statistical field theory, yielding qualitative agreement with experiments. As a practical consequence, our analysis simplifies hyperparameter tuning from a two-dimensional to a one-dimensional search, substantially reducing the computational burden. Experiments on diverse datasets, including UCI datasets and the large-scale ClimSim climate dataset, demonstrate significantly improved performance in various calibration tasks.

Alex Boyd, Yuxin Chang, Stephan Mandt et al.

Continuous-time event sequences, i.e., sequences consisting of continuous time stamps and associated event types ("marks"), are an important type of sequential data with many applications, e.g., in clinical medicine or user behavior modeling. Since these data are typically modeled autoregressively (e.g., using neural Hawkes processes or their classical counterparts), it is natural to ask questions about future scenarios such as "what kind of event will occur next" or "will an event of type $A$ occur before one of type $B$". Unfortunately, some of these queries are notoriously hard to address since current methods are limited to naive simulation, which can be highly inefficient. This paper introduces a new typology of query types and a framework for addressing them using importance sampling. Example queries include predicting the $n^\text{th}$ event type in a sequence and the hitting time distribution of one or more event types. We also leverage these findings further to be applicable for estimating general "$A$ before $B$" type of queries. We prove theoretically that our estimation method is effectively always better than naive simulation and show empirically based on three real-world datasets that it is on average 1,000 times more efficient than existing approaches.

Eshant English, Eliot Wong-Toi, Matteo Fontana et al.

Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (Joint Adaptive predictioN-region Estimation for Time-series), a novel framework for constructing conformal prediction regions that are valid for both univariate and multivariate time series. JANET generalises the inductive conformal framework and efficiently produces joint prediction regions with controlled K-familywise error rates, enabling flexible adaptation to specific application needs. Our empirical evaluation demonstrates JANET's superior performance in multi-step prediction tasks across diverse time series datasets, highlighting its potential for reliable and interpretable uncertainty quantification in sequential data.

Metod Jazbec, Patrick Forré, Stephan Mandt et al.

Early-exit neural networks (EENNs) enable adaptive and efficient inference by providing predictions at multiple stages during the forward pass. In safety-critical applications, these predictions are meaningful only when accompanied by reliable uncertainty estimates. A popular method for quantifying the uncertainty of predictive models is the use of prediction sets. However, we demonstrate that standard techniques such as conformal prediction and Bayesian credible sets are not suitable for EENNs. They tend to generate non-nested sets across exits, meaning that labels deemed improbable at one exit may reappear in the prediction set of a subsequent exit. To address this issue, we investigate anytime-valid confidence sequences (AVCSs), an extension of traditional confidence intervals tailored for data-streaming scenarios. These sequences are inherently nested and thus well-suited for an EENN's sequential predictions. We explore the theoretical and practical challenges of using AVCSs in EENNs and show that they indeed yield nested sets across exits. Thus our work presents a promising approach towards fast, yet still safe, predictive modeling

Justus C. Will, Andrea M. Jenney, Kara D. Lamb et al.

Thorough analysis of local droplet-level interactions is crucial to better understand the microphysical processes in clouds and their effect on the global climate. High-accuracy simulations of relevant droplet size distributions from Large Eddy Simulations (LES) of bin microphysics challenge current analysis techniques due to their high dimensionality involving three spatial dimensions, time, and a continuous range of droplet sizes. Utilizing the compact latent representations from Variational Autoencoders (VAEs), we produce novel and intuitive visualizations for the organization of droplet sizes and their evolution over time beyond what is possible with clustering techniques. This greatly improves interpretation and allows us to examine aerosol-cloud interactions by contrasting simulations with different aerosol concentrations. We find that the evolution of the droplet spectrum is similar across aerosol levels but occurs at different paces. This similarity suggests that precipitation initiation processes are alike despite variations in onset times.

Thanh-Tung Le, Tuan Pham, Tung Nguyen et al.

