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Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning

Wenjun Zhang, Liangxiao Jiang, Chaoqun Li

To reduce annotation costs, it is common in crowdsourcing to collect only a few noisy labels from different crowd workers for each instance. However, the limited noisy labels restrict the performance of label integration algorithms in inferring the unknown true label for the instance. Recent works have shown that leveraging neighbor instances can help alleviate this problem. Yet, these works all assume that each instance has the same neighborhood size, which defies common sense. To address this gap, we propose a novel label integration algorithm called K-free nearest neighbor (KFNN). In KFNN, the neighborhood size of each instance is automatically determined based on its attributes and noisy labels. Specifically, KFNN initially estimates a Mahalanobis distance distribution from the attribute space to model the relationship between each instance and all classes. This distance distribution is then utilized to enhance the multiple noisy label distribution of each instance. Subsequently, a Kalman filter is designed to mitigate the impact of noise incurred by neighbor instances. Finally, KFNN determines the optimal neighborhood size by the max-margin learning. Extensive experimental results demonstrate that KFNN significantly outperforms all the other state-of-the-art algorithms and exhibits greater robustness in various crowdsourcing scenarios.

Miscellaneous Aspects of Machine Learning · Kernel methods

Alexander Modell

In this paper, we derive *entrywise* error bounds for low-rank approximations of kernel matrices obtained using the truncated eigen-decomposition (or singular value decomposition). While this approximation is well-known to be optimal with respect to the spectral and Frobenius norm error, little is known about the statistical behaviour of individual entries. Our error bounds fill this gap. A key technical innovation is a delocalisation result for the eigenvectors of the kernel matrix corresponding to small eigenvalues, which takes inspiration from the field of Random Matrix Theory. Finally, we validate our theory with an empirical study of a collection of synthetic and real-world datasets.

Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning

Qian Shao, Jiangrui Kang, Qiyuan Chen, Zepeng Li, Hongxia Xu, Yiwen Cao, JIAJUAN LIANG, Jian Wu

Semi-Supervised Learning (SSL) has become a preferred paradigm in many deep learning tasks, which reduces the need for human labor. Previous studies primarily focus on effectively utilising the labelled and unlabeled data to improve performance. However, we observe that how to select samples for labelling also significantly impacts performance, particularly under extremely low-budget settings. The sample selection task in SSL has been under-explored for a long time. To fill in this gap, we propose a Representative and Diverse Sample Selection approach (RDSS). By adopting a modified Frank-Wolfe algorithm to minimise a novel criterion $\alpha$-Maximum Mean Discrepancy ($\alpha$-MMD), RDSS samples a representative and diverse subset for annotation from the unlabeled data. We demonstrate that minimizing $\alpha$-MMD enhances the generalization ability of low-budget learning. Experimental results show that RDSS consistently improves the performance of several popular SSL frameworks and outperforms the state-of-the-art sample selection approaches used in Active Learning (AL) and Semi-Supervised Active Learning (SSAL), even with constrained annotation budgets. Our code is available at [RDSS](https://github.com/YanhuiAILab/RDSS).

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Chen Huang, Skyler Seto, Samira Abnar, David Grangier, Navdeep Jaitly, Joshua Susskind

Large pretrained vision-language models like CLIP have shown promising generalization capability, but may struggle in specialized domains (e.g., satellite imagery) or fine-grained classification (e.g., car models) where the visual concepts are unseen or under-represented during pretraining. Prompt learning offers a parameter-efficient finetuning framework that can adapt CLIP to downstream tasks even when limited annotation data are available. In this paper, we improve prompt learning by distilling the textual knowledge from natural language prompts (either human- or LLM-generated) to provide rich priors for those under-represented concepts. We first obtain a prompt ``summary'' aligned to each input image via a learned prompt aggregator. Then we jointly train a prompt generator, optimized to produce a prompt embedding that stays close to the aggregated summary while minimizing task loss at the same time. We dub such prompt embedding as Aggregate-and-Adapted Prompt Embedding (AAPE). AAPE is shown to be able to generalize to different downstream data distributions and tasks, including vision-language understanding tasks (e.g., few-shot classification, VQA) and generation tasks (image captioning) where AAPE achieves competitive performance. We also show AAPE is particularly helpful to handle non-canonical and OOD examples. Furthermore, AAPE learning eliminates LLM-based inference cost as required by baselines, and scales better with data and LLM model size.

