dataset-review/dataset-review huggingface dataset:
Conformal Prediction as Bayesian Quadrature
ICML 2025

Conformal Prediction as Bayesian Quadrature
Jake C. Snell 1 Thomas L. Griffiths 1 2
Abstract
As machine learning-based prediction systems are
increasingly used in high-stakes situations, it is
important to understand how such predictive mod-
els will perform upon deployment. Distribution-
free uncertainty quantification techniques such as
conformal prediction provide guarantees about
the loss black-box models will incur even when
the details of the models are hidden. However,
such methods are based on frequentist probability,
which unduly limits their applicability. We revisit
the central aspects of conformal prediction from
a Bayesian perspective and thereby illuminate the
shortcomings of frequentist guarantees. We pro-
pose a practical alternative based on Bayesian
quadrature that provides interpretable guarantees
and offers a richer representation of the likely
range of losses to be observed at test time.
1. Introduction
Machine learning systems based on deep learning are in-
creasingly used in high-stakes settings, such as medical
diagnosis or financial applications. These settings impose
unique constraints on the performance of these systems: we
want them to produce good outcomes in the aggregate, but
also do so fairly and with a guarantee of a low probability of
harm. However, predictive models based on deep learning
can be difficult to interpret, and commercial models increas-
ingly tend to offer little information about the techniques
used in training. This creates a new challenge: How can we
flexibly and reliably quantify the suitability of a model for
deployment without making too many assumptions about
how the model was trained or in which settings it will be
used?
Recent research on quantifying uncertainty has employed
methods based on conformal prediction (Vovk et al., 2005),
1Department of Computer Science, Princeton University
2Department of Psychology, Princeton University. Correspondence
to: Jake C. Snell <jsnell@princeton.edu>.
Proceedings of the 4...
Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification
ICML 2025

Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation
and parameter identification
Jan Blechschmidt 1 2 Tom-Christian Riemer 1 Max Winkler 1 Martin Stoll 1 Jan-F. Pietschmann 3
Abstract
We develop a novel physics informed deep learn-
ing approach for solving nonlinear drift-diffusion
equations on metric graphs. These models repre-
sent an important model class with a large number
of applications in areas ranging from transport in
biological cells to the motion of human crowds.
While traditional numerical schemes require a
large amount of tailoring, especially in the case
of model design or parameter identification prob-
lems, physics informed deep operator networks
(DEEPONETS) have emerged as a versatile tool
for the solution of partial differential equations
with the particular advantage that they easily in-
corporate parameter identification questions. We
here present an approach where we first learn
three DEEPONET models for representative in-
flow, inner and outflow edges, resp., and then
subsequently couple these models for the solu-
tion of the drift-diffusion metric graph problem
by relying on an edge-based domain decomposi-
tion approach. We illustrate that our framework
is applicable for the accurate evaluation of graph-
coupled physics models and is well suited for
solving optimization or inverse problems on these
coupled networks.
1. Introduction
Dynamic processes on graphs (Newman, 2018; Barab´asi,
2016) are crucial for understanding complex phenomena
1Department of Mathematics, TU Chemnitz, Chemnitz,
Germany 2Department of Mathematics and Computer Science,
TU Bergakademie Freiberg, Freiberg, Germany 3Department
of Mathematics, University of Augsburg, Augsburg, Germany
and Centre for Advanced Analytics and Predictive Sciences
(CAAPS), University of Augsburg, Universit¨atsstr. 12a, 86159
Augsburg, Germany.
.
Correspondence to:
Jan Blech-
schmidt <jan.blechschmidt@math.tu-chemnitz.de>, Martin Stoll
<martin.stoll@math.tu-chemnitz.de>.
...
Causal Logistic Bandits with Counterfactual Fairness Constraints
ICML 2025