Novel view synthesis (NVS) seeks to render photorealistic, 3D-consistent images of a scene from unseen camera poses given only a sparse set of posed views. Existing deterministic networks render observed regions quickly but blur unobserved areas, whereas stochastic diffusion-based methods hallucinate plausible content yet incur heavy training- and inference-time costs. In this paper, we propose a hybrid framework that unifies the strengths of both paradigms. A bidirectional transformer encodes multi-view image tokens and Plucker-ray embeddings, producing a shared latent representation. Two lightweight heads then act on this representation: (i) a feed-forward regression head that renders pixels where geometry is well constrained, and (ii) a masked autoregressive diffusion head that completes occluded or unseen regions. The entire model is trained end-to-end with joint photometric and diffusion losses, without handcrafted 3D inductive biases, enabling scalability across diverse scenes. Experiments demonstrate that our method attains state-of-the-art image quality while reducing rendering time by an order of magnitude compared with fully generative baselines.

Kushagra Pandey, Farrin Marouf Sofian, Felix Draxler et al.

Diffusion models exhibit excellent sample quality, but existing guidance methods often require additional model training or are limited to specific tasks. We revisit guidance in diffusion models from the perspective of variational inference and control, introducing Diffusion Trajectory Matching (DTM) that enables guiding pretrained diffusion trajectories to satisfy a terminal cost. DTM unifies a broad class of guidance methods and enables novel instantiations. We introduce a new method within this framework that achieves state-of-the-art results on several linear, non-linear, and blind inverse problems without requiring additional model training or specificity to pixel or latent space diffusion models. Our code will be available at https://github.com/czi-ai/oc-guidance

Yibo Yang, Stephan Mandt

Rate-distortion (R-D) function, a key quantity in information theory, characterizes the fundamental limit of how much a data source can be compressed subject to a fidelity criterion, by any compression algorithm. As researchers push for ever-improving compression performance, establishing the R-D function of a given data source is not only of scientific interest, but also sheds light on the possible room for improving compression algorithms. Previous work on this problem relied on distributional assumptions on the data source (Gibson, 2017) or only applied to discrete data (Blahut, 1972; Arimoto, 1972). By contrast, this paper makes the first attempt at an algorithm for sandwiching the R-D function of a general (not necessarily discrete) source requiring only i.i.d. data samples. We estimate R-D sandwich bounds for a variety of artificial and real-world data sources, in settings far beyond the feasibility of any known method, and shed light on the optimality of neural data compression (Ballé et al., 2021; Yang et al., 2022). Our R-D upper bound on natural images indicates theoretical room for improving state-of-the-art image compression methods by at least one dB in PSNR at various bitrates. Our data and code can be found at https://github.com/mandt-lab/empirical-RD-sandwich.

Theodore Papamarkou, Maria Skoularidou, Konstantina Palla et al.

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

Laura Manduchi, Clara Meister, Kushagra Pandey et al.

The field of deep generative modeling has grown rapidly in the last few years. With the availability of massive amounts of training data coupled with advances in scalable unsupervised learning paradigms, recent large-scale generative models show tremendous promise in synthesizing high-resolution images and text, as well as structured data such as videos and molecules. However, we argue that current large-scale generative AI models exhibit several fundamental shortcomings that hinder their widespread adoption across domains. In this work, our objective is to identify these issues and highlight key unresolved challenges in modern generative AI paradigms that should be addressed to further enhance their capabilities, versatility, and reliability. By identifying these challenges, we aim to provide researchers with insights for exploring fruitful research directions, thus fostering the development of more robust and accessible generative AI solutions.

Kushagra Pandey, Jaideep Pathak, Yilun Xu et al.

Diffusion models achieve state-of-the-art generation quality across many applications, but their ability to capture rare or extreme events in heavy-tailed distributions remains unclear. In this work, we show that traditional diffusion and flow-matching models with standard Gaussian priors fail to capture heavy-tailed behavior. We address this by repurposing the diffusion framework for heavy-tail estimation using multivariate Student-t distributions. We develop a tailored perturbation kernel and derive the denoising posterior based on the conditional Student-t distribution for the backward process. Inspired by $γ$-divergence for heavy-tailed distributions, we derive a training objective for heavy-tailed denoisers. The resulting framework introduces controllable tail generation using only a single scalar hyperparameter, making it easily tunable for diverse real-world distributions. As specific instantiations of our framework, we introduce t-EDM and t-Flow, extensions of existing diffusion and flow models that employ a Student-t prior. Remarkably, our approach is readily compatible with standard Gaussian diffusion models and requires only minimal code changes. Empirically, we show that our t-EDM and t-Flow outperform standard diffusion models in heavy-tail estimation on high-resolution weather datasets in which generating rare and extreme events is crucial.

