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Theory · Domain Adaptation and Transfer Learning

Dexin Duan, Rui Xu, Peilin Liu, Fei Wen

Test-time adaptation (TTA) aims to adapt a source model to a target domain using only test data. Existing methods predominantly rely on unsupervised entropy minimization or its variants, which suffer from degeneration, leading to trivial solutions with low-entropy but inaccurate predictions. In this work, we identify *entropy-deceptive* (ED) samples, instances where the model makes highly confident yet incorrect predictions, as the underlying cause of degeneration. Further, we reveal that the gradients of entropy minimization in TTA have an intrinsic low-dimensional structure, driven primarily by *entropy-truthful* (ET) samples whose gradients are highly correlated. In contrast, ED samples have scattered, less correlated gradients. Leveraging this observation, we show that the detrimental impact of ED samples can be suppressed by constraining model updates within the principal subspace of backward gradients. Building on this insight, we propose LCoTTA, a lifelong continual TTA method that tracks the principal subspace of gradients online and utilizes their projections onto this subspace for adaptation. Further, we provide theoretical analysis to show that the proposed subspace-based method can enhance the robustness against detrimental ED samples. Extensive experiments demonstrate that LCoTTA effectively overcomes degeneration and significantly outperforms existing methods in long-term continual adaptation scenarios. Code is available online.

Theory · Domain Adaptation and Transfer Learning

Christoph Dann, Yishay Mansour, Teodor Vanislavov Marinov, Mehryar Mohri

The rapid proliferation of domain-specialized machine learning models presents a challenge: while individual models excel in specific domains, their performance varies significantly across diverse applications. This makes selecting the optimal model when faced with an unknown mixture of tasks, especially with limited or no data to estimate the mixture, a difficult problem. We address this challenge by formulating it as a multiple-source domain adaptation (MSA) problem. We introduce a novel, scalable algorithm that effectively routes each input to the best-suited model from a pool of available models. Our approach provides a strong performance guarantee: remarkably, for any mixture domain, the accuracy achieved by the best source model is maintained. This guarantee is established through a theoretical bound on the regret for new domains, expressed as a convex combination of the best regrets in the source domains, plus a concentration term that diminishes as the amount of source data increases. While our primary contributions are theoretical and algorithmic, we also present empirical results demonstrating the effectiveness of our approach.

Theory · Domain Adaptation and Transfer Learning

Yuwu Lu, Chunzhi Liu

Domain Adaptation of Black-box Predictors (DABP) transfers knowledge from a labeled source domain to an unlabeled target domain, without requiring access to either source data or source model. Common practices of DABP leverage reliable samples to suppress negative information about unreliable samples. However, there are still some problems: i) Excessive attention to reliable sample aggregation leads to premature overfitting; ii) Valuable information in unreliable samples is often overlooked. To address them, we propose a novel spatial learning approach, called Controlled Visual Hallucination via Thalamus-driven Decoupling Network (CVH-TDN). Specifically, CVH-TDN is the first work that introduces the thalamus-driven decoupling network in the visual task, relying on its connection with hallucination to control the direction of sample generation in feature space. CVH-TDN is composed of Hallucination Generation (HG), Hallucination Alignment (HA), and Hallucination Calibration (HC), aiming to explore the spatial relationship information between samples and hallucinations. Extensive experiments confirm that CVH-TDN achieves SOTA performance on four standard benchmarks.

Theory · Domain Adaptation and Transfer Learning

Boyang Peng, Sanqing Qu, Tianpei Zou, Fan Lu, Ya Wu, Kai Chen, Siheng Chen, Yong Wu, Guang Chen

In real-world environments, a well-designed model must be capable of handling dynamically evolving distributions, where both in-distribution (ID) and out-of-distribution (OOD) samples appear unpredictably and individually, making real-time adaptation particularly challenging. While open-set test-time adaptation has demonstrated effectiveness in adjusting to distribution shifts, existing methods often rely on batch processing and struggle to manage single-sample data stream in open-set environments. To address this limitation, we propose Open-IRT, a novel open-set Intermediate-Representation-based Test-time adaptation framework tailored for single-image test-time adaptation with vision-language models. Open-IRT comprises two key modules designed for dynamic, single-sample adaptation in open-set scenarios. The first is Polarity-aware Prompt-based OOD Filter module, which fully constructs the ID-OOD distribution, considering both the absolute semantic alignment and relative semantic polarity. The second module, Intermediate Domain-based Test-time Adaptation module, constructs an intermediate domain and indirectly decomposes the ID-OOD distributional discrepancy to refine the separation boundary during the test-time. Extensive experiments on a range of domain adaptation benchmarks demonstrate the superiority of Open-IRT. Compared to previous state-of-the-art methods, it achieves significant improvements on representative benchmarks, such as CIFAR-100C and SVHN — with gains of +8.45\% in accuracy, -10.80\% in FPR95, and +11.04\% in AUROC.

