ICML 2026 论文列表

International Conference on Machine Learning

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Safe Reinforcement Learning with Preference-based Constraint Inference

Chenglin Li, Grant Ruan, Hua Geng

展开摘要

Safe reinforcement learning (RL) is a standard paradigm for safety-critical decision making. However, real-world safety constraints can be complex, subjective, and even hard to explicitly specify. Existing works on constraint inference rely on restrictive assumptions or extensive expert demonstrations, which are not realistic in many real-world applications. How to cheaply and reliably learn these constraints is the major challenge we focus on in this study. While inferring constraints from human preferences offers a data-efficient alternative, we identify popular Bradley-Terry (BT) models fail to capture the asymmetric, heavy-tailed nature of safety costs, resulting in risk underestimation. It is still rare in the literature to understand the impacts of BT models on the downstream policy learning. To address the above knowledge gaps, we propose a novel approach namely Preference-based Constrained Reinforcement Learning (PbCRL). We introduce a novel dead zone mechanism into preference modeling and theoretically prove that it encourages heavy-tailed cost distributions, thereby achieving better constraint alignment. Additionally, we incorporate a Signal-to-Noise Ratio (SNR) loss to encourage exploration by cost variances, which is found to benefit policy learning. Further, two-stage training strategy is deployed to lower online labeling burdens while adaptively enhancing constraint satisfaction. Empirical results demonstrate that PbCRL achieves superior alignment with true safety requirements and outperforms state-of-the-art baselines in terms of safety and reward. Our work explores a promising and effective way for constraint inference in Safe RL, with great potential in various safety-critical applications.

Poster
M-Star: Markovian Projection of Star-Shaped Diffusion for Exponential Family Distributions

François Bertholom, Khalid Oublal

展开摘要

Diffusion models achieve state-of-the-art performance in generative modeling but are limited by their reliance on Gaussian noise and the high computational cost of iterative sampling. Star-shaped diffusion addresses the former by introducing a non-Markovian forward process, yet this comes at the expense of temporal coherence in the reverse process. We propose a novel framework that resolves this trade-off by learning a Markovian projection of a star-shaped forward process, and its reversal. This design enables learning over a broad class of exponential models and recovers DDPM as a special case. It is particularly well-suited for knowledge distillation, allowing few-step or even single-step generation. Experiments demonstrate the effectiveness and flexibility of our approach across multiple generative tasks. Code and demo are available at: https://oublalkhalid.github.io/MStar-Diffusion/.

Poster
Disentangling Consensus and Value-Specific Representations for Controllable Pluralistic Value Alignment of LLMs

JianKui Zhou, Jing Yao, Xiaoyuan Yi, Peng Zhang, Ning Gu, Zhan Hu, Xing Xie, Tun Lu

展开摘要

With the widespread deployment of large language models (LLMs), aligning model outputs with pluralistic human values has become an important research problem. Recent approaches that train task-specific experts and merge them through parameter aggregation have shown promise for pluralistic alignment. However, these methods often overlook the intrinsic complexity of real-world value data, where multiple correlated value dimensions coexist, resulting in highly similar and entangled expert representations. Consequently, modifying the contribution of one value expert may unintentionally influence other values, limiting fine-grained controllability. To address this issue, we propose DisAlign, a model-merging framework that explicitly decomposes value representations into consensus and value-specific components using an information-geometric perspective. DisAlign first extracts a consensus anchor and subspace to capture shared structure across values, and then applies spectral decomposition to the residual representations to construct disentangled value subspaces. This design enables more precise and independent modulation of multiple values. Experiments on three datasets covering different value frameworks demonstrate that DisAlign consistently improves value disentanglement and achieves more accurate pluralistic value control compared to existing baselines. Our code is available at \url{https://anonymous.4open.science/r/DisAlign-7F35}

