Existing prompt-tuning methods have demonstrated impressive performances in continual learning (CL), by selecting and updating relevant prompts in the vision-transformer models. On the contrary, this paper aims to learn each task by tuning the prompts in the direction orthogonal to the subspace spanned by previous tasks' features, so as to ensure no interference on tasks that have been learned to overcome catastrophic forgetting in CL. However, different from the orthogonal projection in the traditional CNN architecture, the prompt gradient orthogonal projection in the ViT architecture shows completely different and greater challenges, i.e., 1) the high-order and non-linear self-attention operation; 2) the drift of prompt distribution brought by the LayerNorm in the transformer block. Theoretically, we have finally deduced two consistency conditions to achieve the prompt gradient orthogonal projection, which provide a theoretical guarantee of eliminating interference on previously learned knowledge via the self-attention mechanism in visual prompt tuning. In practice, an effective null-space-based approximation solution has been proposed to implement the prompt gradient orthogonal projection. Extensive experimental results demonstrate the effectiveness of anti-forgetting on four class-incremental benchmarks with diverse pre-trained baseline models, and our approach achieves superior performances to state-of-the-art methods.

Thousands of new scientific papers are published each month. Such information overload complicates researcher efforts to stay current with the state-of-the-art as well as to verify and correctly attribute claims. We pose the following research question: Given a text excerpt referencing a paper, could an LM act as a research assistant to correctly identify the referenced paper? We advance efforts to answer this question by building a benchmark that evaluates the abilities of LMs in citation attribution. Our benchmark, CiteME, consists of text excerpts from recent machine learning papers, each referencing a single other paper. CiteME use reveals a large gap between frontier LMs and human performance, with LMs achieving only 4.2-18.5% accuracy and humans 69.7%. We close this gap by introducing CiteAgent, an autonomous system built on the GPT-4o LM that can also search and read papers, which achieves an accuracy of 35.3% on CiteME. Overall, CiteME serves as a challenging testbed for open-ended claim attribution, driving the research community towards a future where any claim made by an LM can be automatically verified and discarded if found to be incorrect.

To understand neural network behavior, recent works quantitatively compare different networks' learned representations using canonical correlation analysis (CCA), centered kernel alignment (CKA), and other dissimilarity measures. Unfortunately, these widely used measures often disagree on fundamental observations, such as whether deep networks differing only in random initialization learn similar representations. These disagreements raise the question: which, if any, of these dissimilarity measures should we believe? We provide a framework to ground this question through a concrete test: measures should have \emph{sensitivity} to changes that affect functional behavior, and \emph{specificity} against changes that do not. We quantify this through a variety of functional behaviors including probing accuracy and robustness to distribution shift, and examine changes such as varying random initialization and deleting principal components. We find that current metrics exhibit different weaknesses, note that a classical baseline performs surprisingly well, and highlight settings where all metrics appear to fail, thus providing a challenge set for further improvement.

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries.Hypothesizing that difficult queries are crucial to learning complex reasoning, we propose (), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples.Utilizing, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4.We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called .In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models.

Large Language Models (LLMs) have exhibited an impressive ability to perform In-Context Learning (ICL) from only a few examples. Recent works have indicated that the functions learned by ICL can be represented through compressed vectors derived from the transformer. However, the working mechanisms and optimization of these vectors are yet to be thoroughly explored. In this paper, we address this gap by presenting a comprehensive analysis of these compressed vectors, drawing parallels to the parameters trained with gradient descent, and introducing the concept of state vector. Inspired by the works on model soup and momentum-based gradient descent, we propose inner and momentum optimization methods that are applied to refine the state vector progressively as test-time adaptation. Moreover, we simulate state vector aggregation in the multiple example setting, where demonstrations comprising numerous examples are usually too lengthy for regular ICL, and further propose a divide-and-conquer aggregation method to address this challenge. We conduct extensive experiments using Llama-2 and GPT-J in both zero-shot setting and few-shot setting. The experimental results show that our optimization method effectively enhances the state vector and achieves the state-of-the-art performance on diverse tasks.