Theory · Domain Adaptation and Transfer Learning

Kecheng Chen, Pingping Zhang, Hui Liu, Jie Liu, Yibing Liu, Jiaxin Huang, Shiqi Wang, Hong Yan, Haoliang Li

We have recently witnessed that ''Intelligence" and `''Compression" are the two sides of the same coin, where the language large model (LLM) with unprecedented intelligence is a general-purpose lossless compressor for various data modalities. This attribute is particularly appealing to the lossless image compression community, given the increasing need to compress high-resolution images in the current streaming media era. Consequently, a spontaneous envision emerges: Can the compression performance of the LLM elevate lossless image compression to new heights? However, our findings indicate that the naive application of LLM-based lossless image compressors suffers from a considerable performance gap compared with existing state-of-the-art (SOTA) codecs on common benchmark datasets. In light of this, we are dedicated to fulfilling the unprecedented intelligence (compression) capacity of the LLM for lossless image compression tasks, thereby bridging the gap between theoretical and practical compression performance. Specifically, we propose P -LLM, a next-pixel prediction-based LLM, which integrates various elaborated insights and methodologies, \textit{e.g.,} pixel-level priors, the in-context ability of LLM, and a pixel-level semantic preservation strategy, to enhance the understanding capacity of pixel sequences for better next-pixel predictions. Extensive experiments on benchmark datasets demonstrate that P-LLM can beat SOTA classical and learned codecs.

Computer Vision · Image and Video Generation

Chenhui Zhu, Yilu Wu, Shuai Wang, Gangshan Wu, Limin Wang

Image-to-video generation has made remarkable progress with the advancements in diffusion models, yet generating videos with realistic motion remains highly challenging. This difficulty arises from the complexity of accurately modeling motion, which involves capturing physical constraints, object interactions, and domain-specific dynamics that are not easily generalized across diverse scenarios. To address this, we propose MotionRAG, a retrieval-augmented framework that enhances motion realism by adapting motion priors from relevant reference videos through Context-Aware Motion Adaptation (CAMA). The key technical innovations include: (i) a retrieval-based pipeline extracting high-level motion features using video encoder and specialized resamplers to distill semantic motion representations; (ii) an in-context learning approach for motion adaptation implemented through a causal transformer architecture; (iii) an attention-based motion injection adapter that seamlessly integrates transferred motion features into pretrained video diffusion models. Extensive experiments demonstrate that our method achieves significant improvements across multiple domains and various base models, all with negligible computational overhead during inference. Furthermore, our modular design enables zero-shot generalization to new domains by simply updating the retrieval database without retraining any components. This research enhances the core capability of video generation systems by enabling the effective retrieval and transfer of motion priors, facilitating the synthesis of realistic motion dynamics.

General Machine Learning · Representation Learning

Evangelos Dorovatas, Georgios Paraskevopoulos, Alexandros Potamianos

Deep neural networks with short residual connections have demonstrated remarkable success across domains, but increasing depth often introduces computational redundancy without corresponding improvements in representation quality. We introduce Auto-Compressing Networks (ACNs), an architectural variant where additive long feedforward connections from each layer to the output replace traditional short residual connections. By analyzing the distinct dynamics induced by this modification, we reveal a unique property we coin as *auto-compression*—the ability of a network to organically compress information during training with gradient descent, through architectural design alone. Through auto-compression, information is dynamically "pushed" into early layers during training, enhancing their representational quality and revealing potential redundancy in deeper ones. We theoretically show that this property emerges from layer-wise training patterns found only in ACNs, where layers are dynamically utilized during training based on task requirements. We also find that ACNs exhibit enhanced noise robustness compared to residual networks, superior performance in low-data settings, improved transfer learning capabilities, and mitigate catastrophic forgetting suggesting that they learn representations that generalize better despite using fewer parameters. Our results demonstrate up to 18\% reduction in catastrophic forgetting and 30-80\% architectural compression while maintaining accuracy across vision transformers, MLP-mixers, and BERT architectures. These findings establish ACNs as a practical approach to developing efficient neural architectures that automatically adapt their computational footprint to task complexity, while learning robust representations suitable for noisy real-world tasks and continual learning scenarios.