Causal Logistic Bandits with Counterfactual Fairness Constraints
Jiajun Chen 1 Jin Tian 2 Christopher John Quinn 1
Abstract
Artificial intelligence will play a significant role
in decision making in numerous aspects of soci-
ety. Numerous fairness criteria have been pro-
posed in the machine learning community, but
there remains limited investigation into fairness
as defined through specified attributes in a sequen-
tial decision-making framework. In this paper, we
focus on causal logistic bandit problems where
the learner seeks to make fair decisions, under
a notion of fairness that accounts for counterfac-
tual reasoning. We propose and analyze an al-
gorithm by leveraging primal-dual optimization
for constrained causal logistic bandits where the
non-linear constraints are a priori unknown and
must be learned in time. We obtain sub-linear
regret guarantees with leading term similar to
that for unconstrained logistic bandits (Lee et al.,
2024) while guaranteeing sub-linear constraint
violations. We show how to achieve zero cumula-
tive constraint violations with a small increase in
the regret bound.
1. Introduction
Artificial intelligence (AI) models, using techniques from
statistics and machine learning, are increasingly being used
to make decisions that affect people’s lives. In light of this, a
plethora of formal fairness criteria have been proposed (Dar-
lington, 1971; Dwork et al., 2012; Hardt et al., 2016; Zhang
et al., 2016; Kusner et al., 2017; Zafar et al., 2017; Nabi
& Shpitser, 2018; Chiappa, 2019; Chouldechova & Roth,
2020; Imai & Jiang, 2023; Plecko & Bareinboim, 2024).
There has been growing interest in the sequential decision-
making community for accounting for fairness, including in
settings such as classic and contextual bandits (Joseph et al.,
2018), combinatorial bandits (Xu et al., 2020), bandits with
1Department of Computer Science, Iowa State University,
Ames, IA, USA 2Mohamed bin Zayed University of Artificial
Intelligence, Abu Dhabi, UAE. C...
Physics-Informed Diffusion Models
ICLR 2025

Published as a conference paper at ICLR 2025
PHYSICS-INFORMED DIFFUSION MODELS
Jan-Hendrik Bastek
Dept. of Mechanical and Process Eng.
ETH Zurich
Zurich, Switzerland
jbastek@ethz.ch
WaiChing Sun
Dept. of Civil Eng. and Eng. Mechanics
Columbia University
New York, NY, USA
wsun@columbia.edu
Dennis M. Kochmann
Dept. of Mechanical and Process Eng.
ETH Zurich
Zurich, Switzerland
dmk@ethz.ch
ABSTRACT
Generative models such as denoising diffusion models are quickly advancing their
ability to approximate highly complex data distributions. They are also increasingly
leveraged in scientific machine learning, where samples from the implied data
distribution are expected to adhere to specific governing equations. We present
a framework that unifies generative modeling and partial differential equation
fulfillment by introducing a first-principle-based loss term that enforces generated
samples to fulfill the underlying physical constraints. Our approach reduces the
residual error by up to two orders of magnitude compared to previous work in a
fluid flow case study and outperforms task-specific frameworks in relevant metrics
for structural topology optimization. We also present numerical evidence that
our extended training objective acts as a natural regularization mechanism against
overfitting. Our framework is simple to implement and versatile in its applicability
for imposing equality and inequality constraints as well as auxiliary optimization
objectives.
1
INTRODUCTION
Denoising diffusion models (Sohl-Dickstein et al., 2015) are generative models that have gained
popularity due to their success in learning intricate data distributions across various modalities,
including images (Ho et al., 2020; Nichol et al., 2021; Rombach et al., 2021), videos (Ho et al.,
2022a;b), graphs (Niu et al., 2020; Hoogeboom et al., 2022), text (Li et al., 2022; Wu et al., 2023), and
audio waveforms (Kong et al., 2021). Originally popularized within the image generation community,
their outstandin...
Synonymous Variational Inference for Perceptual Image Compression
ICML 2025