Miscellaneous Aspects of Machine Learning · Representation Learning

Subash Timilsina, Sagar Shrestha, Xiao Fu

A core task in multi-modal learning is to integrate information from multiple feature spaces (e.g., text and audio), offering modality-invariant essential representations of data. Recent research showed that, classical tools such as canonical correlation analysis (CCA) provably identify the shared components up to minor ambiguities, when samples in each modality are generated from a linear mixture of shared and private components. Such identifiability results were obtained under the condition that the cross-modality samples are aligned/paired according to their shared information. This work takes a step further, investigating shared component identifiability from multi-modal linear mixtures where cross-modality samples are unaligned. A distribution divergence minimization-based loss is proposed, under which a suite of sufficient conditions ensuring identifiability of the shared components are derived. Our conditions are based on cross-modality distribution discrepancy characterization and density-preserving transform removal, which are much milder than existing studies relying on independent component analysis. More relaxed conditions are also provided via adding reasonable structural constraints, motivated by available side information in various applications. The identifiability claims are thoroughly validated using synthetic and real-world data.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Sebastian Damrich, Philipp Berens, Dmitry Kobak

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much higher dimensionality. We show that in this case traditional persistent homology becomes very sensitive to noise and fails to detect the correct topology. The same holds true for existing refinements of persistent homology. As a remedy, we find that spectral distances on the k-nearest-neighbor graph of the data, such as diffusion distance and effective resistance, allow to detect the correct topology even in the presence of high-dimensional noise. Moreover, we derive a novel closed-form formula for effective resistance, and describe its relation to diffusion distances. Finally, we apply these methods to high-dimensional single-cell RNA-sequencing data and show that spectral distances allow robust detection of cell cycle loops.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Hui Chen, Yanbin Liu, Yongqiang Ma, Nanning Zheng, Xin Yu

Pre-trained vision-language models (VLMs) such as CLIP have shown excellent performance for zero-shot classification. Based on CLIP, recent methods design various learnable prompts to evaluate the zero-shot generalization capability on a base-to-novel setting. This setting assumes test samples are already divided into either base or novel classes, limiting its application to realistic scenarios. In this paper, we focus on a more challenging and practical setting: generalized zero-shot learning (GZSL), i.e., testing with no information about the base/novel division. To address this challenging zero-shot problem, we introduce two unique designs that enable us to classify an image without the need of knowing whether it comes from seen or unseen classes. Firstly, most existing methods only adopt a single latent space to align visual and linguistic features, which has a limited ability to represent complex visual-linguistic patterns, especially for fine-grained tasks. Instead, we propose a dual-space feature alignment module that effectively augments the latent space with a novel attribute space induced by a well-devised attribute reservoir. In particular, the attribute reservoir consists of a static vocabulary and learnable tokens complementing each other for flexible control over feature granularity. Secondly, finetuning CLIP models (e.g., prompt learning) on seen base classes usually sacrifices the model's original generalization capability on unseen novel classes. To mitigate this issue, we present a new topology-preserving objective that can enforce feature topology structures of the combined base and novel classes to resemble the topology of CLIP. In this manner, our model will inherit the generalization ability of CLIP through maintaining the pairwise class angles in the attribute space. Extensive experiments on twelve object recognition datasets demonstrate that our model, termed Topology-Preserving Reservoir (TPR), outperforms strong baselines including both prompt learning and conventional generative-based zero-shot methods.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Lixu Wang, Xinyu Du, Qi Zhu

Cross-domain retrieval (CDR) is finding increasingly broad applications across various domains. However, existing efforts have several major limitations, with the most critical being their reliance on accurate supervision. Recent studies thus focus on achieving unsupervised CDR, but they typically assume that the category spaces across domains are identical, an assumption that is often unrealistic in real-world scenarios. This is because only through dedicated and comprehensive analysis can the category composition of a data domain be obtained, which contradicts the premise of unsupervised scenarios. Therefore, in this work, we introduce the problem of **U**niversal **U**nsupervised **C**ross-**D**omain **R**etrieval (U^2CDR) for the first time and design a two-stage semantic feature learning framework to address it. In the first stage, a cross-domain unified prototypical structure is established under the guidance of an instance-prototype-mixed contrastive loss and a semantic-enhanced loss, to counteract category space differences. In the second stage, through a modified adversarial training mechanism, we ensure minimal changes for the established prototypical structure during domain alignment, enabling more accurate nearest-neighbor searching. Extensive experiments across multiple datasets and scenarios, including close-set, partial, and open-set CDR, demonstrate that our approach significantly outperforms existing state-of-the-art CDR methods and other related methods in solving U^2CDR challenges.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Atsutoshi Kumagai, Tomoharu Iwata, Hiroshi Takahashi, Taishi Nishiyama, Yasuhiro Fujiwara

