Vasilii Feofanov

Ambroise Odonnat, Vasilii Feofanov, Ievgen Redko

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax prediction probabilities are often used as a confidence measure, although they are known to be overconfident, even for wrong predictions. This phenomenon is particularly intensified in the presence of sample selection bias, i.e., when data labeling is subject to some constraint. To address this issue, we propose a novel confidence measure, called $\mathcal{T}$-similarity, built upon the prediction diversity of an ensemble of linear classifiers. We provide the theoretical analysis of our approach by studying stationary points and describing the relationship between the diversity of the individual members and their performance. We empirically demonstrate the benefit of our confidence measure for three different pseudo-labeling policies on classification datasets of various data modalities. The code is available at https://github.com/ambroiseodt/tsim.

Vasilii Feofanov, Romain Ilbert, Malik Tiomoko et al.

Foundation models, while highly effective, are often resource-intensive, requiring substantial inference time and memory. This paper addresses the challenge of making these models more accessible with limited computational resources by exploring dimensionality reduction techniques. Our goal is to enable users to run large pre-trained foundation models on standard GPUs without sacrificing performance. We investigate classical methods such as Principal Component Analysis alongside neural network-based adapters, aiming to reduce the dimensionality of multivariate time series data while preserving key features. Our experiments show up to a 10x speedup compared to the baseline model, without performance degradation, and enable up to 4.5x more datasets to fit on a single GPU, paving the way for more user-friendly and scalable foundation models.

Romain Ilbert, Ambroise Odonnat, Vasilii Feofanov et al.

Transformer-based architectures achieved breakthrough performance in natural language processing and computer vision, yet they remain inferior to simpler linear baselines in multivariate long-term forecasting. To better understand this phenomenon, we start by studying a toy linear forecasting problem for which we show that transformers are incapable of converging to their true solution despite their high expressive power. We further identify the attention of transformers as being responsible for this low generalization capacity. Building upon this insight, we propose a shallow lightweight transformer model that successfully escapes bad local minima when optimized with sharpness-aware optimization. We empirically demonstrate that this result extends to all commonly used real-world multivariate time series datasets. In particular, SAMformer surpasses current state-of-the-art methods and is on par with the biggest foundation model MOIRAI while having significantly fewer parameters. The code is available at https://github.com/romilbert/samformer.

Alexis Roger, Prateek Humane, Zhenghan Tai et al.

Can language-pretrained transformers become effective time-series forecasters, and why? In this paper, we show that cross-modal transfer arises because language pretraining preconditions time series training with a reusable manifold. A linear probe on frozen LLM states decodes realistic time-series trajectories without paired supervision, and retrieval in this projected space yields competitive forecasts, showing that structure and dynamics exist before finetuning. Pretrained initialization also improves optimization, producing coherent gradients and a highly anisotropic loss landscape unlike random initialization. Finetuning then acts as low-dimensional alignment, reusing existing directions rather than learning temporal primitives from scratch, as evidenced by low-rank updates, subspace alignment, and shared features for periodicity, trend, and repetition. Together, these results support a geometric account of LLM-to-time-series transfer: language pretraining builds the manifold, and finetuning projects numerical dynamics onto task-relevant directions.

Vasilii Feofanov, Malik Tiomoko, Aladin Virmaux

We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density separation assumption is implemented via quadratic margin maximization. The algorithm has an explicit solution with rich theoretical properties, and we show that particular cases of our algorithm are the least-square support vector machine in the supervised case, the spectral clustering in the fully unsupervised regime, and a class of semi-supervised graph-based approaches. As such, QLDS establishes a smooth bridge between these supervised and unsupervised learning methods. Using recent advances in the random matrix theory, we formally derive a theoretical evaluation of the classification error in the asymptotic regime. As an application, we derive a hyperparameter selection policy that finds the best balance between the supervised and the unsupervised terms of our learning criterion. Finally, we provide extensive illustrations of our framework, as well as an experimental study on several benchmarks to demonstrate that QLDS, while being computationally more efficient, improves over cross-validation for hyperparameter selection, indicating a high promise of the usage of random matrix theory for semi-supervised model selection.

Vasilii Feofanov, Songkang Wen, Marius Alonso et al.

In recent years, there has been increasing interest in developing foundation models for time series data that can generalize across diverse downstream tasks. While numerous forecasting-oriented foundation models have been introduced, there is a notable scarcity of models tailored for time series classification. To address this gap, we present Mantis, a new open-source foundation model for time series classification based on the Vision Transformer (ViT) architecture that has been pre-trained using a contrastive learning approach. Our experimental results show that Mantis outperforms existing foundation models both when the backbone is frozen and when fine-tuned, while achieving the lowest calibration error. In addition, we propose several adapters to handle the multivariate setting, reducing memory requirements and modeling channel interdependence.