Theory · Domain Adaptation and Transfer Learning

Jing Wang, Wonho Bae, Jiahong Chen, Wenxu Wang, Junhyug Noh

Recent work on latent diffusion models (LDMs) has focused almost exclusively on generative tasks, leaving their potential for discriminative transfer largely unexplored. We introduce Discriminative Vicinity Diffusion (DVD), a novel LDM-based framework for a more practical variant of source-free domain adaptation (SFDA): the source provider may share not only a pre-trained classifier but also an auxiliary latent diffusion module, trained once on the source data and never exposing raw source samples. DVD encodes each source feature’s label information into its latent vicinity by fitting a Gaussian prior over its k-nearest neighbors and training the diffusion network to drift noisy samples back to label-consistent representations. During adaptation, we sample from each target feature’s latent vicinity, apply the frozen diffusion module to generate source-like cues, and use a simple InfoNCE loss to align the target encoder to these cues, explicitly transferring decision boundaries without source access. Across standard SFDA benchmarks, DVD outperforms state-of-the-art methods. We further show that the same latent diffusion module enhances the source classifier’s accuracy on in-domain data and boosts performance in supervised classification and domain generalization experiments. DVD thus reinterprets LDMs as practical, privacy-preserving bridges for explicit knowledge transfer, addressing a core challenge in source-free domain adaptation that prior methods have yet to solve. Code is available on our Github: https://github.com/JingWang18/DVD-SFDA.

General Machine Learning · Transfer, Multitask and Meta-learning

Hsi-Ling Chen, Chun-Shien Lu, Pau-Choo Chung

The effectiveness of domain translation in addressing image-based problems of Unsupervised Domain Adaptation (UDA) depends on the quality of the translated images and the preservation of crucial discriminative features. However, achieving high-quality and stable translations typically requires paired data, which poses a challenge in scenarios with limited annotations in the target domain. To address this issue, this paper proposes a novel method termed Stain-Guided Cycle Diffusion (SGCD), employing a dual diffusion model with bidirectional generative constraints to synthesize highly realistic data for downstream task fine-tuning. The bidirectional generative constraints ensure that the translated images retain the features critical to the downstream model in properly controlling the generation process. Additionally, a stain-guided consistency loss is introduced to enhance the denoising capability of the dual diffusion model, thereby improving the quality of images translated between different domains using latents from one domain and a diffusion model trained on another. Experiments conducted on four public datasets demonstrate that SGCD can effectively enhance the performance of downstream task models on the target domain.

Applications · Robotics

Shuo Cheng, Liqian Ma, Zhenyang Chen, Ajay Mandlekar, Caelan Garrett, Danfei Xu

Behavior cloning has shown promise for robot manipulation, but real-world demonstrations are costly to acquire at scale. While simulated data offers a scalable alternative, particularly with advances in automated demonstration generation, transferring policies to the real world is hampered by various simulation and real domain gaps. In this work, we propose a unified sim-and-real co-training framework for learning generalizable manipulation policies that primarily leverages simulation and only requires a few real-world demonstrations. Central to our approach is learning a domain-invariant, task-relevant feature space. Our key insight is that aligning the joint distributions of observations and their corresponding actions across domains provides a richer signal than aligning observations (marginals) alone. We achieve this by embedding an Optimal Transport (OT)-inspired loss within the co-training framework, and extend this to an Unbalanced OT framework to handle the imbalance between abundant simulation data and limited real-world examples. We validate our method on challenging manipulation tasks, showing it can leverage abundant simulation data to achieve up to a 30\% improvement in the real-world success rate and even generalize to scenarios seen only in simulation.