Synonymous Variational Inference for Perceptual Image Compression
Zijian Liang 1 Kai Niu 1 2 Changshuo Wang 1 Jin Xu 1 Ping Zhang 3
Abstract
Recent contributions of semantic information the-
ory reveal the set-element relationship between
semantic and syntactic information, represented
as synonymous relationships. In this paper, we
propose a synonymous variational inference (SVI)
method based on this synonymity viewpoint to re-
analyze the perceptual image compression prob-
lem. It takes perceptual similarity as a typical syn-
onymous criterion to build an ideal synonymous
set (Synset), and approximate the posterior of its
latent synonymous representation with a paramet-
ric density by minimizing a partial semantic KL
divergence. This analysis theoretically proves
that the optimization direction of perception im-
age compression follows a triple tradeoff that
can cover the existing rate-distortion-perception
schemes. Additionally, we introduce synonymous
image compression (SIC), a new image compres-
sion scheme that corresponds to the analytical
process of SVI, and implement a progressive
SIC codec to fully leverage the model’s capabili-
ties. Experimental results demonstrate compara-
ble rate-distortion-perception performance using
a single progressive SIC codec, thus verifying the
effectiveness of our proposed analysis method.
1. Introduction
Image compression is a typical topic for lossy source cod-
ing, aiming to achieve the optimal tradeoff between recon-
structed image quality and coding rate. Following the rate-
distortion optimization instructed by Shannon’s classic in-
formation theory (1948; 1959), traditional image compres-
sion like JPEG (Wallace, 1991) and BPG (Bellard, 2015)
1Key Laboratory of Universal Wireless Communications, Min-
istry of Education, Beijing University of Posts and Telecommuni-
cations, Beijing, China 2Peng Cheng Laboratory, Shenzhen, China
3State Key Laboratory of Networking and Switching Technol-
ogy, Beijing University of Posts an...
Circumventing Backdoor Space via Weight Symmetry
ICML 2025

Circumventing Backdoor Space via Weight Symmetry
Jie Peng 1 Hongwei Yang 1 Jing Zhao 1 Hengji Dong 1 Hui He 1 Weizhe Zhang 1 2 Haoyu He 3
Abstract
Deep neural networks are vulnerable to backdoor
attacks, where malicious behaviors are implanted
during training. While existing defenses can effec-
tively purify compromised models, they typically
require labeled data or speciﬁc training proce-
dures, making them difﬁcult to apply beyond su-
pervised learning settings. Notably, recent studies
have shown successful backdoor attacks across
various learning paradigms, highlighting a crit-
ical security concern. To address this gap, we
propose Two-stage Symmetry Connectivity (TSC),
a novel backdoor puriﬁcation defense that oper-
ates independently of data format and requires
only a small fraction of clean samples. Through
theoretical analysis, we prove that by leverag-
ing permutation invariance in neural networks
and quadratic mode connectivity, TSC ampliﬁes
the loss on poisoned samples while maintaining
bounded clean accuracy. Experiments demon-
strate that TSC achieves robust performance com-
parable to state-of-the-art methods in supervised
learning scenarios. Furthermore, TSC generalizes
to self-supervised learning frameworks, such as
SimCLR and CLIP, maintaining its strong defense
capabilities. Our code is available at https:
//github.com/JiePeng104/TSC.
1. Introduction
Modern classiﬁers require substantial data and computa-
tional resources to achieve high accuracy, providing adver-
saries with opportunities to implant backdoors into deep
neural networks (Gu et al., 2017; Chen et al., 2017). This
vulnerability arises from either injecting poisoned data (Gu
et al., 2017; Turner et al., 2019) (i.e., data-poisoning attack),
or manipulating the training process (Pang et al., 2019;
1School of Cyberspace Science, Harbin Institute of Technol-
ogy, Harbin, China.
2Pengcheng Laboratory, Shenzhen, China.
3Department of Data Science and AI, Faculty of IT, Monash
University, Melb...
SING: SDE Inference via Natural Gradients
NeurIPS 2025

SING: SDE Inference via Natural Gradients
Amber Hu∗
Stanford University
amberhu@stanford.edu
Henry D. Smith∗
Stanford University
smithhd@stanford.edu
Scott W. Linderman
Stanford University
swl1@stanford.edu
Abstract
Latent stochastic differential equation (SDE) models are important tools for the
unsupervised discovery of dynamical systems from data, with applications ranging
from engineering to neuroscience. In these complex domains, exact posterior
inference of the latent state path is typically intractable, motivating the use of
approximate methods such as variational inference (VI). However, existing VI
methods for inference in latent SDEs often suffer from slow convergence and
numerical instability. Here, we propose SDE Inference via Natural Gradients
(SING), a method that leverages natural gradient VI to efficiently exploit the un-
derlying geometry of the model and variational posterior. SING enables fast and
reliable inference in latent SDE models by approximating intractable integrals
and parallelizing computations in time. We provide theoretical guarantees that
SING approximately optimizes the intractable, continuous-time objective of inter-
est. Moreover, we demonstrate that better state inference enables more accurate
estimation of nonlinear drift functions using, for example, Gaussian process SDE
models. SING outperforms prior methods in state inference and drift estimation
on a variety of datasets, including a challenging application to modeling neural
dynamics in freely behaving animals. Altogether, our results illustrate the potential
of SING as a tool for accurate inference in complex dynamical systems, especially
those characterized by limited prior knowledge and non-conjugate structure.1
1
Introduction
Stochastic differential equations (SDEs) are powerful tools for modeling complex, time-varying
systems in scientific domains such as physics, engineering, and neuroscience [1, 2]. In many real-
world settings, we do not observe the state of the syste...
Angle Domain Guidance: Latent Diffusion Requires Rotation Rather Than Extrapolation
ICML 2025

