AtomThink: A Slow Thinking Framework for Multimodal Mathematical Reasoning

In this paper, we address the challenging task of multimodal mathematical reasoning by incorporating the ability of ``slow thinking" into multimodal large language models (MLLMs). Contrary to existing methods that rely on direct or fast thinking, our key idea is to construct long chains of thought (CoT) consisting of atomic actions in a step-by-step manner, guiding MLLMs to perform complex reasoning. To this end, we design a novel AtomThink framework composed of three key modules: (i) a CoT annotation engine that automatically generates high-quality CoT annotations to address the lack of high-quality visual mathematical data; (ii) an atomic step fine-tuning strategy that jointly optimizes an MLLM and a policy reward model (PRM) for step-wise reasoning; and (iii) four different search strategies that can be applied with the PRM to complete reasoning. Additionally, we propose AtomMATH, a large-scale multimodal dataset of long CoTs, and an atomic capability evaluation metric for mathematical tasks. Extensive experimental results show that the proposed AtomThink significantly improves the performance of baseline MLLMs, achieving approximately 50\% relative accuracy gains on MathVista and 120\% on MathVerse. To support the advancement of multimodal slow-thinking models, we will make our code and dataset publicly available on https://github.com/Quinn777/AtomThink.

SAFE: Slow and Fast Parameter-Efficient Tuning for Continual Learning with Pre-Trained Models

Continual learning aims to incrementally acquire new concepts in data streams while resisting forgetting previous knowledge. With the rise of powerful pre-trained models (PTMs), there is a growing interest in training incremental learning systems using these foundation models, rather than learning from scratch. Existing works often view PTMs as a strong initial point and directly apply parameter-efficient tuning (PET) in the first session for adapting to downstream tasks. In the following sessions, most methods freeze model parameters for tackling forgetting issues. However, applying PET directly to downstream data cannot fully explore the inherent knowledge in PTMs. Additionally, freezing the parameters in incremental sessions hinders models' plasticity to novel concepts not covered in the first session. To solve the above issues, we propose a Slow And Fast parameter-Efficient tuning (SAFE) framework. In particular, to inherit general knowledge from foundation models, we include a transfer loss function by measuring the correlation between the PTM and the PET-applied model. After calibrating in the first session, the slow efficient tuning parameters can capture more informative features, improving generalization to incoming classes. Moreover, to further incorporate novel concepts, we strike a balance between stability and plasticity by fixing slow efficient tuning parameters and continuously updating the fast ones. Specifically, a cross-classification loss with feature alignment is proposed to circumvent catastrophic forgetting. During inference, we introduce an entropy-based aggregation strategy to dynamically utilize the complementarity in the slow and fast learners. Extensive experiments on seven benchmark datasets verify the effectiveness of our method by significantly surpassing the state-of-the-art.

CrystalX: Ultra-Precision Crystal Structure Resolution and Error Correction Using Deep Learning

Atomic structure analysis of crystalline materials is a paramount endeavor in both chemical and material sciences. This sophisticated technique necessitates not only a solid foundation in crystallography but also a profound comprehension of the intricacies of the accompanying software, posing a significant challenge in meeting the rigorous daily demands. For the first time, we confront this challenge head-on by harnessing the power of deep learning for ultra-precise structural analysis at the full-atom level. To validate the performance of the model, named CrystalX, we employed a vast dataset comprising over 50,000 X-ray diffraction measurements derived from authentic experiments, demonstrating performance that is commensurate with human experts and adept at deciphering intricate geometric patterns. Remarkably, CrystalX revealed that even peer-reviewed publications can harbor errors that are stealthy to human scrutiny, yet CrystalX adeptly rectifies them. This deep learning model revolutionizes the time frame for crystal structure analysis, slashing it down to seconds. It has already been successfully applied in the structure analysis of newly discovered compounds in the latest research without human intervention. Overall, CrystalX marks the beginning of a new era in automating routine structural analysis within self-driving laboratories.

ATLAS: Adapter-Based Multi-Modal Continual Learning with a Two-Stage Learning Strategy

While vision-and-language models significantly advance in many fields, the challenge of continual learning is unsolved. Parameter-efficient modules like adapters and prompts present a promising way to alleviate catastrophic forgetting. However, existing works usually learn individual adapters for each task, which may result in redundant knowledge among adapters. Moreover, they continue to use the original pre-trained model to initialize the downstream model, leading to negligible changes in the model's generalization compared to the original model. In addition, there is still a lack of research investigating the consequences of integrating a multi-modal model into the updating procedure for both uni-modal and multi-modal tasks and the subsequent impacts it has on downstream tasks. In this paper, we propose an adapter-based two-stage learning paradigm, a multi-modal continual learning scheme that consists of experience-based learning and novel knowledge expansion, which helps the model fully use experience knowledge and compensate for novel knowledge. Extensive experiments demonstrate that our method is proficient for continual learning. It expands the distribution of representation upstream while also minimizing the negative impact of forgetting previous tasks. Additionally, it enhances the generalization capability for downstream tasks. Furthermore, we incorporate both multi-modal and uni-modal tasks into upstream continual learning. We observe that learning from upstream tasks can help with downstream tasks. Our code will be available at: https://github.com/lihong2303/ATLAS.