Prakhar Srivastava, Ruihan Yang, Gavin Kerrigan et al.

In climate science and meteorology, high-resolution local precipitation (rain and snowfall) predictions are limited by the computational costs of simulation-based methods. Statistical downscaling, or super-resolution, is a common workaround where a low-resolution prediction is improved using statistical approaches. Unlike traditional computer vision tasks, weather and climate applications require capturing the accurate conditional distribution of high-resolution given low-resolution patterns to assure reliable ensemble averages and unbiased estimates of extreme events, such as heavy rain. This work extends recent video diffusion models to precipitation super-resolution, employing a deterministic downscaler followed by a temporally-conditioned diffusion model to capture noise characteristics and high-frequency patterns. We test our approach on FV3GFS output, an established large-scale global atmosphere model, and compare it against six state-of-the-art baselines. Our analysis, capturing CRPS, MSE, precipitation distributions, and qualitative aspects using California and the Himalayas as examples, establishes our method as a new standard for data-driven precipitation downscaling.

Thomas M. Sutter, Yang Meng, Andrea Agostini et al.

Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or both across modalities to learn a shared representation. Such architectures impose hard constraints on the model. In this work, we show that a better latent representation can be obtained by replacing these hard constraints with a soft constraint. We propose a new mixture-of-experts prior, softly guiding each modality's latent representation towards a shared aggregate posterior. This approach results in a superior latent representation and allows each encoding to preserve information better from its uncompressed original features. In extensive experiments on multiple benchmark datasets and two challenging real-world datasets, we show improved learned latent representations and imputation of missing data modalities compared to existing methods.

Yibo Yang, Justus C. Will, Stephan Mandt

Diffusion probabilistic models have achieved mainstream success in many generative modeling tasks, from image generation to inverse problem solving. A distinct feature of these models is that they correspond to deep hierarchical latent variable models optimizing a variational evidence lower bound (ELBO) on the data likelihood. Drawing on a basic connection between likelihood modeling and compression, we explore the potential of diffusion models for progressive coding, resulting in a sequence of bits that can be incrementally transmitted and decoded with progressively improving reconstruction quality. Unlike prior work based on Gaussian diffusion or conditional diffusion models, we propose a new form of diffusion model with uniform noise in the forward process, whose negative ELBO corresponds to the end-to-end compression cost using universal quantization. We obtain promising first results on image compression, achieving competitive rate-distortion and rate-realism results on a wide range of bit-rates with a single model, bringing neural codecs a step closer to practical deployment.

Andrea Agostini, Daphné Chopard, Yang Meng et al.

Multimodal data integration and label scarcity pose significant challenges for machine learning in medical settings. To address these issues, we conduct an in-depth evaluation of the newly proposed Multimodal Variational Mixture-of-Experts (MMVM) VAE on the challenging MIMIC-CXR dataset. Our analysis demonstrates that the MMVM VAE consistently outperforms other multimodal VAEs and fully supervised approaches, highlighting its strong potential for real-world medical applications.

Sonia Laguna, Andrea Agostini, Alain Ryser et al.

Building robust medical machine learning systems requires pretraining strategies that exploit the intrinsic structure present in clinical data. We introduce Multiview Masked Autoencoder (MVMAE), a self-supervised framework that leverages the natural multi-view organization of radiology studies to learn view-invariant and disease-relevant representations. MVMAE combines masked image reconstruction with cross-view alignment, transforming clinical redundancy across projections into a powerful self-supervisory signal. We further extend this approach with MVMAE-V2T, which incorporates radiology reports as an auxiliary text-based learning signal to enhance semantic grounding while preserving fully vision-based inference. Evaluated on a downstream disease classification task on three large-scale public datasets, MIMIC-CXR, CheXpert, and PadChest, MVMAE consistently outperforms supervised and vision-language baselines. Furthermore, MVMAE-V2T provides additional gains, particularly in low-label regimes where structured textual supervision is most beneficial. Together, these results establish the importance of structural and textual supervision as complementary paths toward scalable, clinically grounded medical foundation models.