Théo Gnassounou, Yessin Moakher, Shifeng Xie et al.

Foundation models for time series are emerging as powerful general-purpose backbones, yet their potential for domain-specific biomedical signals such as electroencephalography (EEG) remains rather unexplored. In this work, we investigate the applicability a recently proposed time series classification foundation model, to a different EEG tasks such as motor imagery classification and sleep stage prediction. We test two pretraining regimes: (a) pretraining on heterogeneous real-world time series from multiple domains, and (b) pretraining on purely synthetic data. We find that both variants yield strong performance, consistently outperforming EEGNet, a widely used convolutional baseline, and CBraMod, the most recent EEG-specific foundation model. These results suggest that generalist time series foundation models, even when pretrained on data of non-neural origin or on synthetic signals, can transfer effectively to EEG. Our findings highlight the promise of leveraging cross-domain pretrained models for brain signal analysis, suggesting that EEG may benefit from advances in the broader time series literature.

Yessin Moakher, Youssef Attia El Hili, Vasilii Feofanov

Self-supervised foundation models have achieved remarkable success across domains, including time series. However, the potential of non-contrastive methods, a paradigm that has driven significant advances in computer vision, remains underexplored for time series. In this work, we adapt DINOv2-style self-distillation to pretrain a time series foundation model, building on the Mantis tokenizer and transformer encoder architecture as our backbone. Through a student-teacher framework, our method Utica learns representations that capture both temporal invariance via augmented crops and fine-grained local structure via patch masking. Our approach achieves state-of-the-art classification performance on both UCR and UEA benchmarks. These results suggest that non-contrastive methods are a promising and complementary pretraining strategy for time series foundation models.

Abdelhakim Benechehab, Vasilii Feofanov, Giuseppe Paolo et al.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

Renchunzi Xie, Ambroise Odonnat, Vasilii Feofanov et al.

Estimating the test performance of a model, possibly under distribution shift, without having access to the ground-truth labels is a challenging, yet very important problem for the safe deployment of machine learning algorithms in the wild. Existing works mostly rely on information from either the outputs or the extracted features of neural networks to estimate a score that correlates with the ground-truth test accuracy. In this paper, we investigate -- both empirically and theoretically -- how the information provided by the gradients can be predictive of the ground-truth test accuracy even under distribution shifts. More specifically, we use the norm of classification-layer gradients, backpropagated from the cross-entropy loss after only one gradient step over test data. Our intuition is that these gradients should be of higher magnitude when the model generalizes poorly. We provide the theoretical insights behind our approach and the key ingredients that ensure its empirical success. Extensive experiments conducted with various architectures on diverse distribution shifts demonstrate that our method significantly outperforms current state-of-the-art approaches. The code is available at https://github.com/Renchunzi-Xie/GdScore

Simon Roschmann, Quentin Bouniot, Vasilii Feofanov et al.

Time series classification is a fundamental task in healthcare and industry, yet the development of time series foundation models (TSFMs) remains limited by the scarcity of publicly available time series datasets. In this work, we propose Time Vision Transformer (TiViT), a framework that converts time series into images to leverage the representational power of frozen Vision Transformers (ViTs) pretrained on large-scale image datasets. First, we theoretically motivate our approach by analyzing the 2D patching of ViTs for time series, showing that it can increase the number of label-relevant tokens and reduce the sample complexity. Second, we empirically demonstrate that TiViT achieves state-of-the-art performance on standard time series classification benchmarks by utilizing the hidden representations of large OpenCLIP models. We explore the structure of TiViT representations and find that intermediate layers with high intrinsic dimension are the most effective for time series classification. Finally, we assess the alignment between TiViT and TSFM representation spaces and identify a strong complementarity, with further performance gains achieved by combining their features. Our findings reveal a new direction for reusing vision representations in a non-visual domain. Code is available at https://github.com/ExplainableML/TiViT.

Shifeng Xie, Vasilii Feofanov, Marius Alonso et al.

Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pretraining on large-scale, carefully curated collections of real-world sequences. To allow for a sample-efficient pretraining of TSFMs, we propose CauKer, a novel algorithm designed to generate diverse, causally coherent synthetic time series with realistic trends, seasonality, and nonlinear interactions. CauKer combines Gaussian Process (GP) kernel composition with Structural Causal Models (SCM) to produce data for sample-efficient pretraining of state-of-the-art classification TSFMs having different architectures and following different pretraining approaches. Additionally, our experiments reveal that CauKer-generated datasets exhibit clear scaling laws for both dataset size (10K to 10M samples) and model capacity (1M to 783M parameters), unlike real-world datasets, which display irregular scaling behavior.