Poster
Computational Arbitrage in AI Model Markets

Ricardo Olmedo, Bernhard Schölkopf, Moritz Hardt

展开摘要

Consider a market of competing model providers selling query access to models with varying costs and capabilities. Customers submit problem instances and are willing to pay up to a budget for a verifiable solution. An arbitrageur efficiently allocates inference budget across providers to undercut the market, thus creating a competitive offering with no model-development risk. In this work, we initiate the study of arbitrage in AI model markets, empirically demonstrating the viability of arbitrage and illustrating its economic consequences. We conduct an in-depth case study of SWE-bench GitHub issue resolution using two representative models, GPT-5 mini and DeepSeek v3.2. In this verifiable domain, simple arbitrage strategies generate net profit margins of up to 40\%. Robust arbitrage strategies that generalize across different domains remain profitable. Distillation further creates strong arbitrage opportunities, potentially at the expense of the teacher model’s revenue. Multiple competing arbitrageurs drive down consumer prices, reducing the marginal revenue of model providers. At the same time, arbitrage reduces market segmentation and facilitates market entry for smaller model providers by enabling earlier revenue capture. Our results suggest that arbitrage can be a powerful force in AI model markets with implications for model development, distillation, and deployment.

Poster
BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fields

Rui-Yang Zhang, Lachlan Astfalck, Edward Cripps, David S. Leslie, Henry Moss

展开摘要

We introduce a formal active learning methodology for guiding the placement of Lagrangian observers to infer time-dependent vector fields -- a key task in oceanography, marine science, and ocean engineering -- using a physics-informed spatio-temporal Gaussian process surrogate model. The majority of existing placement campaigns either follow standard `space-filling' designs or relatively ad-hoc expert opinions. A key challenge to applying principled active learning in this setting is that Lagrangian observers are continuously advected through the vector field, so they make measurements at different locations and times. It is, therefore, important to consider the likely future trajectories of placed observers to account for the utility of candidate placement locations. To this end, we present BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories. We observe noticeable benefits of BALLAST-aided sequential observer placement strategies on both synthetic and high-fidelity ocean current models. In addition, we developed a novel GP inference method -- the Vanilla SPDE Exchange (VaSE) -- to boost the GP posterior sampling efficiency, which is also of independent interest.

Poster
Explicitly Modeling Censoring Produces Superior Survival Predictors

Shi-ang Qi, Yakun Yu, Russell Greiner

展开摘要

Likelihood-based training is the dominant paradigm in survival prediction. Under independent censoring, we can factorize the likelihood and optimize only the terms related to event modeling, effectively treating the censoring mechanism as incidental. This is justified when censoring is *non-informative*, i.e., when the censoring process shares no parameters with the event-time model. However, this may not hold in practice, and ignoring censoring contributions may discard useful signals for learning representations that can help to effectively estimate event distributions. Motivated by this, we argue that explicitly modeling censoring can improve representation learning and time-to-event estimation, particularly when event and censoring processes are coupled. We introduce a latent decomposition view in which observed covariates are mapped to latent components corresponding to event-specific, censoring-specific, confounding, and irrelevant information. We then learn decomposed representations for the first three categories to guide a better estimation of the event distribution. We instantiate our method on 4 popular deep-learning survival models and evaluate on 10 datasets (2 semi-synthetic and 8 real-world), showing consistent gains over strong baselines and multiple SOTA methods.

Poster
Pull Requests as a Training Signal for Repo-Level Code Editing

Qinglin Zhu, Tianyu Chen, Shuai Lu, Lei Ji, Runcong Zhao, Murong Ma, Xiangxiang Dai, Yulan He, Lin Gui, Peng Cheng, Yeyun Gong

展开摘要

Repository-level code editing requires models to understand complex dependencies and execute precise multi-file modifications across a large codebase. While recent gains on SWE-bench rely heavily on complex agent scaffolding, it remains unclear how much of this capability can be internalised via high-quality training signals. To address this, we propose Clean Pull Request (Clean-PR), a mid-training paradigm that leverages real-world GitHub pull requests as a training signal for repository-level editing. We introduce a scalable pipeline that converts noisy pull request diffs into Search/Replace edit blocks through reconstruction and validation, resulting in the largest publicly available corpus of 2 million pull requests spanning 12 programming languages. Using this training signal, we perform a mid-training stage followed by an agentless-aligned supervised fine-tuning process with error-driven data augmentation. On SWE-bench, our model significantly outperforms the instruction-tuned baseline, achieving absolute improvements of 13.6% on SWE-bench Lite and 12.3% on SWE-bench Verified. These results demonstrate that repository-level code understanding and editing capabilities can be effectively internalised into model weights under a simplified, agentless protocol, without relying on heavy inference-time scaffolding.