Maximizing the area under the receiver operating characteristic curve (AUC) is a popular approach to imbalanced binary classification problems. Existing AUC maximization methods usually assume that training and test distributions are identical. However, this assumption is often violated in practice due to {\it a positive distribution shift}, where the negative-conditional density does not change but the positive-conditional density can vary. This shift often occurs in imbalanced classification since positive data are often more diverse and time-varying than negative data. To deal with this shift, we theoretically show that the AUC on the test distribution can be expressed by using the positive and marginal training densities and the marginal test density. Based on this result, we can maximize the AUC on the test distribution by using positive and unlabeled data in the training distribution and unlabeled data in the test distribution. The proposed method requires only positive labels in the training distribution as supervision. Moreover, the derived AUC has a simple form and thus is easy to implement. The effectiveness of the proposed method is shown with four real-world datasets.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Yuyang Huo, Lin Lu, Haojie Ren, Changliang Zou

Real-time decision-making gets more attention in the big data era. Here, we consider the problem of sample selection in the online setting, where one encounters a possibly infinite sequence of individuals collected over time with covariate information available. The goal is to select samples of interest that are characterized by their unobserved responses until the user-specified stopping time. We derive a new decision rule that enables us to find more preferable samples that meet practical requirements by simultaneously controlling two types of general constraints: individual and interactive constraints, which include the widely utilized False Selection Rate (FSR), cost limitations, and diversity of selected samples. The key elements of our approach involve quantifying the uncertainty of response predictions via predictive inference and addressing individual and interactive constraints in a sequential manner. Theoretical and numerical results demonstrate the effectiveness of the proposed method in controlling both individual and interactive constraints.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Wangbo Zhao, Jiasheng Tang, Yizeng Han, Yibing Song, Kai Wang, Gao Huang, Fan Wang, Yang You

Existing parameter-efficient fine-tuning (PEFT) methods have achieved significant success on vision transformers (ViTs) adaptation by improving parameter efficiency. However, the exploration of enhancing inference efficiency during adaptation remains underexplored. This limits the broader application of pre-trained ViT models, especially when the model is computationally extensive. In this paper, we propose Dynamic Tuning (DyT), a novel approach to improve both parameter and inference efficiency for ViT adaptation. Specifically, besides using the lightweight adapter modules, we propose a token dispatcher to distinguish informative tokens from less important ones, allowing the latter to dynamically skip the original block, thereby reducing the redundant computation during inference. Additionally, we explore multiple design variants to find the best practice of DyT. Finally, inspired by the mixture-of-experts (MoE) mechanism, we introduce an enhanced adapter to further boost the adaptation performance. We validate DyT across various tasks, including image/video recognition and semantic segmentation. For instance, DyT achieves superior performance compared to existing PEFT methods while evoking only 71% of their FLOPs on the VTAB-1K benchmark.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Felix Dangel

Despite their simple intuition, convolutions are more tedious to analyze than dense layers, which complicates the transfer of theoretical and algorithmic ideas to convolutions. We simplify convolutions by viewing them as tensor networks (TNs) that allow reasoning about the underlying tensor multiplications by drawing diagrams, manipulating them to perform function transformations like differentiation, and efficiently evaluating them with `einsum`. To demonstrate their simplicity and expressiveness, we derive diagrams of various autodiff operations and popular curvature approximations with full hyper-parameter support, batching, channel groups, and generalization to any convolution dimension. Further, we provide convolution-specific transformations based on the connectivity pattern which allow to simplify diagrams before evaluation. Finally, we probe performance. Our TN implementation accelerates a recently-proposed KFAC variant up to 4.5 x while removing the standard implementation's memory overhead, and enables new hardware-efficient tensor dropout for approximate backpropagation.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Mingjia Li, Shuang Li, Tongrui Su, Longhui Yuan, Jian Liang, Wei Li