Investigating the Impact of Model Complexity in Large Language Models

Large Language Models (LLMs) based on the pre-trained fine-tuning paradigm have become pivotal in solving natural language processing tasks, consistently achieving state-of-the-art performance. Nevertheless, the theoretical understanding of how model complexity influences fine-tuning performance remains challenging and has not been well explored yet. In this paper, we focus on autoregressive LLMs and propose to employ Hidden Markov Models (HMMs) to model them. Based on the HMM modeling, we investigate the relationship between model complexity and the generalization capability in downstream tasks. Specifically, we consider a popular tuning paradigm for downstream tasks, head tuning, where all pre-trained parameters are frozen and only individual heads are trained atop pre-trained LLMs. Our theoretical analysis reveals that the risk initially increases and then decreases with rising model complexity, showcasing a "double descent" phenomenon. In this case, the initial "descent" is degenerate, signifying that the "sweet spot" where bias and variance are balanced occurs when the model size is zero. Obtaining the presented in this study conclusion confronts several challenges, primarily revolving around effectively modeling autoregressive LLMs and downstream tasks, as well as conducting a comprehensive risk analysis for multivariate regression. Our research is substantiated by experiments conducted on data generated from HMMs, which provided empirical support and alignment with our theoretical insights.

Exploring Information-Theoretic Metrics Associated with Neural Collapse in Supervised Training

In this paper, we utilize information-theoretic metrics like matrix entropy and mutual information to analyze supervised learning. We explore the information content of data representations and classification head weights and their information interplay during supervised training. Experiments show that matrix entropy cannot solely describe the interaction of the information content of data representation and classification head weights but it can effectively reflect the similarity and clustering behavior of the data. Inspired by this, we propose a cross-modal alignment loss to improve the alignment between the representations of the same class from different modalities. Moreover, in order to assess the interaction of the information content of data representation and classification head weights more accurately, we utilize new metrics like matrix mutual information ratio (MIR) and matrix information entropy difference ratio (HDR). Through theory and experiment, we show that HDR and MIR can not only effectively describe the information interplay of supervised training but also improve the performance of supervised and semi-supervised learning.

A Statistical Theory of Regularization-Based Continual Learning

We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate for the oracle estimator obtained as if all data were available simultaneously. Next, we consider a family of generalized $\ell_2$-regularization algorithms indexed by matrix-valued hyperparameters, which includes the minimum norm estimator and continual ridge regression as special cases. As more tasks are introduced, we derive an iterative update formula for the estimation error of generalized $\ell_2$-regularized estimators, from which we determine the hyperparameters resulting in the optimal algorithm. Interestingly, the choice of hyperparameters can effectively balance the trade-off between forward and backward knowledge transfer and adjust for data heterogeneity. Moreover, the estimation error of the optimal algorithm is derived explicitly, which is of the same order as that of the oracle estimator. In contrast, our lower bounds for the minimum norm estimator and continual ridge regression show their suboptimality. A byproduct of our theoretical analysis is the equivalence between early stopping and generalized $\ell_2$-regularization in continual learning, which may be of independent interest. Finally, we conduct experiments to complement our theory.

Can I understand what I create? Self-Knowledge Evaluation of Large Language Models

Large language models (LLMs) have achieved remarkable progress in linguistic tasks, necessitating robust evaluation frameworks to understand their capabilities and limitations. Inspired by Feynman's principle of understanding through creation, we introduce a self-knowledge evaluation framework that is easy to implement, evaluating models on their ability to comprehend and respond to self-generated questions. Our findings, based on testing multiple models across diverse tasks, reveal significant gaps in the model's self-knowledge ability. Further analysis indicates these gaps may be due to misalignment with human attention mechanisms. Additionally, fine-tuning on self-generated math task may enhance the model's math performance, highlighting the potential of the framework for efficient and insightful model evaluation and may also contribute to the improvement of LLMs.

Unveiling the Dynamics of Information Interplay in Supervised Learning

In this paper, we use matrix information theory as an analytical tool to analyze the dynamics of the information interplay between data representations and classification head vectors in the supervised learning process. Specifically, inspired by the theory of Neural Collapse, we introduce matrix mutual information ratio (MIR) and matrix entropy difference ratio (HDR) to assess the interactions of data representation and class classification heads in supervised learning, and we determine the theoretical optimal values for MIR and HDR when Neural Collapse happens. Our experiments show that MIR and HDR can effectively explain many phenomena occurring in neural networks, for example, the standard supervised training dynamics, linear mode connectivity, and the performance of label smoothing and pruning. Additionally, we use MIR and HDR to gain insights into the dynamics of grokking, which is an intriguing phenomenon observed in supervised training, where the model demonstrates generalization capabilities long after it has learned to fit the training data. Furthermore, we introduce MIR and HDR as loss terms in supervised and semi-supervised learning to optimize the information interactions among samples and classification heads. The empirical results provide evidence of the method's effectiveness, demonstrating that the utilization of MIR and HDR not only aids in comprehending the dynamics throughout the training process but can also enhances the training procedure itself.

Provable Contrastive Continual Learning

Continual learning requires learning incremental tasks with dynamic data distributions. So far, it has been observed that employing a combination of contrastive loss and distillation loss for training in continual learning yields strong performance. To the best of our knowledge, however, this contrastive continual learning framework lacks convincing theoretical explanations. In this work, we fill this gap by establishing theoretical performance guarantees, which reveal how the performance of the model is bounded by training losses of previous tasks in the contrastive continual learning framework. Our theoretical explanations further support the idea that pre-training can benefit continual learning. Inspired by our theoretical analysis of these guarantees, we propose a novel contrastive continual learning algorithm called CILA, which uses adaptive distillation coefficients for different tasks. These distillation coefficients are easily computed by the ratio between average distillation losses and average contrastive losses from previous tasks. Our method shows great improvement on standard benchmarks and achieves new state-of-the-art performance.