Poster
Shift-Dependent Asymmetry: Orthogonal Inverse Low-Rank Adaptation for Federated Medical Segmentation

Xingyue Zhao, Wenke Huang, Linghao Zhuang, Haoran Wu, Anwen Jiang, Zhifeng Wang, Wenwen He, Ming Feng, Mang Ye, bo xu

展开摘要

Low-Rank Adaptation (LoRA) enables efficient federated fine-tuning of segmentation foundation models for medical imaging. However, most federated LoRA methods adopt a uniform aggregation rule, which breaks under the encoder–decoder asymmetry in medical segmentation: the encoder is dominated by appearance shifts, while the decoder is dominated by supervision variations. This mismatch entangles shared anatomy with site-specific biases and harms generalization. To address this, we propose Inverse Asymmetric Tuning (IAT). IAT aligns adaptation with heterogeneity sources by personalizing module-specific components in the encoder to absorb appearance shifts and in the decoder to accommodate site-dependent supervision, while retaining a shared pathway for transferable consensus. However, structural separation alone is insufficient under LoRA’s bilinear parameterization, where multiplicative coupling can still cause site-specific updates to leak into the shared direction. We therefore introduce a Subspace Orthogonality Regularizer that penalizes shared–local collinearity in the effective update space, mitigating leakage without extra communication. Experiments show consistent improvements over strong federated LoRA and parameter-efficient FL baselines.

Poster
MetaOthello: A Controlled Study of Multiple World Models in Transformers

Aviral Chawla, Galen Hall, Juniper L Lovato

展开摘要

Foundation models must handle multiple generative processes, yet mechanistic interpretability largely studies capabilities in isolation; it remains unclear how a single transformer organizes multiple, potentially conflicting "world models". Previous experiments on Othello-playing neural networks test world-model learning, but focus on a single game with a single set of rules. We introduce *MetaOthello*, a controlled suite of Othello-like games with shared syntax but different rules or tokenizations, and train small GPTs on mixed-variant data. We show that transformers trained on multiple Othello variants learn **shared world-state representations**: linear probes trained on one game intervene on another's board state nearly as well as matched probes. When the games conflict, the model resolves the resulting *ambiguity* through a localized mechanism we identify and steer. For isomorphic games with token remapping, representations are equivalent up to a single orthogonal rotation that generalizes across layers, showing the shared structure is abstract rather than tied to surface form. Together, these results show that transformers reconcile conflicting world models by sharing structure and localizing conflict. *MetaOthello* thus offers a path toward understanding how transformers organize many world models at once.

Poster
CausalProfiler: Generating Synthetic Benchmarks for Rigorous and Transparent Evaluation of Causal Machine Learning

Panayiotis Panayiotou, Audrey Poinsot, Alessandro Leite, Nicolas CHESNEAU, Marc Schoenauer, Özgür Şimşek

展开摘要

Causal machine learning aims to answer "what if" questions using machine learning algorithms, making it a promising tool for high-stakes decision-making. Yet, empirical evaluation practices remain limited. Existing benchmarks often rely on a handful of hand-crafted or semi-synthetic datasets, leading to brittle, non-generalizable conclusions. To bridge this gap, we introduce CausalProfiler, a synthetic benchmark generator for causal machine learning methods. Based on a set of explicit design choices about the class of causal models, queries, and data considered, CausalProfiler randomly samples causal models, data, queries, and ground truths constituting the synthetic causal benchmarks. In this way, causal machine learning can be rigorously and transparently evaluated under a variety of conditions. This work offers the first random generator of synthetic causal benchmarks with coverage guarantees and transparent assumptions operating on the three levels of causal reasoning: observation, intervention, and counterfactual. We demonstrate its utility by evaluating several state-of-the-art methods under diverse conditions and assumptions, both in and out of the identification regime, illustrating the types of analyses and insights CausalProfiler enables.