Eliot Wong-Toi, Alex Boyd, Vincent Fortuin et al.

Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty quantification. However, overparameterized mean-variance models struggle with signal-to-noise ambiguity, deciding whether prediction targets should be attributed to signal (mean) or noise (variance). At one extreme, models fit all training targets perfectly with zero residual noise, while at the other, they provide constant, uninformative predictions and explain the targets as noise. We observe a sharp phase transition between these extremes, driven by model regularization. Empirical studies with varying regularization levels illustrate this transition, revealing substantial variability across repeated runs. To explain this behavior, we develop a statistical field theory framework, which captures the observed phase transition in alignment with experimental results. This analysis reduces the regularization hyperparameter search space from two dimensions to one, significantly lowering computational costs. Experiments on UCI datasets and the large-scale ClimSim dataset demonstrate robust calibration performance, effectively quantifying predictive uncertainty.

Dennis Wagner, Arjun Nair, Billy Joe Franks et al.

Undetected anomalies in time series can trigger catastrophic failures in safety-critical systems, such as chemical plant explosions or power grid outages. Although many detection methods have been proposed, their performance remains unclear because current metrics capture only narrow aspects of the task and often yield misleading results. We address this issue by introducing verifiable properties that formalize essential requirements for evaluating time-series anomaly detection. These properties enable a theoretical framework that supports principled evaluations and reliable comparisons. Analyzing 37 widely used metrics, we show that most satisfy only a few properties, and none satisfy all, explaining persistent inconsistencies in prior results. To close this gap, we propose LARM, a flexible metric that provably satisfies all properties, and extend it to ALARM, an advanced variant meeting stricter requirements.

Prakhar Srivastava, Farrin Marouf Sofian, Francesco Immorlano et al.

Despite recent advances in test-time scaling and finetuning of diffusion models, guidance in Auto-Regressive Diffusion Models (ARDMs) remains underexplored. We introduce an amortized framework that augments pretrained ARDMs with a lightweight controller network, trained offline by previewing future ARDM rollouts and learning stepwise controls that anticipate upcoming observations under a terminal cost objective. We evaluate this framework in the context of data assimilation (DA) for chaotic spatiotemporal partial differential equations (PDEs), a setting where existing methods are often computationally prohibitive and prone to forecast drift under sparse observations. Our approach reduces DA inference to a single forward rollout with on-the-fly corrections, avoiding expensive adjoint computations and/or optimizations during inference. We demonstrate that our method consistently outperforms four state-of-the-art baselines in stability, accuracy, and physical fidelity across two canonical PDEs and six observation regimes. We will release code and checkpoints publicly.

Marco Hoffmann, Thomas Specht, Quirin Göttl et al.

The excess Gibbs energy plays a central role in chemical engineering and chemistry, providing a basis for modeling the thermodynamic properties of liquid mixtures. Predicting the excess Gibbs energy of multi-component mixtures solely from the molecular structures of their components is a long-standing challenge. In this work, we address this challenge by integrating physical laws as hard constraints within a flexible neural network. The resulting model, HANNA, was trained end-to-end on an extensive experimental dataset for binary mixtures from the Dortmund Data Bank, guaranteeing thermodynamically consistent predictions. A novel surrogate solver developed in this work enabled the inclusion of liquid-liquid equilibrium data in the training process. Furthermore, a geometric projection method was applied to enable robust extrapolations to multi-component mixtures, without requiring additional parameters. We demonstrate that HANNA delivers excellent predictions, clearly outperforming state-of-the-art benchmark methods in accuracy and scope. The trained model and corresponding code are openly available, and an interactive interface is provided on our website, MLPROP.

Tuan Truong, Rithwik Sudharsan, Yibo Yang et al.

