Analyzing the Role of Permutation Invariance in Linear Mode Connectivity

It was empirically observed in Entezari et al. (2021) that when accounting for the permutation invariance of neural networks, there is likely no loss barrier along the linear interpolation between two SGD solutions -- a phenomenon known as linear mode connectivity (LMC) modulo permutation. This phenomenon has sparked significant attention due to both its theoretical interest and practical relevance in applications such as model merging. In this paper, we provide a fine-grained analysis of this phenomenon for two-layer ReLU networks under a teacher-student setup. We show that as the student network width $m$ increases, the LMC loss barrier modulo permutation exhibits a {\bf double descent} behavior. Particularly, when $m$ is sufficiently large, the barrier decreases to zero at a rate $O(m^{-1/2})$. Notably, this rate does not suffer from the curse of dimensionality and demonstrates how substantial permutation can reduce the LMC loss barrier. Moreover, we observe a sharp transition in the sparsity of GD/SGD solutions when increasing the learning rate and investigate how this sparsity preference affects the LMC loss barrier modulo permutation. Experiments on both synthetic and MNIST datasets corroborate our theoretical predictions and reveal a similar trend for more complex network architectures.

Computational Analysis of Degradation Modeling in Blind Panoramic Image Quality Assessment

Blind panoramic image quality assessment (BPIQA) has recently brought new challenge to the visual quality community, due to the complex interaction between immersive content and human behavior. Although many efforts have been made to advance BPIQA from both conducting psychophysical experiments and designing performance-driven objective algorithms, \textit{limited content} and \textit{few samples} in those closed sets inevitably would result in shaky conclusions, thereby hindering the development of BPIQA, we refer to it as the \textit{easy-database} issue. In this paper, we present a sufficient computational analysis of degradation modeling in BPIQA to thoroughly explore the \textit{easy-database issue}, where we carefully design three types of experiments via investigating the gap between BPIQA and blind image quality assessment (BIQA), the necessity of specific design in BPIQA models, and the generalization ability of BPIQA models. From extensive experiments, we find that easy databases narrow the gap between the performance of BPIQA and BIQA models, which is unconducive to the development of BPIQA. And the easy databases make the BPIQA models be closed to saturation, therefore the effectiveness of the associated specific designs can not be well verified. Besides, the BPIQA models trained on our recently proposed databases with complicated degradation show better generalization ability. Thus, we believe that much more efforts are highly desired to put into BPIQA from both subjective viewpoint and objective viewpoint.

The Sharpness Disparity Principle in Transformers for Accelerating Language Model Pre-Training

Transformers consist of diverse building blocks, such as embedding layers, normalization layers, self-attention mechanisms, and point-wise feedforward networks. Thus, understanding the differences and interactions among these blocks is important. In this paper, we uncover a clear Sharpness Disparity across these blocks, which emerges early in training and intriguingly persists throughout the training process. Motivated by this finding, we propose Blockwise Learning Rate (LR), a strategy that tailors the LR to each block's sharpness, accelerating large language model (LLM) pre-training. By integrating Blockwise LR into AdamW, we consistently achieve lower terminal loss and nearly $2\times$ speedup compared to vanilla AdamW. We demonstrate this acceleration across GPT-2 and LLaMA, with model sizes ranging from 0.12B to 1.1B and datasets of OpenWebText and MiniPile. Finally, we incorporate Blockwise LR into Adam-mini (Zhang et al., 2024), a recently proposed memory-efficient variant of Adam, achieving a combined $2\times$ speedup and $2\times$ memory saving. These results underscore the potential of exploiting the sharpness disparity to improve LLM training.

Video Quality Assessment for Online Processing: From Spatial to Temporal Sampling

With the rapid development of multimedia processing and deep learning technologies, especially in the field of video understanding, video quality assessment (VQA) has achieved significant progress. Although researchers have moved from designing efficient video quality mapping models to various research directions, in-depth exploration of the effectiveness-efficiency trade-offs of spatio-temporal modeling in VQA models is still less sufficient. Considering the fact that videos have highly redundant information, this paper investigates this problem from the perspective of joint spatial and temporal sampling, aiming to seek the answer to how little information we should keep at least when feeding videos into the VQA models while with acceptable performance sacrifice. To this end, we drastically sample the video's information from both spatial and temporal dimensions, and the heavily squeezed video is then fed into a stable VQA model. Comprehensive experiments regarding joint spatial and temporal sampling are conducted on six public video quality databases, and the results demonstrate the acceptable performance of the VQA model when throwing away most of the video information. Furthermore, with the proposed joint spatial and temporal sampling strategy, we make an initial attempt to design an online VQA model, which is instantiated by as simple as possible a spatial feature extractor, a temporal feature fusion module, and a global quality regression module. Through quantitative and qualitative experiments, we verify the feasibility of online VQA model by simplifying itself and reducing input.