Poster
VideoSEG-O3: A Multi-turn Reinforcement Learning Framework for Reasoning Video Object Segmentation

Ming Dai, Sen Yang, Boqiang Duan, Boyuan Tong, Jiedong Zhuang, Wankou Yang, Jingdong Wang

展开摘要

Reasoning Video Object Segmentation (RVOS) demands a sophisticated integration of temporal dynamics, spatial details, and linguistic reasoning to achieve precise pixel-level localization. Existing methods are limited to reasoning over fixed initial inputs and lack the capacity to actively acquire further visual evidence, which is often essential for resolving complex references in long or intricate videos. To address this, we propose $\textbf{VideoSEG-O3}$, the first multi-turn reinforcement learning framework for RVOS that emulates the human $\textit{``coarse-to-fine''}$ cognitive process. It employs a $\textit{multi-turn temporal-spatial chain-of-thought}$ to capture fine-grained details by iteratively pinpointing critical intervals and keyframes. Additionally, to enable the policy to perceive segmentation quality beyond mere text probability of $\texttt{[SEG]}$ during the RL stage, we introduce $\textit{SEG-aware logit calibration}$, which integrates pixel-wise segmentation feedback directly into the token-level logits. Furthermore, we design a $\textit{decoupled thinking trace}$ to hierarchically decompose the reasoning process into temporal, spatial, and linguistic dimensions, and construct $\textbf{VTS-CoT}$, a specialized cold-start dataset featuring comprehensive reasoning trajectories. Extensive experiments demonstrate that VideoSEG-O3 achieves advanced performance across 8 mainstream RVOS benchmarks, particularly excelling in long-horizon and complex reasoning tasks.

Poster
StepCodeReasoner: Aligning Code Reasoning with Stepwise Execution Traces via Reinforcement Learning

Hao Wang, Lei Sha, Jie M. Zhang

展开摘要

Existing code reasoning methods primarily supervise final code outputs, ignoring intermediate states, often leading to reward hacking where correct answers are obtained through inconsistent reasoning. We propose StepCodeReasoner, a framework that introduces explicit intermediate execution-state supervision. By automatically inserting structured print-based execution-trace anchors into code, the model is trained to predict runtime states at each step, transforming code reasoning into a verifiable, stepwise execution modeling problem. Building on this execution-aware method, we introduce Dual-Granularity GRPO (DG-GRPO), a reinforcement learning algorithm for structured credit assignment at two complementary granularities: inter-trajectory comparison across sampled execution paths and intra-trajectory shaping based on downstream correctness. Extensive experiments demonstrate that StepCodeReasoner achieves state-of-the-art performance in code reasoning. In particular, our 7B model achieves 91.1\% on CRUXEval and 86.5\% on LiveCodeBench, outperforming the CodeReasoner-7B baseline (86.0\% and 77.7\%) and GPT-4o (85.6\% and 75.1\%). Furthermore, on the execution-trace benchmark REval, our model scores 82.9\%, outperforming baseline CodeReasoner-7B (72.3\%), its 14B counterpart (81.1\%), and GPT-4o (77.3\%). In addition, StepCodeReasoner improves code generation, achieving 90.1 on HumanEval, 85.0 on MBPP, and 19.4 on LiveCodeBench generation, with an average score of 64.8 versus 62.6 for CodeReasoner-7B.

Poster
Fast Estimation for Forest Matrix of Signed Graphs

Haoxin Sun, Zhongzhi Zhang

展开摘要

The forest matrix of a signed graph plays an important role in network science and social opinion dynamics, yet existing algorithms are mainly designed for unsigned graphs and are difficult to extend to signed graphs. In this paper, we study the problem of efficiently estimating the forest matrix of signed graphs with \(n\) nodes and introduce the signed forest matrix theorem, which establishes the relationship between generalized spanning converging forests and the forest matrix. Based on this result, we propose a novel algorithm \textsc{GSCF}, built on a variant of loop-erased random walks, to generate generalized spanning converging forests in expected \(O(n)\) time. We further develop two sampling algorithms, \textsc{FMDE} and \textsc{FMDE+}, for estimating the diagonal of the forest matrix, both with time complexity \(O(ln)\), where \(l\) is the number of samples. Extensive experiments on various signed graphs show that our methods achieve high estimation accuracy, significantly improve computational efficiency, and scale to graphs with over twenty million nodes. Our source code is publicly available on \url{https://github.com/HaoxinSun98/SignedForestDiagonal}.