The site conditions that make astronomical observatories in space and on the ground so desirable -- cold and dark -- demand a physical remoteness that leads to limited data transmission capabilities. Such transmission limitations directly bottleneck the amount of data acquired and in an era of costly modern observatories, any improvements in lossless data compression has the potential scale to billions of dollars worth of additional science that can be accomplished on the same instrument. Traditional lossless methods for compressing astrophysical data are manually designed. Neural data compression, on the other hand, holds the promise of learning compression algorithms end-to-end from data and outperforming classical techniques by leveraging the unique spatial, temporal, and wavelength structures of astronomical images. This paper introduces AstroCompress: a neural compression challenge for astrophysics data, featuring four new datasets (and one legacy dataset) with 16-bit unsigned integer imaging data in various modes: space-based, ground-based, multi-wavelength, and time-series imaging. We provide code to easily access the data and benchmark seven lossless compression methods (three neural and four non-neural, including all practical state-of-the-art algorithms). Our results on lossless compression indicate that lossless neural compression techniques can enhance data collection at observatories, and provide guidance on the adoption of neural compression in scientific applications. Though the scope of this paper is restricted to lossless compression, we also comment on the potential exploration of lossy compression methods in future studies.

Aodong Li, Yunhan Zhao, Chen Qiu et al.

Large language models (LLMs) have shown their potential in long-context understanding and mathematical reasoning. In this paper, we study the problem of using LLMs to detect tabular anomalies and show that pre-trained LLMs are zero-shot batch-level anomaly detectors. That is, without extra distribution-specific model fitting, they can discover hidden outliers in a batch of data, demonstrating their ability to identify low-density data regions. For LLMs that are not well aligned with anomaly detection and frequently output factual errors, we apply simple yet effective data-generating processes to simulate synthetic batch-level anomaly detection datasets and propose an end-to-end fine-tuning strategy to bring out the potential of LLMs in detecting real anomalies. Experiments on a large anomaly detection benchmark (ODDS) showcase i) GPT-4 has on-par performance with the state-of-the-art transductive learning-based anomaly detection methods and ii) the efficacy of our synthetic dataset and fine-tuning strategy in aligning LLMs to this task.

Tuan Pham, Stephan Mandt

Neural Radiance Fields (NeRFs) have emerged as powerful tools for capturing detailed 3D scenes through continuous volumetric representations. Recent NeRFs utilize feature grids to improve rendering quality and speed; however, these representations introduce significant storage overhead. This paper presents a novel method for efficiently compressing a grid-based NeRF model, addressing the storage overhead concern. Our approach is based on the non-linear transform coding paradigm, employing neural compression for compressing the model's feature grids. Due to the lack of training data involving many i.i.d scenes, we design an encoder-free, end-to-end optimized approach for individual scenes, using lightweight decoders. To leverage the spatial inhomogeneity of the latent feature grids, we introduce an importance-weighted rate-distortion objective and a sparse entropy model employing a masking mechanism. Our experimental results validate that our proposed method surpasses existing works in terms of grid-based NeRF compression efficacy and reconstruction quality.

Kushagra Pandey, Maja Rudolph, Stephan Mandt

Diffusion models suffer from slow sample generation at inference time. Despite recent efforts, improving the sampling efficiency of stochastic samplers for diffusion models remains a promising direction. We propose Splitting Integrators for fast stochastic sampling in pre-trained diffusion models in augmented spaces. Commonly used in molecular dynamics, splitting-based integrators attempt to improve sampling efficiency by cleverly alternating between numerical updates involving the data, auxiliary, or noise variables. However, we show that a naive application of splitting integrators is sub-optimal for fast sampling. Consequently, we propose several principled modifications to naive splitting samplers for improving sampling efficiency and denote the resulting samplers as Reduced Splitting Integrators. In the context of Phase Space Langevin Diffusion (PSLD) [Pandey \& Mandt, 2023] on CIFAR-10, our stochastic sampler achieves an FID score of 2.36 in only 100 network function evaluations (NFE) as compared to 2.63 for the best baselines.