Capitalizing on the complementary advantages of generative and discriminative models has always been a compelling vision in machine learning, backed by a growing body of research. This work discloses the hidden semantic structure within score-based generative models, unveiling their potential as effective discriminative priors. Inspired by our theoretical findings, we propose DUSA to exploit the structured semantic priors underlying diffusion score to facilitate the test-time adaptation of image classifiers or dense predictors. Notably, DUSA extracts knowledge from a single timestep of denoising diffusion, lifting the curse of Monte Carlo-based likelihood estimation over timesteps. We demonstrate the efficacy of our DUSA in adapting a wide variety of competitive pre-trained discriminative models on diverse test-time scenarios. Additionally, a thorough ablation study is conducted to dissect the pivotal elements in DUSA. Code is publicly available at https://github.com/BIT-DA/DUSA.

Miscellaneous Aspects of Machine Learning · Representation Learning

Baao Xie, Qiuyu Chen, Yunnan Wang, Zequn Zhang, Xin Jin, Wenjun Zeng

Disentangled representation learning (DRL) aims to identify and decompose underlying factors behind observations, thus facilitating data perception and generation. However, current DRL approaches often rely on the unrealistic assumption that semantic factors are statistically independent. In reality, these factors may exhibit correlations, which off-the-shelf solutions have yet to properly address. To tackle this challenge, we introduce a bidirectional weighted graph-based framework, to learn factorized attributes and their interrelations within complex data. Specifically, we propose a $\beta$-VAE based module to extract factors as the initial nodes of the graph, and leverage the multimodal large language model (MLLM) to discover and rank latent correlations, thereby updating the weighted edges. By integrating these complementary modules, our model successfully achieves fine-grained, practical and unsupervised disentanglement. Experiments demonstrate our method's superior performance in disentanglement and reconstruction. Furthermore, the model inherits enhanced interpretability and generalizability from MLLMs.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Jiangyuan Li, Jiayi Wang, Raymond K. W. Wong, Kwun Chuen Gary Chan

While several recent matrix completion methods are developed to deal with non-uniform observation probabilities across matrix entries, very few allow the missingness to depend on the mostly unobserved matrix measurements, which is generally ill-posed. We aim to tackle a subclass of these ill-posed settings, characterized by a flexible separable observation probability assumption that can depend on the matrix measurements. We propose a regularized pairwise pseudo-likelihood approach for matrix completion and prove that the proposed estimator can asymptotically recover the low-rank parameter matrix up to an identifiable equivalence class of a constant shift and scaling, at a near-optimal asymptotic convergence rate of the standard well-posed (non-informative missing) setting, while effectively mitigating the impact of informative missingness. The efficacy of our method is validated via numerical experiments, positioning it as a robust tool for matrix completion to mitigate data bias.

Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning

Miguel A. Carreira-Perpinan, Kuat Gazizov

We propose a new model for dimensionality reduction, the PCA tree, which works like a regular autoencoder, having explicit projection and reconstruction mappings. The projection is effected by a sparse oblique tree, having hard, hyperplane splits using few features and linear leaves. The reconstruction mapping is a set of local linear mappings. Thus, rather than producing a global map as in t-SNE and other methods, which often leads to distortions, it produces a hierarchical set of local PCAs. The use of a sparse oblique tree and PCA makes the overall model interpretable and very fast to project or reconstruct new points. Joint optimization of all the parameters in the tree is a nonconvex nondifferentiable problem. We propose an algorithm that is guaranteed to decrease the error monotonically and which scales to large datasets without any approximation. In experiments, we show PCA trees are able to identify a wealth of low-dimensional and cluster structure in image and document datasets.

Miscellaneous Aspects of Machine Learning · Representation Learning

Connor Mclaughlin, Lili Su

Federated learning (FL) is a distributed learning framework that leverages commonalities between distributed client datasets to train a global model. Under heterogeneous clients, however, FL can fail to produce stable training results. Personalized federated learning (PFL) seeks to address this by learning individual models tailored to each client. One approach is to decompose model training into shared representation learning and personalized classifier training. Nonetheless, previous works struggle to navigate the bias-variance trade-off in classifier learning, relying solely on limited local datasets or introducing costly techniques to improve generalization.In this work, we frame representation learning as a generative modeling task, where representations are trained with a classifier based on the global feature distribution. We then propose an algorithm, pFedFDA, that efficiently generates personalized models by adapting global generative classifiers to their local feature distributions. Through extensive computer vision benchmarks, we demonstrate that our method can adjust to complex distribution shifts with significant improvements over current state-of-the-art in data-scarce settings.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Hanwen Zhong, Jiaxin Chen, Yutong Zhang, Di Huang, Yunhong Wang