General Machine Learning · Transfer, Multitask and Meta-learning

Zixi Wang, Yushe Cao, Yubo Huang, Jinzhu Wei, Jingzehua Xu, Shuai Zhang, Xin Lai

In this paper, we propose a new method called \textit{Self-Training with Dynamic Weighting} (STDW), which aims to enhance robustness in Gradual Domain Adaptation (GDA) by addressing the challenge of smooth knowledge migration from the source to the target domain. Traditional GDA methods mitigate domain shift through intermediate domains and self-training but often suffer from inefficient knowledge migration or incomplete intermediate data. Our approach introduces a dynamic weighting mechanism that adaptively balances the loss contributions of the source and target domains during training. Specifically, we design an optimization framework governed by a time-varying hyperparameter $\varrho$ (progressing from 0 to 1), which controls the strength of domain-specific learning and ensures stable adaptation. The method leverages self-training to generate pseudo-labels and optimizes a weighted objective function for iterative model updates, maintaining robustness across intermediate domains. Experiments on rotated MNIST, color-shifted MNIST, portrait datasets, and the Cover Type dataset demonstrate that STDW outperforms existing baselines. Ablation studies further validate the critical role of $\varrho$'s dynamic scheduling in achieving progressive adaptation, confirming its effectiveness in reducing domain bias and improving generalization. This work provides both theoretical insights and a practical framework for robust gradual domain adaptation, with potential applications in dynamic real-world scenarios.

General Machine Learning · Transfer, Multitask and Meta-learning

Ruilong Yu, Mingyan Liu, Fei Ye, Adrian G. Bors, Rongyao Hu, Jingling sun, shijie zhou

Extant studies predominantly address catastrophic forgetting within a simplified continual learning paradigm, typically confined to a singular data domain. Conversely, real-world applications frequently encompass multiple, evolving data domains, wherein models often struggle to retain many critical past information, thereby leading to performance degradation. This paper addresses this complex scenario by introducing a novel dynamic expansion approach called Learning Expandable and Adaptable Representations (LEAR). This framework orchestrates a collaborative backbone structure, comprising global and local backbones, designed to capture both general and task-specific representations. Leveraging this collaborative backbone, the proposed framework dynamically create a lightweight expert to delineate decision boundaries for each novel task, thereby facilitating the prediction process. To enhance new task learning, we introduce a novel Mutual Information-Based Prediction Alignment approach, which incrementally optimizes the global backbone via a mutual information metric, ensuring consistency in the prediction patterns of historical experts throughout the optimization phase. To mitigate network forgetting, we propose a Kullback–Leibler (KL) Divergence-Based Feature Alignment approach, which employs a probabilistic distance measure to prevent significant shifts in critical local representations. Furthermore, we introduce a novel Hilbert-Schmidt Independence Criterion (HSIC)-Based Collaborative Optimization approach, which encourages the local and global backbones to capture distinct semantic information in a collaborative manner, thereby mitigating information redundancy and enhancing model performance. Moreover, to accelerate new task learning, we propose a novel Expert Selection Mechanism that automatically identifies the most relevant expert based on data characteristics. This selected expert is then utilized to initialize a new expert, thereby fostering positive knowledge transfer. This approach also enables expert selection during the testing phase without requring any task information. Empirical results demonstrate that the proposed framework achieves state-of-the-art performance.

Deep Learning · Generative Models and Autoencoders

Guilin Li, Yun Zhang, Xiuyuan Chen, Chengqi Li, Bo Wang, Linghe Kong, Wenjia Wang, Weiran Huang, Matthias Tan

Large language models (LLMs) have shown that generative pretraining can distill vast world knowledge into compact token representations. While LLMs encapsulate extensive world knowledge, they remain limited in modeling the behavioral knowledge contained within user interaction histories. User behavior forms a distinct modality, where each action—defined by multi-dimensional attributes such as time, context, and transaction type—constitutes a behavioral token. Modeling these high-cardinality, sparse, and irregular sequences is challenging, and discriminative models often falter under limited supervision. To bridge this gap, we extend generative pretraining to user behavior, learning transferable representations from unlabeled behavioral data analogous to how LLMs learn from text. We present PANTHER, a hybrid generative–discriminative framework that unifies user behavior pretraining and downstream adaptation, enabling large-scale sequential user representation learning and real-time inference. PANTHER introduces: (1) Structured Tokenization to compress multi-dimensional transaction attributes into an interpretable vocabulary; (2) Sequence Pattern Recognition Module (SPRM) for modeling periodic transaction motifs; (3) a Unified User-Profile Embedding that fuses static demographics with dynamic transaction histories, enabling both personalized predictions and population-level knowledge transfer; and (4) Real-time scalability enabled by offline caching of pre-trained embeddings for millisecond-level inference.Fully deployed and operational online at WeChat Pay, PANTHER delivers a 25.6\% boost in next-transaction prediction HitRate@1 and a 38.6\% relative improvement in fraud detection recall over baselines. Cross-domain evaluations on public benchmarks (CCT, MBD, MovieLens-1M, Yelp) show strong generalization, achieving up to 21\% HitRate@1 gains over transformer baselines, establishing PANTHER as a scalable, high-performance framework for industrial user sequential behavior modeling.

