A Convex Relaxation Approach to Generalization Analysis for Parallel Positively Homogeneous Networks

We propose a general framework for deriving generalization bounds for parallel positively homogeneous neural networks--a class of neural networks whose input-output map decomposes as the sum of positively homogeneous maps. Examples of such networks include matrix factorization and sensing, single-layer multi-head attention mechanisms, tensor factorization, deep linear and ReLU networks, and more. Our general framework is based on linking the non-convex empirical risk minimization (ERM) problem to a closely related convex optimization problem over prediction functions, which provides a global, achievable lower-bound to the ERM problem. We exploit this convex lower-bound to perform generalization analysis in the convex space while controlling the discrepancy between the convex model and its non-convex counterpart. We apply our general framework to a wide variety of models ranging from low-rank matrix sensing, to structured matrix sensing, two-layer linear networks, two-layer ReLU networks, and single-layer multi-head attention mechanisms, achieving generalization bounds with a sample complexity that scales almost linearly with the network width.

ICL-TSVD: Bridging Theory and Practice in Continual Learning with Pre-trained Models

The goal of continual learning (CL) is to train a model that can solve multiple tasks presented sequentially. Recent CL approaches have achieved strong performance by leveraging large pre-trained models that generalize well to downstream tasks. However, such methods lack theoretical guarantees, making them prone to unexpected failures. Conversely, principled CL approaches often fail to achieve competitive performance. In this work, we bridge this gap between theory and practice by integrating an empirically strong approach (RanPAC) into a principled framework, Ideal Continual Learner (ICL), designed to prevent forgetting. Specifically, we lift pre-trained features into a higher dimensional space and formulate an over-parametrized minimum-norm least-squares problem. We find that the lifted features are highly ill-conditioned, potentially leading to large training errors (numerical instability) and increased generalization errors (double descent). We address these challenges by continually truncating the singular value decomposition (SVD) of the lifted features. Our approach, termed ICL-TSVD, is stable with respect to the choice of hyperparameters, can handle hundreds of tasks, and outperforms state-of-the-art CL methods on multiple datasets. Importantly, our method satisfies a recurrence relation throughout its continual learning process, which allows us to prove it maintains small training and generalization errors by appropriately truncating a fraction of SVD factors. This results in a stable continual learning method with strong empirical performance and theoretical guarantees.

Extracting and Encoding: Leveraging Large Language Models and Medical Knowledge to Enhance Radiological Text Representation

Advancing representation learning in specialized fields like medicine remains challenging due to the scarcity of expert annotations for text and images. To tackle this issue, we present a novel two-stage framework designed to extract high-quality factual statements from free-text radiology reports in order to improve the representations of text encoders and, consequently, their performance on various downstream tasks. In the first stage, we propose a \textit{Fact Extractor} that leverages large language models (LLMs) to identify factual statements from well-curated domain-specific datasets. In the second stage, we introduce a \textit{Fact Encoder} (CXRFE) based on a BERT model fine-tuned with objective functions designed to improve its representations using the extracted factual data. Our framework also includes a new embedding-based metric (CXRFEScore) for evaluating chest X-ray text generation systems, leveraging both stages of our approach. Extensive evaluations show that our fact extractor and encoder outperform current state-of-the-art methods in tasks such as sentence ranking, natural language inference, and label extraction from radiology reports. Additionally, our metric proves to be more robust and effective than existing metrics commonly used in the radiology report generation literature. The code of this project is available at \url{https://github.com/PabloMessina/CXR-Fact-Encoder}.

PaCE: Parsimonious Concept Engineering for Large Language Models

Large Language Models (LLMs) are being used for a wide variety of tasks. While they are capable of generating human-like responses, they can also produce undesirable output including potentially harmful information, racist or sexist language, and hallucinations. Alignment methods are designed to reduce such undesirable output, via techniques such as fine-tuning, prompt engineering, and representation engineering. However, existing methods face several challenges: some require costly fine-tuning for every alignment task; some do not adequately remove undesirable concepts, failing alignment; some remove benign concepts, lowering the linguistic capabilities of LLMs. To address these issues, we propose Parsimonious Concept Engineering (PaCE), a novel activation engineering framework for alignment. First, to sufficiently model the concepts, we construct a large-scale concept dictionary in the activation space, in which each atom corresponds to a semantic concept. Then, given any alignment task, we instruct a concept partitioner to efficiently annotate the concepts as benign or undesirable. Finally, at inference time, we decompose the LLM activations along the concept dictionary via sparse coding, to accurately represent the activation as a linear combination of the benign and undesirable components. By removing the latter ones from the activation, we reorient the behavior of LLMs towards alignment goals. We conduct experiments on tasks such as response detoxification, faithfulness enhancement, and sentiment revising, and show that PaCE achieves state-of-the-art alignment performance while maintaining linguistic capabilities.

Can Implicit Bias Imply Adversarial Robustness?

The implicit bias of gradient-based training algorithms has been considered mostly beneficial as it leads to trained networks that often generalize well. However, Frei et al. (2023) show that such implicit bias can harm adversarial robustness. Specifically, when the data consists of clusters with small inter-cluster correlation, a shallow (two-layer) ReLU network trained by gradient flow generalizes well, but it is not robust to adversarial attacks of small radius, despite the existence of a much more robust classifier that can be explicitly constructed from a shallow network. In this paper, we extend recent analyses of neuron alignment to show that a shallow network with a polynomial ReLU activation (pReLU) trained by gradient flow not only generalizes well but is also robust to adversarial attacks. Our results highlight the importance of the interplay between data structure and architecture design in the implicit bias and robustness of trained networks.