Fabian Jirasek, Robert Bamler, Stephan Mandt

We present a generic way to hybridize physical and data-driven methods for predicting physicochemical properties. The approach `distills' the physical method's predictions into a prior model and combines it with sparse experimental data using Bayesian inference. We apply the new approach to predict activity coefficients at infinite dilution and obtain significant improvements compared to the data-driven and physical baselines and established ensemble methods from the machine learning literature.

Chen Qiu, Aodong Li, Marius Kloft et al.

Anomaly detection aims at identifying data points that show systematic deviations from the majority of data in an unlabeled dataset. A common assumption is that clean training data (free of anomalies) is available, which is often violated in practice. We propose a strategy for training an anomaly detector in the presence of unlabeled anomalies that is compatible with a broad class of models. The idea is to jointly infer binary labels to each datum (normal vs. anomalous) while updating the model parameters. Inspired by outlier exposure (Hendrycks et al., 2018) that considers synthetically created, labeled anomalies, we thereby use a combination of two losses that share parameters: one for the normal and one for the anomalous data. We then iteratively proceed with block coordinate updates on the parameters and the most likely (latent) labels. Our experiments with several backbone models on three image datasets, 30 tabular data sets, and a video anomaly detection benchmark showed consistent and significant improvements over the baselines.

Yibo Yang, Stephan Mandt, Lucas Theis

Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression algorithms to be learned end-to-end from data using powerful generative models such as normalizing flows, variational autoencoders, diffusion probabilistic models, and generative adversarial networks. The present article aims to introduce this field of research to a broader machine learning audience by reviewing the necessary background in information theory (e.g., entropy coding, rate-distortion theory) and computer vision (e.g., image quality assessment, perceptual metrics), and providing a curated guide through the essential ideas and methods in the literature thus far.

Tim Schneider, Chen Qiu, Marius Kloft et al.

We develop a new method to detect anomalies within time series, which is essential in many application domains, reaching from self-driving cars, finance, and marketing to medical diagnosis and epidemiology. The method is based on self-supervised deep learning that has played a key role in facilitating deep anomaly detection on images, where powerful image transformations are available. However, such transformations are widely unavailable for time series. Addressing this, we develop Local Neural Transformations(LNT), a method learning local transformations of time series from data. The method produces an anomaly score for each time step and thus can be used to detect anomalies within time series. We prove in a theoretical analysis that our novel training objective is more suitable for transformation learning than previous deep Anomaly detection(AD) methods. Our experiments demonstrate that LNT can find anomalies in speech segments from the LibriSpeech data set and better detect interruptions to cyber-physical systems than previous work. Visualization of the learned transformations gives insight into the type of transformations that LNT learns.

Harshini Mangipudi, Griffin Mooers, Mike Pritchard et al.

Understanding the details of small-scale convection and storm formation is crucial to accurately represent the larger-scale planetary dynamics. Presently, atmospheric scientists run high-resolution, storm-resolving simulations to capture these kilometer-scale weather details. However, because they contain abundant information, these simulations can be overwhelming to analyze using conventional approaches. This paper takes a data-driven approach and jointly embeds spatial arrays of vertical wind velocities, temperatures, and water vapor information as three "channels" of a VAE architecture. Our "multi-channel VAE" results in more interpretable and robust latent structures than earlier work analyzing vertical velocities in isolation. Analyzing and clustering the VAE's latent space identifies weather patterns and their geographical manifestations in a fully unsupervised fashion. Our approach shows that VAEs can play essential roles in analyzing high-dimensional simulation data and extracting critical weather and climate characteristics.