Multi-Task Learning (MTL) for Vision Transformer aims at enhancing the model capability by tackling multiple tasks simultaneously. Most recent works have predominantly focused on designing Mixture-of-Experts (MoE) structures and integrating Low-Rank Adaptation (LoRA) to efficiently perform multi-task learning. However, their rigid combination hampers both the optimization of MoE and the effectiveness of reparameterization of LoRA, leading to sub-optimal performance and low inference speed. In this work, we propose a novel approach dubbed Efficient Multi-Task Learning (EMTAL) by transforming a pre-trained Vision Transformer into an efficient multi-task learner during training, and reparameterizing the learned structure for efficient inference. Specifically, we firstly develop the MoEfied LoRA structure, which decomposes the pre-trained Transformer into a low-rank MoE structure and employ LoRA to fine-tune the parameters. Subsequently, we take into account the intrinsic asynchronous nature of multi-task learning and devise a learning Quality Retaining (QR) optimization mechanism, by leveraging the historical high-quality class logits to prevent a well-trained task from performance degradation. Finally, we design a router fading strategy to integrate the learned parameters into the original Transformer, archiving efficient inference. Extensive experiments on public benchmarks demonstrate the superiority of our method, compared to the state-of-the-art multi-task learning approaches.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Yunqiao Yang, Long-Kai Huang, Shengzhuang Chen, Kede Ma, Ying Wei

Model editing aims to data-efficiently correct predictive errors of large pre-trained models while ensuring generalization to neighboring failures and locality to minimize unintended effects on unrelated examples. While significant progress has been made in editing Transformer-based large language models, effective strategies for editing vision Transformers (ViTs) in computer vision remain largely untapped. In this paper, we take initial steps towards correcting predictive errors of ViTs, particularly those arising from subpopulation shifts. Taking a locate-then-edit approach, we first address the ``where-to-edit`` challenge by meta-learning a hypernetwork on CutMix-augmented data generated for editing reliability. This trained hypernetwork produces generalizable binary masks that identify a sparse subset of structured model parameters, responsive to real-world failure samples. Afterward, we solve the ``how-to-edit`` problem by simply fine-tuning the identified parameters using a variant of gradient descent to achieve successful edits. To validate our method, we construct an editing benchmark that introduces subpopulation shifts towards natural underrepresented images and AI-generated images, thereby revealing the limitations of pre-trained ViTs for object recognition. Our approach not only achieves superior performance on the proposed benchmark but also allows for adjustable trade-offs between generalization and locality. Our code is available at https://github.com/hustyyq/Where-to-Edit.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Samuel Lippl, Jack Lindsey

Neural networks are often trained on multiple tasks, either simultaneously (multi-task learning, MTL) or sequentially (pretraining and subsequent finetuning, PT+FT). In particular, it is common practice to pretrain neural networks on a large auxiliary task before finetuning on a downstream task with fewer samples. Despite the prevalence of this approach, the inductive biases that arise from learning multiple tasks are poorly characterized. In this work, we address this gap. We describe novel implicit regularization penalties associated with MTL and PT+FT in diagonal linear networks and single-hidden-layer ReLU networks. These penalties indicate that MTL and PT+FT induce the network to reuse features in different ways. 1) Both MTL and PT+FT exhibit biases towards feature reuse between tasks, and towards sparsity in the set of learned features. We show a "conservation law" that implies a direct tradeoff between these two biases. 2) PT+FT exhibits a novel "nested feature selection" regime, not described by either the "lazy" or "rich" regimes identified in prior work, which biases it to *rely on a sparse subset* of the features learned during pretraining. This regime is much narrower for MTL. 3) PT+FT (but not MTL) in ReLU networks benefits from features that are correlated between the auxiliary and main task. We confirm these findings empirically with teacher-student models, and introduce a technique -- weight rescaling following pretraining -- that can elicit the nested feature selection regime. Finally, we validate our theory in deep neural networks trained on image classification. We find that weight rescaling improves performance when it causes models to display signatures of nested feature selection. Our results suggest that nested feature selection may be an important inductive bias for finetuning neural networks.