EVs are poised to age like smartphones. For most of its short life, my Tesla Model 3 has aged beautifully. Since I bought the car, in 2019, it has received a number of new features simply by updating its software. My navigation system no longer just directs me to EV chargers along my route--it also shows me, in real time, how many plugs are free. With the push of a button, I can activate "Car Wash Mode," and the Tesla will put itself in neutral and disable the windshield wipers.

Vision language models (VLMs) excel in multimodal understanding but are prone to adversarial attacks. Existing defenses often demand costly retraining or significant architecture changes. W e introduce a lightweight defense using tensor decomposition suitable for any pre-trained VLM, requiring no retraining. By decomposing and reconstructing vision encoder representations, it filters adversarial noise while preserving meaning. Experiments with CLIP on COCO and Flickr30K show improved robustness. On Flickr30K, it restores 12.3% performance lost to attacks, raising Recall@1 accuracy from 7.5% to 19.8%. On COCO, it recovers 8.1% performance, improving accuracy from 3.8% to 11.9%. Analysis shows T ensor Train decomposition with low rank (8-32) and low residual strength ( α = 0 . 1 0. 2) is optimal. This method is a practical, plug-and-play solution with minimal overhead for existing VLMs.

Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and empirical success, its theoretical foundation, particularly regarding statistical optimality and convergence behavior, remain underdeveloped, especially in noisy, non-orthogonal, and higher-rank settings. In this work, we revisit CP tensor decomposition from a statistical perspective and provide a comprehensive theoretical analysis of ALS under a signal-plus-noise model. We establish non-asymptotic, minimax-optimal error bounds for tensors of general order, dimensions, and rank, assuming suitable initialization. To enable such initialization, we propose Tucker-based Approximation with Simultaneous Diagonalization (TASD), a robust method that improves stability and accuracy in noisy regimes. Combined with ALS, TASD yields a statistically consistent estimator. We further analyze the convergence dynamics of ALS, identifying a two-phase pattern-initial quadratic convergence followed by linear refinement. We further show that in the rank-one setting, ALS with an appropriately chosen initialization attains optimal error within just one or two iterations.

Tensor classification is gaining importance across fields, yet handling partially observed data remains challenging. In this paper, we introduce a novel approach to tensor classification with incomplete data, framed within high-dimensional tensor linear discriminant analysis. Specifically, we consider a high-dimensional tensor predictor with missing observations under the Missing Completely at Random (MCR) assumption and employ the Tensor Gaussian Mixture Model (TGMM) to capture the relationship between the tensor predictor and class label. We propose a Tensor Linear Discriminant Analysis with Missing Data (Tensor LDA-MD) algorithm, which manages high-dimensional tensor predictors with missing entries by leveraging the decomposable low-rank structure of the discriminant tensor. Our work establishes convergence rates for the estimation error of the discriminant tensor with incomplete data and minimax optimal bounds for the misclassification rate, addressing key gaps in the literature. Additionally, we derive large deviation bounds for the generalized mode-wise sample covariance matrix and its inverse, which are crucial tools in our analysis and hold independent interest. Our method demonstrates excellent performance in simulations and real data analysis, even with significant proportions of missing data.

The ability to learn compact, high-quality, and easy-to-optimize representations for visual data is paramount to many applications such as novel view synthesis and 3D reconstruction. Recent work has shown substantial success in using tensor networks to design such compact and high-quality representations. However, the ability to optimize tensor-based representations, and in particular, the highly compact tensor train representation, is still lacking. This has prevented practitioners from deploying the full potential of tensor networks for visual data. To this end, we propose 'Prolongation Upsampling Tensor Train (PuTT)', a novel method for learning tensor train representations in a coarse-to-fine manner. Our method involves the prolonging or `upsampling' of a learned tensor train representation, creating a sequence of 'coarse-to-fine' tensor trains that are incrementally refined. We evaluate our representation along three axes: (1). compression, (2). denoising capability, and (3). image completion capability. To assess these axes, we consider the tasks of image fitting, 3D fitting, and novel view synthesis, where our method shows an improved performance compared to state-of-the-art tensor-based methods. For full results see our project webpage: https://sebulo.github.io/PuTT_website/

We present an expectation-maximization (EM) based unified framework for non-negative tensor decomposition that optimizes the Kullback-Leibler divergence. To avoid iterations in each M-step and learning rate tuning, we establish a general relationship between low-rank decomposition and many-body approximation. Using this connection, we exploit that the closed-form solution of the many-body approximation can be used to update all parameters simultaneously in the M-step. Our framework not only offers a unified methodology for a variety of low-rank structures, including CP, Tucker, and Train decompositions, but also their combinations forming mixtures of tensors as well as robust adaptive noise modeling. Empirically, we demonstrate that our framework provides superior generalization for discrete density estimation compared to conventional tensor-based approaches.

In this work, we introduce and analyze an approach to knowledge transfer from one collection of facts to another without the need for entity or relation matching. The method works for both canonicalized knowledge bases and uncanonicalized or open knowledge bases, i.e., knowledge bases where more than one copy of a real-world entity or relation may exist. The main contribution is a method that can make use of large-scale pre-training on facts, which were collected from unstructured text, to improve predictions on structured data from a specific domain. The introduced method is most impactful on small datasets such as ReVerb20k, where a 6% absolute increase of mean reciprocal rank and 65% relative decrease of mean rank over the previously best method was achieved, despite not relying on large pre-trained models like Bert. To understand the obtained pre-trained models better, we then introduce a novel dataset for the analysis of pre-trained models for Open Knowledge Base Completion, called Doge (Diagnostics of Open knowledge Graph Embeddings). It consists of 6 subsets and is designed to measure multiple properties of a pre-trained model: robustness against synonyms, ability to perform deductive reasoning, presence of gender stereotypes, consistency with reverse relations, and coverage of different areas of general knowledge. Using the introduced dataset, we show that the existing OKBC models lack consistency in the presence of synonyms and inverse relations and are unable to perform deductive reasoning. Moreover, their predictions often align with gender stereotypes, which persist even when presented with counterevidence. We additionally investigate the role of pre-trained word embeddings and demonstrate that avoiding biased word embeddings is not a sufficient measure to prevent biased behavior of OKBC models.

Tensor decomposition methods are popular tools for analysis of multi-way datasets from social media, healthcare, spatio-temporal domains, and others. Widely adopted models such as Tucker and canonical polyadic decomposition (CPD) follow a data-driven philosophy: they decompose a tensor into factors that approximate the observed data well. In some cases side information is available about the tensor modes. For example, in a temporal user-item purchases tensor a user influence graph, an item similarity graph, and knowledge about seasonality or trends in the temporal mode may be available. Such side information may enable more succinct and interpretable tensor decomposition models and improved quality in downstream tasks. We propose a framework for Multi-Dictionary Tensor Decomposition (MDTD) which takes advantage of prior structural information about tensor modes in the form of coding dictionaries to obtain sparsely encoded tensor factors. We derive a general optimization algorithm for MDTD that handles both complete input and input with missing values. Our framework handles large sparse tensors typical to many real-world application domains. We demonstrate MDTD's utility via experiments with both synthetic and real-world datasets. It learns more concise models than dictionary-free counterparts and improves (i) reconstruction quality ($60\%$ fewer non-zero coefficients coupled with smaller error); (ii) missing values imputation quality (two-fold MSE reduction with up to orders of magnitude time savings) and (iii) the estimation of the tensor rank. MDTD's quality improvements do not come with a running time premium: it can decompose $19GB$ datasets in less than a minute. It can also impute missing values in sparse billion-entry tensors more accurately and scalably than state-of-the-art competitors.