Poster
Optimality of FSQ Tokens for Continuous Diffusion for Categorical Data with Application to Text-to-Speech

Vadim Popov, Wenju Gu, Tasnima Sadekova, Georgii Aparin, Assel Yermekova

展开摘要

Continuous diffusion for categorical data is a framework belonging to the diffusion family and aiming at generating discrete data. The scientific interest to such models has been constantly increasing these days because researchers try to achieve a challenging goal of finding reasonable alternatives to autoregressive large language models. In this paper, we study the properties of the structure of the latent space corresponding to discrete tokens expressed in terms of Kullback-Leibler divergence on diffusion path measures and accuracy of the correct token prediction by the optimally trained diffusion model. We find that FSQ tokenization scheme has the latent space structure with the properties that make it best suited for continuous diffusion for categorical data as verified through rigorous theoretical analysis and numerical experiments. To validate our findings in real-life scenario, we train several text-to-speech diffusion models having speech tokens as intermediate acoustic features, and show that the one based on FSQ tokens indeed performs the best, and, moreover, it outperforms its strong LLM-based counterpart, at the same time being significantly smaller and faster.

Poster
TriAttention: Efficient Long Reasoning with Trigonometric KV Compression

Weian Mao, Xi Lin, Wei Huang, Yuxin Xie, Tianfu Fu, Bohan Zhuang, Song Han, Yukang Chen

展开摘要

Extended reasoning in large language models (LLMs) requires long and accurate decoding and creates severe KV cache memory bottlenecks. Leading KV cache compression methods estimate KV importance using attention scores from recent post-RoPE queries. However, queries rotate with position during RoPE, making representative queries very few, leading to poor top-key selection and unstable reasoning. To avoid this issue, we turn to the pre-RoPE space, where we observe that Q and K vectors are highly concentrated around fixed non-zero centers and remain stable across positions—*Q/K concentration*. We show that this concentration causes queries to preferentially attend to keys at specific distances (e.g., nearest keys), with the centers determining which distances are preferred via a trigonometric series. Based on this, we propose TriAttention to estimate key importance by leveraging these centers. Via the trigonometric series, we use the distance preference characterized by these centers to score keys according to their positions, and also leverage Q/K norms as an additional signal for importance estimation. On AIME25 with 32K-token generation, TriAttention matches Full Attention reasoning accuracy while achieving 2.5× higher throughput or 10.7× KV memory reduction, whereas leading baselines achieve only about half the accuracy at the same efficiency.

Poster
Language Bias in LVLMs: From In-Depth Analysis to Simple and Effective Mitigation

Yangneng Chen, Jing Li

展开摘要

Large Vision-Language Models (LVLMs) extend large language models with visual understanding, but remain vulnerable to hallucination, where outputs are fluent yet inconsistent with images. Recent studies link this issue to language bias—the tendency of LVLMs to over-rely on text while neglecting visual inputs. Yet most analyses remain empirical without uncovering its underlying cause. In this paper, we provide a systematic study of language bias and identify its root in modality misalignment during training. Our analysis shows that both Visual Instruction Tuning (VIT) and Direct Preference Optimization (DPO) often prioritize textual improvements, which may cause LVLMs to overly lean toward language modeling rather than balanced multimodal understanding. To address this, we propose two simple yet effective methods: Language Bias Regularization (LBR), which mitigates language bias through regularization during instruction tuning, and Language Bias Penalty (LBP), which penalizes language bias in the DPO training process. Extensive experiments across diverse models and benchmarks demonstrate the effectiveness of our approach. LBR consistently improves performance on over ten general benchmarks, while LBP significantly reduces hallucination and improves trustworthiness. Together, these methods not only mitigate language bias but also advance the overall alignment of LVLMs, all without introducing any additional data or auxiliary models. Our code is publicly available at [https://github.com/lab-klc/HAVAE](https://github.com/lab-klc/HAVAE).

Poster
HECTOR: Hybrid Editable Compositional Object References for Video Generation

Guofeng Zhang, Angtian Wang, Jacob Zhiyuan Fang, Liming Jiang, Haotian Yang, Alan Yuille, Chongyang Ma

展开摘要

Real-world videos naturally portray complex interactions among distinct physical objects, effectively forming dynamic compositions of visual elements. However, most current video generation models synthesize scenes holistically and therefore lack mechanisms for explicit compositional manipulation. To address this limitation, we propose HECTOR, a generative pipeline that enables fine-grained compositional control. In contrast to prior methods, HECTOR supports hybrid reference conditioning, allowing generation to be simultaneously guided by static images and/or dynamic videos. Moreover, users can explicitly specify the trajectory of each referenced element, precisely controlling its location, scale, and speed (see Figure1). This design allows the model to synthesize coherent videos that satisfy complex spatiotemporal constraints while preserving high-fidelity adherence to references. Extensive experiments demonstrate that HECTOR achieves superior visual quality, stronger reference preservation, and improved motion controllability compared with existing approaches.