Certified Robustness against Sparse Adversarial Perturbations via Data Localization

Recent work in adversarial robustness suggests that natural data distributions are localized, i.e., they place high probability in small volume regions of the input space, and that this property can be utilized for designing classifiers with improved robustness guarantees for $\ell_2$-bounded perturbations. Yet, it is still unclear if this observation holds true for more general metrics. In this work, we extend this theory to $\ell_0$-bounded adversarial perturbations, where the attacker can modify a few pixels of the image but is unrestricted in the magnitude of perturbation, and we show necessary and sufficient conditions for the existence of $\ell_0$-robust classifiers. Theoretical certification approaches in this regime essentially employ voting over a large ensemble of classifiers. Such procedures are combinatorial and expensive or require complicated certification techniques. In contrast, a simple classifier emerges from our theory, dubbed Box-NN, which naturally incorporates the geometry of the problem and improves upon the current state-of-the-art in certified robustness against sparse attacks for the MNIST and Fashion-MNIST datasets.

Scalable 3D Registration via Truncated Entry-wise Absolute Residuals

Given an input set of $3$D point pairs, the goal of outlier-robust $3$D registration is to compute some rotation and translation that align as many point pairs as possible. This is an important problem in computer vision, for which many highly accurate approaches have been recently proposed. Despite their impressive performance, these approaches lack scalability, often overflowing the $16$GB of memory of a standard laptop to handle roughly $30,000$ point pairs. In this paper, we propose a $3$D registration approach that can process more than ten million ($10^7$) point pairs with over $99\%$ random outliers. Moreover, our method is efficient, entails low memory costs, and maintains high accuracy at the same time. We call our method TEAR, as it involves minimizing an outlier-robust loss that computes Truncated Entry-wise Absolute Residuals. To minimize this loss, we decompose the original $6$-dimensional problem into two subproblems of dimensions $3$ and $2$, respectively, solved in succession to global optimality via a customized branch-and-bound method. While branch-and-bound is often slow and unscalable, this does not apply to TEAR as we propose novel bounding functions that are tight and computationally efficient. Experiments on various datasets are conducted to validate the scalability and efficiency of our method.

A Review of Modern Recommender Systems Using Generative Models

Traditional recommender systems (RS) have used user-item rating histories as their primary data source, with collaborative filtering being one of the principal methods. However, generative models have recently developed abilities to model and sample from complex data distributions, including not only user-item interaction histories but also text, images, and videos - unlocking this rich data for novel recommendation tasks. Through this comprehensive and multi-disciplinary survey, we aim to connect the key advancements in RS using Generative Models (Gen-RecSys), encompassing: a foundational overview of interaction-driven generative models; the application of large language models (LLM) for generative recommendation, retrieval, and conversational recommendation; and the integration of multimodal models for processing and generating image and video content in RS. Our holistic perspective allows us to highlight necessary paradigms for evaluating the impact and harm of Gen-RecSys and identify open challenges. A more up-to-date version of the papers is maintained at: https://github.com/yasdel/LLM-RecSys.

Stochastic Extragradient with Random Reshuffling: Improved Convergence for Variational Inequalities

The Stochastic Extragradient (SEG) method is one of the most popular algorithms for solving finite-sum min-max optimization and variational inequality problems (VIPs) appearing in various machine learning tasks. However, existing convergence analyses of SEG focus on its with-replacement variants, while practical implementations of the method randomly reshuffle components and sequentially use them. Unlike the well-studied with-replacement variants, SEG with Random Reshuffling (SEG-RR) lacks established theoretical guarantees. In this work, we provide a convergence analysis of SEG-RR for three classes of VIPs: (i) strongly monotone, (ii) affine, and (iii) monotone. We derive conditions under which SEG-RR achieves a faster convergence rate than the uniform with-replacement sampling SEG. In the monotone setting, our analysis of SEG-RR guarantees convergence to an arbitrary accuracy without large batch sizes, a strong requirement needed in the classical with-replacement SEG. As a byproduct of our results, we provide convergence guarantees for Shuffle Once SEG (shuffles the data only at the beginning of the algorithm) and the Incremental Extragradient (does not shuffle the data). We supplement our analysis with experiments validating empirically the superior performance of SEG-RR over the classical with-replacement sampling SEG.

Knowledge Pursuit Prompting for Zero-Shot Multimodal Synthesis

Hallucinations and unfaithful synthesis due to inaccurate prompts with insufficient semantic details are widely observed in multimodal generative models. A prevalent strategy to align multiple modalities is to fine-tune the generator with a large number of annotated text-image pairs. However, such a procedure is labor-consuming and resource-draining. The key question we ask is: can we enhance the quality and faithfulness of text-driven generative models beyond extensive text-image pair annotations? To address this question, we propose Knowledge Pursuit Prompting (KPP), a zero-shot framework that iteratively incorporates external knowledge to help generators produce reliable visual content. Instead of training generators to handle generic prompts, KPP employs a recursive knowledge query process to gather informative external facts from the knowledge base, instructs a language model to compress the acquired knowledge for prompt refinement, and utilizes text-driven generators for visual synthesis. The entire process is zero-shot, without accessing the architectures and parameters of generative models. We evaluate the framework across multiple text-driven generative tasks (image, 3D rendering, and video) on datasets of different domains. We further demonstrate the extensibility and adaptability of KPP through varying foundation model bases and instructions. Our results show that KPP is capable of generating faithful and semantically rich content across diverse visual domains, offering a promising solution to improve multimodal generative models.