BlueLM-V-3B: Algorithm and System Co-Design for Multimodal Large Language Models on Mobile Devices

The emergence and growing popularity of multimodal large language models (MLLMs) have significant potential to enhance various aspects of daily life, from improving communication to facilitating learning and problem-solving. Mobile phones, as essential daily companions, represent the most effective and accessible deployment platform for MLLMs, enabling seamless integration into everyday tasks. However, deploying MLLMs on mobile phones presents challenges due to limitations in memory size and computational capability, making it difficult to achieve smooth and real-time processing without extensive optimization. In this paper, we present BlueLM-V-3B, an algorithm and system co-design approach specifically tailored for the efficient deployment of MLLMs on mobile platforms. To be specific, we redesign the dynamic resolution scheme adopted by mainstream MLLMs and implement system optimization for hardware-aware deployment to optimize model inference on mobile phones. BlueLM-V-3B boasts the following key highlights: (1) Small Size: BlueLM-V-3B features a language model with 2.7B parameters and a vision encoder with 400M parameters. (2) Fast Speed: BlueLM-V-3B achieves a generation speed of 24.4 token/s on the MediaTek Dimensity 9300 processor with 4-bit LLM weight quantization. (3) Strong Performance: BlueLM-V-3B has attained the highest average score of 66.1 on the OpenCompass benchmark among models with $\leq$ 4B parameters and surpassed a series of models with much larger parameter sizes (e.g., MiniCPM-V-2.6, InternVL2-8B).

Prove Your Point!: Bringing Proof-Enhancement Principles to Argumentative Essay Generation

Argumentative essay generation (AEG) aims to generate complete texts on specific controversial topics or debates. Although current AEG methods can generate individual opinions, they often overlook the high-level connections between these opinions. This often leads to the generated results being mired in logical confusion, unable to proof their own arguments effectively. The generated essay may present evidence that contradicts the claims or they may fail to assemble the claims into logical flow. In this paper, we present a unified two-stage framework: Proof-Enhancement and Self-Annotation (PESA) for AEG with a focus on logical enhancement. Specifically, we first construct pseudo-labels for logical information,claims and grounds, using a large language model. We then propose a tree planning approach that introduces proof principles and ensures logical consistency. Extensive experimental results show that, benefiting from proof principle guidance, PESA generates argumentative essays with better logical validity and persuasiveness than strong baseline models.

How Transformers Implement Induction Heads: Approximation and Optimization Analysis

Transformers have demonstrated exceptional in-context learning capabilities, yet the theoretical understanding of the underlying mechanisms remain limited. A recent work (Elhage et al., 2021) identified a "rich" in-context mechanism known as induction head, contrasting with "lazy" $n$-gram models that overlook long-range dependencies. In this work, we provide both approximation and optimization analyses of how transformers implement induction heads. In the approximation analysis, we formalize both standard and generalized induction head mechanisms, and examine how transformers can efficiently implement them, with an emphasis on the distinct role of each transformer submodule. For the optimization analysis, we study the training dynamics on a synthetic mixed target, composed of a 4-gram and an in-context 2-gram component. This setting enables us to precisely characterize the entire training process and uncover an {\em abrupt transition} from lazy (4-gram) to rich (induction head) mechanisms as training progresses.

DTactive: A Vision-Based Tactile Sensor with Active Surface

The development of vision-based tactile sensors has significantly enhanced robots' perception and manipulation capabilities, especially for tasks requiring contact-rich interactions with objects. In this work, we present DTactive, a novel vision-based tactile sensor with active surfaces. DTactive inherits and modifies the tactile 3D shape reconstruction method of DTact while integrating a mechanical transmission mechanism that facilitates the mobility of its surface. Thanks to this design, the sensor is capable of simultaneously performing tactile perception and in-hand manipulation with surface movement. Leveraging the high-resolution tactile images from the sensor and the magnetic encoder data from the transmission mechanism, we propose a learning-based method to enable precise angular trajectory control during in-hand manipulation. In our experiments, we successfully achieved accurate rolling manipulation within the range of [ -180{\deg},180{\deg} ] on various objects, with the root mean square error between the desired and actual angular trajectories being less than 12{\deg} on nine trained objects and less than 19{\deg} on three novel objects. The results demonstrate the potential of DTactive for in-hand object manipulation in terms of effectiveness, robustness and precision.

Why Do You Grok? A Theoretical Analysis of Grokking Modular Addition

We present a theoretical explanation of the ``grokking'' phenomenon, where a model generalizes long after overfitting,for the originally-studied problem of modular addition. First, we show that early in gradient descent, when the ``kernel regime'' approximately holds, no permutation-equivariant model can achieve small population error on modular addition unless it sees at least a constant fraction of all possible data points. Eventually, however, models escape the kernel regime. We show that two-layer quadratic networks that achieve zero training loss with bounded $\ell_{\infty}$ norm generalize well with substantially fewer training points, and further show such networks exist and can be found by gradient descent with small $\ell_{\infty}$ regularization. We further provide empirical evidence that these networks as well as simple Transformers, leave the kernel regime only after initially overfitting. Taken together, our results strongly support the case for grokking as a consequence of the transition from kernel-like behavior to limiting behavior of gradient descent on deep networks.

Improving Generalization and Convergence by Enhancing Implicit Regularization

In this work, we propose an Implicit Regularization Enhancement (IRE) framework to accelerate the discovery of flat solutions in deep learning, thereby improving generalization and convergence. Specifically, IRE decouples the dynamics of flat and sharp directions, which boosts the sharpness reduction along flat directions while maintaining the training stability in sharp directions. We show that IRE can be practically incorporated with {\em generic base optimizers} without introducing significant computational overload. Experiments show that IRE consistently improves the generalization performance for image classification tasks across a variety of benchmark datasets (CIFAR-10/100, ImageNet) and models (ResNets and ViTs). Surprisingly, IRE also achieves a $2\times$ {\em speed-up} compared to AdamW in the pre-training of Llama models (of sizes ranging from 60M to 229M) on datasets including Wikitext-103, Minipile, and Openwebtext. Moreover, we provide theoretical guarantees, showing that IRE can substantially accelerate the convergence towards flat minima in Sharpness-aware Minimization (SAM).