Large language models (LLMs) have sparked a new wave of AI applications; however, their substantial computational costs and memory demands pose significant challenges to democratizing access to LLMs for a broader audience. Singular Value Decomposition (SVD), a technique studied for decades, offers a hardware-independent and flexibly tunable solution for LLM compression. In this paper, we present new directions using SVD: we first theoretically analyze the optimality of truncating weights and truncating activations, then we further identify three key issues on SVD-based LLM compression, including (1) How can we determine the optimal truncation position for each weight matrix in LLMs? (2) How can we efficiently update the weight matrices based on truncation position? (3) How can we address the inherent "injection" nature that results in the information loss of the SVD? We propose an effective approach, **Dobi-SVD**, to tackle the three issues. First, we propose a **differentiable** truncation-value learning mechanism, along with gradient-robust backpropagation, enabling the model to adaptively find the optimal truncation positions. Next, we utilize the Eckart-Young-Mirsky theorem to derive a theoretically **optimal** weight update formula through rigorous mathematical analysis. Lastly, by observing and leveraging the quantization-friendly nature of matrices after SVD decomposition, we reconstruct a mapping between truncation positions and memory requirements, establishing a **bijection** from truncation positions to memory. Experimental results show that with a 40\% parameter-compression rate, our method achieves a perplexity of 9.07 on the Wikitext2 dataset with the compressed LLama-7B model, a 78.7\% improvement over the state-of-the-art SVD for LLM compression method. We emphasize that Dobi-SVD is the first to achieve such a high-ratio LLM compression with minimal performance drop. We also extend our Dobi-SVD to VLM compression, achieving a 20\% increase in throughput with minimal performance degradation. We hope that the inference speedup—up to 12.4x on 12GB NVIDIA Titan Xp GPUs and 3x on 80GB A100 GPUs for LLMs, and 1.2x on 80GB A100 GPUs for VLMs—will bring significant benefits to the broader community such as robotics.

Current Reinforcement Fine-tuning (RFT) paradigms for Large Language Models (LLMs) suffer from sample inefficiency due to the redundant exposure of identical queries under uniform data sampling. While previous work has explored curriculum learning via heuristic difficulty metrics, these strategies exhibit limitations by neglecting the intrinsic learning signals generated by the model itself, thus leading to suboptimal training regimes. In this paper, we identify a model-inherent signal termed *angle concentration* that effectively reflects an LLM's capacity to learn from specific data. We theoretically and empirically demonstrate a correlation between the angular distribution of token hidden state vectors and the resulting gradient, revealing a learning preference for data exhibiting higher angle concentration. Inspired by this finding, we propose GAIN-RL, a Gradient-driven Angle-Informed Navigated RL framework. By leveraging the model's intrinsic angle concentration signal, GAIN-RL dynamically selects training data in each epoch, ensuring consistently impactful gradient updates and thus significantly enhancing overall training efficiency. Empirical evaluations show that GAIN-RL (GRPO) achieves over a 2.5$\times$ acceleration in training efficiency across diverse mathematical and coding tasks and varying model scales. Furthermore, GAIN-RL (GRPO)'s efficient sampling yields data-efficient training, achieving better performance with half the original data compared to vanilla GRPO with full training data.

Detecting 3D keypoints with semantic consistency is widely used in many scenarios such as pose estimation, shape registration and robotics. Currently, most unsupervised 3D keypoint detection methods focus on the rigid-body objects. However, when faced with deformable objects, the keypoints they identify do not preserve semantic consistency well. In this paper, we introduce an innovative unsupervised keypoint detector Key-Grid for both the rigid-body and deformable objects, which is an autoencoder framework. The encoder predicts keypoints and the decoder utilizes the generated keypoints to reconstruct the objects. Unlike previous work, we leverage the identified keypoint in formation to form a 3D grid feature heatmap called grid heatmap, which is used in the decoder section. Grid heatmap is a novel concept that represents the latent variables for grid points sampled uniformly in the 3D cubic space, where these variables are the shortest distance between the grid points and the “skeleton” connected by keypoint pairs. Meanwhile, we incorporate the information from each layer of the encoder into the decoder section. We conduct an extensive evaluation of Key-Grid on a list of benchmark datasets. Key-Grid achieves the state-of-the-art performance on the semantic consistency and position accuracy of keypoints. Moreover, we demonstrate the robustness of Key-Grid to noise and downsampling. In addition, we achieve SE-(3) invariance of keypoints though generalizing Key-Grid to a SE(3)-invariant backbone.

Neural Architecture Search (NAS) has emerged as a favoured method for unearthing effective neural architectures. Recent development of large models has intensified the demand for faster search speeds and more accurate search results. However, designing large models by NAS is challenging due to the dramatical increase of search space and the associated huge performance evaluation cost. Consider a typical modular search space widely used in NAS, in which a neural architecture consists of $m$ block nodes and a block node has $n$ alternative blocks. Facing the space containing $n^m$ candidate networks, existing NAS methods attempt to find the best one by searching and evaluating candidate networks directly. Different from the general strategy that takes architecture search as a whole problem, we propose a novel divide-and-conquer strategy by making use of the modular nature of the search space. Here, we introduce MathNAS, a general NAS framework based on mathematical programming. In MathNAS, the performances of all possible building blocks in the search space are calculated first, and then the performance of a network is directly predicted based on the performances of its building blocks. Although estimating block performances involves network training, just as what happens for network performance evaluation in existing NAS methods, predicting network performance is completely training-free and thus extremely fast. In contrast to the $n^m$ candidate networks to evaluate in existing NAS methods, which requires training and a formidable computational burden, there are only $m*n$ possible blocks to handle in MathNAS. Therefore, our approach effectively reduces the complexity of network performance evaluation. The superiority of MathNAS is validated on multiple large-scale CV and NLP benchmark datasets. Notably on ImageNet-1k, MathNAS achieves 82.5\% top-1 accuracy, 1.2\% and 0.96\% higher than Swin-T and LeViT-256, respectively. In addition, when deployed on mobile device, MathNAS achieves real-time search and dynamic network switching within 1s (0.4s on TX2 GPU), surpassing baseline dynamic networks in on-device performance.