Poster
You Can Learn Tokenization End-to-End with Reinforcement Learning

Sam Dauncey, Roger Wattenhofer

展开摘要

Tokenization is a hardcoded compression step which remains in the training pipeline of Large Language Models (LLMs), despite a general trend towards architectures becoming increasingly end-to-end. Prior work has shown promising results at scale in bringing this compression step inside the LLMs' architecture with heuristics to draw token boundaries, and also attempts to learn these token boundaries with straight-through estimates, which treat the problem of drawing discrete token boundaries as a continuous one. We show that these token boundaries can instead be learned using score function estimates, which have tighter theoretical guarantees due to directly optimizing the problem of drawing discrete token boundaries to minimize loss. We observe that techniques from reinforcement learning, such as time discounting, are necessary to reduce the variance of this score function sufficiently to make it practicable. We demonstrate that the resultant method outperforms prior proposed straight-through estimates, both qualitatively and quantitatively at the $100$ million parameter scale.

Poster
SWE-fficiency: Can Language Models Optimize Real-World Repositories on Real Workloads?

Jeffrey Jian Ma, Milad Hashemi, Amir Yazdanbakhsh, Kevin Swersky, Ofir Press, Enhui Li, Vijay Janapa Reddi, Parthasarathy Ranganathan

展开摘要

Optimizing the performance of large-scale software repositories demands expertise in code reasoning and software engineering (SWE) to reduce runtime while preserving program correctness. However, most benchmarks emphasize what to fix rather than how to fix code. We introduce SWE-fficiency, a benchmark for evaluating repository-level performance optimization on real workloads. Our suite contains 498 tasks across nine widely used data-science, machine-learning, and HPC repositories (e.g., numpy, pandas, scipy): given a complete codebase and a slow workload, an agent must investigate code semantics, localize bottlenecks and relevant tests, and produce a patch that matches or exceeds expert speedup while passing the same unit tests. To enable this how-to-fix evaluation, our automated pipeline scrapes GitHub pull requests for performance-improving edits, combining keyword filtering, static analysis, coverage tooling, and execution validation to both confirm expert speedup baselines and identify relevant repository unit tests. Empirical evaluation of state-of-the-art agents reveals significant underperformance. On average, top agents achieve less than 0.23x the expert speedup: agents struggle in localizing optimization opportunities, reasoning about execution across functions, and maintaining correctness in proposed edits. We release the benchmark and accompanying data pipeline to facilitate research on automated performance engineering and long-horizon software reasoning.

Poster
Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization

Mikhail Persiianov, Arip Asadulaev, Nikita Andreev, Nikita Starodubcev, Dmitry Baranchuk, Anastasis Kratsios, Evgeny Burnaev, Alexander Korotin

展开摘要

Learning conditional distributions $\pi^\star(\cdot|x)$ is a central problem in machine learning, which is typically approached via supervised methods with paired data $(x,y) \sim \pi^\star$. However, acquiring paired data samples is often challenging, especially in problems such as domain translation. This necessitates the development of *semi-supervised* models that utilize both limited paired data and additional unpaired i.i.d. samples $x \sim \pi^\star_x$ and $y \sim \pi^\star_y$ from the marginal distributions. The usage of such combined data is complex and often relies on heuristic approaches. To tackle this issue, we propose a new learning paradigm that integrates both paired and unpaired data seamlessly using data likelihood maximization techniques. We demonstrate that our approach also connects intriguingly with inverse entropic optimal transport (OT). This finding allows us to apply recent advances in computational OT to establish an *end-to-end* learning algorithm to get $\pi^\star(\cdot|x)$. In addition, we derive the universal approximation property, demonstrating that our approach can theoretically recover true conditional distributions with arbitrarily small error. Finally, we demonstrate through empirical tests that our method effectively learns conditional distributions using paired and unpaired data simultaneously.

Poster