Songkang Wen, Vasilii Feofanov, Jianfeng Zhang

Recently, there has been a growing interest in time series foundation models that generalize across different downstream tasks. A key to strong foundation models is a diverse pre-training dataset, which is particularly challenging to collect for time series classification. In this work, we explore the performance of a contrastive-learning-based foundation model as a function of the data used for pre-training. We introduce contrastive accuracy, a new measure to evaluate the quality of the representation space learned by the foundation model. Our experiments reveal the positive correlation between the proposed measure and the accuracy of the model on a collection of downstream tasks. This suggests that the contrastive accuracy can serve as a criterion to search for time series datasets that can enhance the pre-training and improve thereby the foundation model's generalization.

Ambroise Odonnat, Vasilii Feofanov, Laetitia Chapel et al.

Recent studies have observed that intermediate layers of foundation models often yield more discriminative representations than the final layer. While initially attributed to autoregressive pretraining, this phenomenon has also been identified in models trained via supervised and discriminative self-supervised objectives. In this paper, we conduct a comprehensive study to analyze the behavior of intermediate layers in pretrained vision transformers. Through extensive linear probing experiments across a diverse set of image classification benchmarks, we find that distribution shift between pretraining and downstream data is the primary cause of performance degradation in deeper layers. Furthermore, we perform a fine-grained analysis at the module level. Our findings reveal that standard probing of transformer block outputs is suboptimal; instead, probing the activation within the feedforward network yields the best performance under significant distribution shift, whereas the normalized output of the multi-head self-attention module is optimal when the shift is weak.

Romain Ilbert, Malik Tiomoko, Cosme Louart et al.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

Massih-Reza Amini, Vasilii Feofanov, Loic Pauletto et al.

Semi-supervised algorithms aim to learn prediction functions from a small set of labeled observations and a large set of unlabeled observations. Because this framework is relevant in many applications, they have received a lot of interest in both academia and industry. Among the existing techniques, self-training methods have undoubtedly attracted greater attention in recent years. These models are designed to find the decision boundary on low density regions without making additional assumptions about the data distribution, and use the unsigned output score of a learned classifier, or its margin, as an indicator of confidence. The working principle of self-training algorithms is to learn a classifier iteratively by assigning pseudo-labels to the set of unlabeled training samples with a margin greater than a certain threshold. The pseudo-labeled examples are then used to enrich the labeled training data and to train a new classifier in conjunction with the labeled training set. In this paper, we present self-training methods for binary and multi-class classification; as well as their variants and two related approaches, namely consistency-based approaches and transductive learning. We examine the impact of significant self-training features on various methods, using different general and image classification benchmarks, and we discuss our ideas for future research in self-training. To the best of our knowledge, this is the first thorough and complete survey on this subject.

Vasilii Feofanov, Emilie Devijver, Massih-Reza Amini

Self-learning is a classical approach for learning with both labeled and unlabeled observations which consists in giving pseudo-labels to unlabeled training instances with a confidence score over a predetermined threshold. At the same time, the pseudo-labeling technique is prone to error and runs the risk of adding noisy labels into unlabeled training data. In this paper, we present a probabilistic framework for analyzing self-learning in the multi-class classification scenario with partially labeled data. First, we derive a transductive bound over the risk of the multi-class majority vote classifier. Based on this result, we propose to automatically choose the threshold for pseudo-labeling that minimizes the transductive bound. Then, we introduce a mislabeling error model to analyze the error of the majority vote classifier in the case of the pseudo-labeled data. We derive a probabilistic C-bound over the majority vote error when an imperfect label is given. Empirical results on different data sets show the effectiveness of our framework compared to several state-of-the-art semi-supervised approaches.

Vasilii Feofanov, Emilie Devijver, Massih-Reza Amini

In this paper, we propose a new wrapper feature selection approach with partially labeled training examples where unlabeled observations are pseudo-labeled using the predictions of an initial classifier trained on the labeled training set. The wrapper is composed of a genetic algorithm for proposing new feature subsets, and an evaluation measure for scoring the different feature subsets. The selection of feature subsets is done by assigning weights to characteristics and recursively eliminating those that are irrelevant. The selection criterion is based on a new multi-class $\mathcal{C}$-bound that explicitly takes into account the mislabeling errors induced by the pseudo-labeling mechanism, using a probabilistic error model. Empirical results on different data sets show the effectiveness of our framework compared to several state-of-the-art semi-supervised feature selection approaches.