Anji Liu, Stephan Mandt, Guy Van den Broeck

Despite extensive progress on image generation, common deep generative model architectures are not easily applied to lossless compression. For example, VAEs suffer from a compression cost overhead due to their latent variables. This overhead can only be partially eliminated with elaborate schemes such as bits-back coding, often resulting in poor single-sample compression rates. To overcome such problems, we establish a new class of tractable lossless compression models that permit efficient encoding and decoding: Probabilistic Circuits (PCs). These are a class of neural networks involving $|p|$ computational units that support efficient marginalization over arbitrary subsets of the $D$ feature dimensions, enabling efficient arithmetic coding. We derive efficient encoding and decoding schemes that both have time complexity $\mathcal{O} (\log(D) \cdot |p|)$, where a naive scheme would have linear costs in $D$ and $|p|$, making the approach highly scalable. Empirically, our PC-based (de)compression algorithm runs 5-40 times faster than neural compression algorithms that achieve similar bitrates. By scaling up the traditional PC structure learning pipeline, we achieve state-of-the-art results on image datasets such as MNIST. Furthermore, PCs can be naturally integrated with existing neural compression algorithms to improve the performance of these base models on natural image datasets. Our results highlight the potential impact that non-standard learning architectures may have on neural data compression.

Yoshitomo Matsubara, Ruihan Yang, Marco Levorato et al.

There has been much interest in deploying deep learning algorithms on low-powered devices, including smartphones, drones, and medical sensors. However, full-scale deep neural networks are often too resource-intensive in terms of energy and storage. As a result, the bulk part of the machine learning operation is therefore often carried out on an edge server, where the data is compressed and transmitted. However, compressing data (such as images) leads to transmitting information irrelevant to the supervised task. Another popular approach is to split the deep network between the device and the server while compressing intermediate features. To date, however, such split computing strategies have barely outperformed the aforementioned naive data compression baselines due to their inefficient approaches to feature compression. This paper adopts ideas from knowledge distillation and neural image compression to compress intermediate feature representations more efficiently. Our supervised compression approach uses a teacher model and a student model with a stochastic bottleneck and learnable prior for entropy coding (Entropic Student). We compare our approach to various neural image and feature compression baselines in three vision tasks and found that it achieves better supervised rate-distortion performance while maintaining smaller end-to-end latency. We furthermore show that the learned feature representations can be tuned to serve multiple downstream tasks.

Ruihan Yang, Yibo Yang, Joseph Marino et al.

While recent machine learning research has revealed connections between deep generative models such as VAEs and rate-distortion losses used in learned compression, most of this work has focused on images. In a similar spirit, we view recently proposed neural video coding algorithms through the lens of deep autoregressive and latent variable modeling. We present these codecs as instances of a generalized stochastic temporal autoregressive transform, and propose new avenues for further improvements inspired by normalizing flows and structured priors. We propose several architectures that yield state-of-the-art video compression performance on high-resolution video and discuss their tradeoffs and ablations. In particular, we propose (i) improved temporal autoregressive transforms, (ii) improved entropy models with structured and temporal dependencies, and (iii) variable bitrate versions of our algorithms. Since our improvements are compatible with a large class of existing models, we provide further evidence that the generative modeling viewpoint can advance the neural video coding field.

Antonios Alexos, Alex Boyd, Stephan Mandt

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models, variational inference (VI) is often the preferable option. Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. In this work, we propose a new non-parametric variational approximation that makes no assumptions about the approximate posterior's functional form and allows practitioners to specify the exact dependencies the algorithm should respect or break. The approach relies on a new Langevin-type algorithm that operates on a modified energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a "dropout" manner, leading to even more scalability. We test our scheme for ResNet-20 on CIFAR-10, SVHN, and FMNIST. In all cases, we find improvements in convergence speed and/or final accuracy compared to SG-MCMC and VI.

Chen Qiu, Timo Pfrommer, Marius Kloft et al.

Data transformations (e.g. rotations, reflections, and cropping) play an important role in self-supervised learning. Typically, images are transformed into different views, and neural networks trained on tasks involving these views produce useful feature representations for downstream tasks, including anomaly detection. However, for anomaly detection beyond image data, it is often unclear which transformations to use. Here we present a simple end-to-end procedure for anomaly detection with learnable transformations. The key idea is to embed the transformed data into a semantic space such that the transformed data still resemble their untransformed form, while different transformations are easily distinguishable. Extensive experiments on time series demonstrate that our proposed method outperforms existing approaches in the one-vs.-rest setting and is competitive in the more challenging n-vs.-rest anomaly detection task. On tabular datasets from the medical and cyber-security domains, our method learns domain-specific transformations and detects anomalies more accurately than previous work.