Self-Distillation is a special type of knowledge distillation where the student model has the same architecture as the teacher model. Despite using the same architecture and the same training data, self-distillation has been empirically observed to improve performance, especially when applied repeatedly. For such a process, there is a fundamental question of interest: How much gain is possible by applying multiple steps of self-distillation? To investigate this relative gain, we propose using the simple but canonical task of linear regression. Our analysis shows that the excess risk achieved by multi-step self-distillation can significantly improve upon a single step of self-distillation, reducing the excess risk by a factor of $d$, where $d$ is the input dimension.

Large Language Models (LLMs) are distinguished by their massive parameter counts, which typically result in significant redundancy. This work introduces MaskLLM, a learnable pruning method that establishes Semi-structured (or N:M'') Sparsity in LLMs, aimed at reducing computational overhead during inference. This approach facilitates end-to-end training on large-scale datasets and offers two notable advantages: 1) High-quality Masks - our method effectively scales to large datasets and learns accurate masks; 2) Transferability - the probabilistic modeling of mask distribution enables the transfer learning of sparsity across domains or tasks. We assessed MaskLLM using 2:4 sparsity on various LLMs, including LLaMA-2, Nemotron-4, and GPT-3, with sizes ranging from 843M to 15B parameters, and our empirical results show substantial improvements over state-of-the-art methods. For instance, leading approaches achieve a perplexity (PPL) of 10 or greater on Wikitext compared to the dense model's 5.12 PPL, but MaskLLM achieves a significantly lower 6.72 PPL solely by learning the masks with frozen weights.

The interest in leveraging physics-based inductive bias in deep learning has resulted in recent development of that integrates known physics-based mathematical expressions in neural generative models. To identify these hybrid-DGMs requires inferring parameters of the physics-based component along with their neural component. The identifiability of these hybrid-DGMs, however, has not yet been theoretically probed or established. How does the existing theory of the un-identifiability of general DGMs apply to hybrid-DGMs? What may be an effective approach to consutrct a hybrid-DGM with theoretically-proven identifiability? This paper provides the first theoretical probe into the identifiability of hybrid-DGMs, and present meta-learning as a novel solution to construct identifiable hybrid-DGMs. On synthetic and real-data benchmarks, we provide strong empirical evidence for the un-identifiability of existing hybrid-DGMs using unconditional priors, and strong identifiability results of the presented meta-formulations of hybrid-DGMs.

Asynchronous stochastic gradient descent (ASGD) has evolved into an indispensable optimization algorithm for training modern large-scale distributed machine learning tasks. Therefore, it is imperative to explore the generalization performance of the ASGD algorithm. However, the existing results are either pessimistic and vacuous or restricted by strict assumptions that fail to reveal the intrinsic impact of asynchronous training on generalization. In this study, we establish sharper stability and generalization bounds for ASGD under much weaker assumptions. Firstly, this paper studies the on-average model stability of ASGD and provides a non-vacuous upper bound on the generalization error, without relying on the Lipschitz assumption. Furthermore, we investigate the excess generalization error of the ASGD algorithm, revealing the effects of asynchronous delay, model initialization, number of training samples and iterations on generalization performance. Secondly, for the first time, this study explores the generalization performance of ASGD in the non-smooth case. We replace smoothness with the much weaker Hölder continuous assumption and achieve similar generalization results as in the smooth case.

We analyze the capabilities of Transformer language models in learning compositional discrete tasks. To this end, we evaluate training LLaMA models and prompting GPT-4 and Gemini on four tasks demanding to learn a composition of several discrete sub-tasks. In particular, we measure how well these models can reuse primitives observable in the sub-tasks to learn the composition task. Our results indicate that compositional learning in state-of-the-art Transformer language models is highly sample inefficient: LLaMA requires more data samples than relearning all sub-tasks from scratch to learn the compositional task; in-context prompting with few samples is unreliable and fails at executing the sub-tasks or correcting the errors in multi-round code generation. Further, by leveraging complexity theory, we support these findings with a theoretical analysis focused on the sample inefficiency of gradient descent in memorizing feedforward models.