Angle Domain Guidance: Latent Diffusion Requires Rotation Rather Than
Extrapolation
Cheng Jin 1 Zhenyu Xiao * 1 Chutao Liu * 2 Yuantao Gu 1
Abstract
Classifier-free guidance (CFG) has emerged as a
pivotal advancement in text-to-image latent diffu-
sion models, establishing itself as a cornerstone
technique for achieving high-quality image syn-
thesis. However, under high guidance weights,
where text-image alignment is significantly en-
hanced, CFG also leads to pronounced color dis-
tortions in the generated images. We identify
that these distortions stem from the amplifica-
tion of sample norms in the latent space. We
present a theoretical framework that elucidates
the mechanisms of norm amplification and anoma-
lous diffusion phenomena induced by classifier-
free guidance. Leveraging our theoretical insights
and the latent space structure, we propose an An-
gle Domain Guidance (ADG) algorithm. ADG
constrains magnitude variations while optimizing
angular alignment, thereby mitigating color dis-
tortions while preserving the enhanced text-image
alignment achieved at higher guidance weights.
Experimental results demonstrate that ADG sig-
nificantly outperforms existing methods, generat-
ing images that not only maintain superior text
alignment but also exhibit improved color fidelity
and better alignment with human perceptual pref-
erences.
1. Introduction
The Stable Diffusion series (Rombach et al., 2022; Esser
et al., 2024), along with other latent-diffusion-based genera-
tive models (Ramesh et al., 2022; Labs, 2024), has revolu-
tionized text-to-image generation and related downstream
tasks (Zhang et al., 2023; Zhao et al., 2024; Zhang et al.,
*Equal contribution
1Department of Electronic Engineering,
Tsinghua University, Beijing, China 2Zhili College, Tsinghua
University, Beijing, China.
Correspondence to: Yuantao Gu
<gyt@tsinghua.edu.cn>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025
by t...
Soup-of-Experts: Pretraining Specialist Models via Parameters Averaging
ICML 2025

Soup-of-Experts: Pretraining Specialist Models via Parameters Averaging
Pierre Ablin 1 Angelos Katharopoulos 1 Skyler Seto 1 David Grangier 1
Abstract
Machine learning models are routinely trained on
a mixture of different data domains. Different
domain weights yield very different downstream
performances. We propose the Soup-of-Experts,
a novel architecture that can instantiate a model
at test time for any domain weights with mini-
mal computational cost and without re-training
the model. Our architecture consists of a bank of
expert parameters, which are linearly combined
to instantiate one model. We learn the linear com-
bination coefficients as a function of the input
domain weights. To train this architecture, we
sample random domain weights, instantiate the
corresponding model, and backprop through one
batch of data sampled with these domain weights.
We demonstrate how our approach obtains small
specialized models on several language modeling
tasks quickly. Soup-of-Experts are particularly
appealing when one needs to ship many different
specialist models quickly under a size constraint.
1. Introduction
Large Language Models (LLMs) work well on diverse tasks
because they have many parameters and are trained on gen-
eralist datasets (Brown et al., 2020; Bommasani et al., 2021).
However, they are costly to train and to serve, both in terms
of memory and inference cost.
Specialist language models hold fewer parameters; they
are, therefore, cheaper to store, send, and use at inference.
However, they must give up the generality of LLMs and
specialize in a few specific topics.
In cases where there is an abundance of specialization data,
training a small model on those data yields a good specialist.
However, in many settings, the specialization data is scarce:
for instance, it may come from a narrow topic of interest
1Apple.
Correspondence
to:
Pierre
Ablin
<p ablin@apple.com>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PM...
SEFE: Superficial and Essential Forgetting Eliminator for Multimodal Continual Instruction Tuning
ICML 2025