Theory · Domain Adaptation and Transfer Learning

Wei Wang, Haifeng Xia, Chao Huang, Zhengming Ding, Cong Wang, Haojie Li, Xiaochun Cao

In domain adaption (DA), joint maximum mean discrepancy (JMMD), as a famous distribution-distance metric, aims to measure joint probability distribution difference between the source domain and target domain, while it is still not fully explored and especially hard to be applied into a subspace-learning framework as its empirical estimation involves a tensor-product operator whose partial derivative is difficult to obtain. To solve this issue, we deduce a concise JMMD based on the Representer theorem that avoids the tensor-product operator and obtains two essential findings. First, we reveal the uniformity of JMMD by proving that previous marginal, class conditional, and weighted class conditional probability distribution distances are three special cases of JMMD with different label reproducing kernels. Second, inspired by graph embedding, we observe that the similarity weights, which strengthen the intra-class compactness in the graph of Hilbert Schmidt independence criterion (HSIC), take opposite signs in the graph of JMMD, revealing why JMMD degrades the feature discrimination. This motivates us to propose a novel loss JMMD-HSIC by jointly considering JMMD and HSIC to promote discrimination of JMMD. Extensive experiments on several cross-domain datasets could demonstrate the validity of our revealed theoretical results and the effectiveness of our proposed JMMD-HSIC.

Theory · Domain Adaptation and Transfer Learning

Zhenyu Wang, Peter Bühlmann, Zijian Guo

Empirical risk minimization often performs poorly when the distribution of the target domain differs from those of the source domains. To address such potential distributional shifts, we develop an unsupervised domain adaptation approach that leverages labeled data from multiple source domains and unlabeled data from the target domain. We introduce a distributionally robust model that optimizes an adversarial reward based on explained variance across a class of target distributions, ensuring generalization to the target domain. We show that the proposed robust model is a weighted average of conditional outcome models from the source domains. This formulation allows us to compute the robust model through the aggregation of source models, which can be estimated using various machine learning algorithms of the user’s choice such as random forests, boosting, and neural networks. Additionally, we introduce a bias-correction step to obtain a more accurate aggregation weight, which is effective for various machine learning algorithms. Our framework can be interpreted as a distributionally robust federated learning approach that satisfies privacy constraints while providing insights into the importance of each source for prediction on the target domain. The performance of our method is evaluated on both simulated and real data.

Theory · Domain Adaptation and Transfer Learning

Jacob Block, Sundararajan Srinivasan, Liam Collins, Aryan Mokhtari, Sanjay Shakkottai

The power of foundation models (FMs) lies in their capacity to learn highly expressive representations that can be adapted to a broad spectrum of tasks. However, these pretrained models require additional training stages to become effective for downstream applications. In the multi-task setting, prior works have shown empirically that specific meta-learning approaches for preparing a model for future adaptation through parameter-efficient fine-tuning (PEFT) can outperform standard retraining methods, but the mechanism of the benefits of meta-learning has been largely unexplored. We introduce a framework for generic PEFT-based meta-learning to learn a model that can easily adapt to unseen tasks. For linear models using LoRA, we show that standard retraining is provably suboptimal for finding an adaptable set of parameters and provide strict performance guarantees for our proposed method. We verify these theoretical insights through experiments on synthetic data as well as real-data vision and language tasks. We observe significant performance benefits using a simple implementation of our proposed meta-learning scheme during retraining relative to the conventional approach.

Theory · Domain Adaptation and Transfer Learning

Siyu Chen, Ting Han, Chengzheng Fu, Changshe Zhang, Chaolei Wang, Jinhe Su, Guorong Cai, Meiliu Wu

Open-Vocabulary semantic segmentation (OVSS) and domain generalization in semantic segmentation (DGSS) highlight a subtle complementarity that motivates Open-Vocabulary Domain-Generalized Semantic Segmentation (OV-DGSS). OV-DGSS aims to generate pixel-level masks for unseen categories while maintaining robustness across unseen domains, a critical capability for real-world scenarios such as autonomous driving in adverse conditions. We introduce Vireo, a novel single-stage framework for OV-DGSS that unifies the strengths of OVSS and DGSS for the first time. Vireo builds upon the frozen Visual Foundation Models (VFMs) and incorporates scene geometry via Depth VFMs to extract domain-invariant structural features. To bridge the gap between visual and textual modalities under domain shift, we propose three key components: (1) GeoText Query, which align geometric features with language cues and progressively refine VFM encoder representations; (2) Coarse Mask Prior Embedding (CMPE) for enhancing gradient flow for faster convergence and stronger textual influence; and (3) the Domain-Open-Vocabulary Vector Embedding Head (DOV-VEH), which fuses refined structural and semantic features for robust prediction. Comprehensive evaluation on these components demonstrates the effectiveness of our designs. Our proposed Vireo achieves the state-of-the-art performance and surpasses existing methods by a large margin in both domain generalization and open-vocabulary recognition, offering a unified and scalable solution for robust visual understanding in diverse and dynamic environments. Code is available at https://github.com/SY-Ch/Vireo.

Theory · Domain Adaptation and Transfer Learning

Liviu Aolaritei, Julie Zhu, Oliver Wang, Michael Jordan, Youssef Marzouk

Conformal prediction provides a powerful framework for constructing prediction intervals with finite-sample guarantees, yet its robustness under distribution shifts remains a significant challenge. This paper addresses this limitation by modeling distribution shifts using Lévy-Prokhorov (LP) ambiguity sets, which capture both local and global perturbations. We provide a self-contained overview of LP ambiguity sets and their connections to popular metrics such as Wasserstein and Total Variation. We show that the link between conformal prediction and LP ambiguity sets is a natural one: by propagating the LP ambiguity set through the scoring function, we reduce complex high-dimensional distribution shifts to manageable one-dimensional distribution shifts, enabling exact quantification of worst-case quantiles and coverage. Building on this analysis, we construct robust conformal prediction intervals that remain valid under distribution shifts, explicitly linking LP parameters to interval width and confidence levels. Experimental results on real-world datasets demonstrate the effectiveness of the proposed approach.

Theory · Domain Adaptation and Transfer Learning

JaeYun Lee, Jae Hyeon Park, Gyoomin Lee, Bogyeong Kim, Min Hee Cha, Hyeok Nam, Joo Jeon, Hyunse Lee, Sung In Cho

Source-free domain adaptation (SFDA) aims to adapt a pre-trained source model to an unlabeled target domain without requiring labeled source data. In a self supervised setting, relying on pseudo labels on target domain samples facilitates the domain adaptation performance providing strong supervision. However, a critical problem of this approach is the inherent instability of the pre-trained source model in the target domain, leading to unreliable pseudo labels for the target domain data. To tackle this, we propose a novel Dual-perspective pseudo labeling strategy that jointly leverages a task-specific perspective and a domain-invariant perspective, assigning pseudo labels only to target samples on which the target model’s predictions and CLIP’s predictions agree. To further enhance representation learning without introducing noisy supervision, we apply consistency training to uncertain samples. Additionally, we introduce a Tsallis mutual information(TMI)-based vision optimization strategy guided by an Uncertainty-based adaptation index (UAI), which dynamically modulates entropy sensitivity based on the model’s adaptation uncertainty. The UAI-based training paradigm enables stable and adaptive domain alignment by effectively balancing exploration and exploitation processes during the optimization process. Our proposed method achieves state-of-the-art performance on domain adaptation benchmark datasets, improving adaptation accuracy by 1.6% on Office-Home, 1.4% on VisDA-C, and 2.9% on DomainNet-126, demonstrating its effectiveness in SFDA. The code is publicly available at https://github.com/l3umblee/duet-sfda.

Theory · Domain Adaptation and Transfer Learning

Masanari Kimura

Label shift adaptation aims to recover target class priors when the labelled source distribution $P$ and the unlabelled target distribution $Q$ share $P(X \mid Y) = Q(X \mid Y)$ but $P(Y) \neq Q(Y)$. Classical black‑box shift estimators invert an empirical confusion matrix of a frozen classifier, producing a brittle point estimate that ignores sampling noise and similarity among classes. We present Graph‑Smoothed Bayesian BBSE (GS‑B$^3$SE), a fully probabilistic alternative that places Laplacian–Gaussian priors on both target log‑priors and confusion‑matrix columns, tying them together on a label‑similarity graph. The resulting posterior is tractable with HMC or a fast block Newton–CG scheme. We prove identifiability, $N^{-1/2}$ contraction, variance bounds that shrink with the graph’s algebraic connectivity, and robustness to Laplacian misspecification. We also reinterpret GS‑B$^3$SE through information geometry, showing that it generalizes existing shift estimators.