SEFE: Superficial and Essential Forgetting Eliminator for
Multimodal Continual Instruction Tuning
Jinpeng Chen * 1 Runmin Cong * 2 Yuzhi Zhao 1 Hongzheng Yang 3
Guangneng Hu 4 Horace Ho Shing Ip 1 Sam Kwong 5
https://github.com/jinpeng0528/SEFE/
Abstract
Multimodal Continual Instruction Tuning (MCIT)
aims to enable Multimodal Large Language Mod-
els (MLLMs) to incrementally learn new tasks
without catastrophic forgetting. In this paper, we
explore forgetting in this context, categorizing it
into superficial forgetting and essential forgetting.
Superficial forgetting refers to cases where the
model’s knowledge may not be genuinely lost,
but its responses to previous tasks deviate from
expected formats due to the influence of subse-
quent tasks’ answer styles, making the results
unusable. By contrast, essential forgetting refers
to situations where the model provides correctly
formatted but factually inaccurate answers, indi-
cating a true loss of knowledge. Assessing essen-
tial forgetting necessitates addressing superficial
forgetting first, as severe superficial forgetting can
obscure the model’s knowledge state. Hence, we
first introduce the Answer Style Diversification
(ASD) paradigm, which defines a standardized
process for transforming data styles across differ-
ent tasks, unifying their training sets into similarly
diversified styles to prevent superficial forgetting
caused by style shifts. Building on this, we pro-
pose RegLoRA to mitigate essential forgetting.
RegLoRA stabilizes key parameters where prior
knowledge is primarily stored by applying regu-
larization, enabling the model to retain existing
competencies. Experimental results demonstrate
that our overall method, SEFE, achieves state-of-
the-art performance.
*Equal contribution 1City University of Hong Kong 2Shandong
University
3The Chinese University of Hong Kong
4Xidian
University 5Lingnan University.
Correspondence to:
Yuzhi
Zhao <yzzhao2-c@my.cityu.edu.hk>, Sam Kwong <samk-
wong@lingnan.edu.hk>....
Multi-Label Test-Time Adaptation with Bound Entropy Minimization
ICLR 2025

Published as a conference paper at ICLR 2025
MULTI-LABEL TEST-TIME ADAPTATION WITH BOUND
ENTROPY MINIMIZATION
Xiangyu Wu1,2, Feng Yu1, Qing-Guo Chen2, Yang Yang1∗, Jianfeng Lu1∗
1Nanjing University of Science and Technology
2Alibaba International Digital Commerce Group
ABSTRACT
Mainstream test-time adaptation (TTA) techniques endeavor to mitigate distri-
bution shifts via entropy minimization for multi-class classification, inherently
increasing the probability of the most confident class. However, when encoun-
tering multi-label instances, the primary challenge stems from the varying num-
ber of labels per image, and prioritizing only the highest probability class in-
evitably undermines the adaptation of other positive labels. To address this issue,
we investigate TTA within multi-label scenario (ML–TTA), developing Bound
Entropy Minimization (BEM) objective to simultaneously increase the confi-
dence of multiple top predicted labels. Specifically, to determine the number of
labels for each augmented view, we retrieve a paired caption with yielded tex-
tual labels for that view. These labels are allocated to both the view and cap-
tion, called weak label set and strong label set with the same size k. Follow-
ing this, the proposed BEM considers the highest top-k predicted labels from
view and caption as a single entity, respectively, learning both view and cap-
tion prompts concurrently. By binding top-k predicted labels, BEM overcomes
the limitation of vanilla entropy minimization, which exclusively optimizes the
most confident class. Across the MSCOCO, VOC, and NUSWIDE multi-label
datasets, our ML–TTA framework equipped with BEM exhibits superior perfor-
mance compared to the latest SOTA methods, across various model architec-
tures, prompt initialization, and varying label scenarios. The code is available
at https://github.com/Jinx630/ML-TTA.
1
INTRODUCTION
The advent of vision-language models (VLMs) (Radford et al., 2021; Li et al., 2023; Zeng et al.,
2024; Ya...