GeoGPT4V: Towards Geometric Multi-modal Large Language Models with Geometric Image Generation

Large language models have seen widespread adoption in math problem-solving. However, in geometry problems that usually require visual aids for better understanding, even the most advanced multi-modal models currently still face challenges in effectively using image information. High-quality data is crucial for enhancing the geometric capabilities of multi-modal models, yet existing open-source datasets and related efforts are either too challenging for direct model learning or suffer from misalignment between text and images. To overcome this issue, we introduce a novel pipeline that leverages GPT-4 and GPT-4V to generate relatively basic geometry problems with aligned text and images, facilitating model learning. We have produced a dataset of 4.9K geometry problems and combined it with 19K open-source data to form our GeoGPT4V dataset. Experimental results demonstrate that the GeoGPT4V dataset significantly improves the geometry performance of various models on the MathVista and MathVision benchmarks. The code is available at https://github.com/Lanyu0303/GeoGPT4V_Project

Enhancing the Resilience of Graph Neural Networks to Topological Perturbations in Sparse Graphs

Graph neural networks (GNNs) have been extensively employed in node classification. Nevertheless, recent studies indicate that GNNs are vulnerable to topological perturbations, such as adversarial attacks and edge disruptions. Considerable efforts have been devoted to mitigating these challenges. For example, pioneering Bayesian methodologies, including GraphSS and LlnDT, incorporate Bayesian label transitions and topology-based label sampling to strengthen the robustness of GNNs. However, GraphSS is hindered by slow convergence, while LlnDT faces challenges in sparse graphs. To overcome these limitations, we propose a novel label inference framework, TraTopo, which combines topology-driven label propagation, Bayesian label transitions, and link analysis via random walks. TraTopo significantly surpasses its predecessors on sparse graphs by utilizing random walk sampling, specifically targeting isolated nodes for link prediction, thus enhancing its effectiveness in topological sampling contexts. Additionally, TraTopo employs a shortest-path strategy to refine link prediction, thereby reducing predictive overhead and improving label inference accuracy. Empirical evaluations highlight TraTopo's superiority in node classification, significantly exceeding contemporary GCN models in accuracy.

Enhancing Sufficient Dimension Reduction via Hellinger Correlation

In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated by the recent introduction of the Hellinger correlation as a dependency measure. Utilizing this measure, we develop a method capable of effectively detecting the dimension reduction subspace, complete with theoretical justification. Through extensive numerical experiments, we demonstrate that our proposed method significantly enhances and outperforms existing SDR methods. This improvement is largely attributed to our proposed method's deeper understanding of data dependencies and the refinement of existing SDR techniques.

Demystify Mamba in Vision: A Linear Attention Perspective

Mamba is an effective state space model with linear computation complexity. It has recently shown impressive efficiency in dealing with high-resolution inputs across various vision tasks. In this paper, we reveal that the powerful Mamba model shares surprising similarities with linear attention Transformer, which typically underperform conventional Transformer in practice. By exploring the similarities and disparities between the effective Mamba and subpar linear attention Transformer, we provide comprehensive analyses to demystify the key factors behind Mamba's success. Specifically, we reformulate the selective state space model and linear attention within a unified formulation, rephrasing Mamba as a variant of linear attention Transformer with six major distinctions: input gate, forget gate, shortcut, no attention normalization, single-head, and modified block design. For each design, we meticulously analyze its pros and cons, and empirically evaluate its impact on model performance in vision tasks. Interestingly, the results highlight the forget gate and block design as the core contributors to Mamba's success, while the other four designs are less crucial. Based on these findings, we propose a Mamba-Like Linear Attention (MLLA) model by incorporating the merits of these two key designs into linear attention. The resulting model outperforms various vision Mamba models in both image classification and high-resolution dense prediction tasks, while enjoying parallelizable computation and fast inference speed. Code is available at https://github.com/LeapLabTHU/MLLA.

ConvLLaVA: Hierarchical Backbones as Visual Encoder for Large Multimodal Models

High-resolution Large Multimodal Models (LMMs) encounter the challenges of excessive visual tokens and quadratic visual complexity. Current high-resolution LMMs address the quadratic complexity while still generating excessive visual tokens. However, the redundancy in visual tokens is the key problem as it leads to more substantial compute. To mitigate this issue, we propose ConvLLaVA, which employs ConvNeXt, a hierarchical backbone, as the visual encoder of LMM to replace Vision Transformer (ViT). ConvLLaVA compresses high-resolution images into information-rich visual features, effectively preventing the generation of excessive visual tokens. To enhance the capabilities of ConvLLaVA, we propose two critical optimizations. Since the low-resolution pretrained ConvNeXt underperforms when directly applied on high resolution, we update it to bridge the gap. Moreover, since ConvNeXt's original compression ratio is inadequate for much higher resolution inputs, we train a successive stage to further compress the visual tokens, thereby reducing redundancy. These optimizations enable ConvLLaVA to support inputs of 1536x1536 resolution generating only 576 visual tokens, capable of handling images of arbitrary aspect ratios. Experimental results demonstrate that our method achieves competitive performance with state-of-the-art models on mainstream benchmarks. The ConvLLaVA model series are publicly available at https://github.com/alibaba/conv-llava.

Dreamer XL: Towards High-Resolution Text-to-3D Generation via Trajectory Score Matching

In this work, we propose a novel Trajectory Score Matching (TSM) method that aims to solve the pseudo ground truth inconsistency problem caused by the accumulated error in Interval Score Matching (ISM) when using the Denoising Diffusion Implicit Models (DDIM) inversion process. Unlike ISM which adopts the inversion process of DDIM to calculate on a single path, our TSM method leverages the inversion process of DDIM to generate two paths from the same starting point for calculation. Since both paths start from the same starting point, TSM can reduce the accumulated error compared to ISM, thus alleviating the problem of pseudo ground truth inconsistency. TSM enhances the stability and consistency of the model's generated paths during the distillation process. We demonstrate this experimentally and further show that ISM is a special case of TSM. Furthermore, to optimize the current multi-stage optimization process from high-resolution text to 3D generation, we adopt Stable Diffusion XL for guidance. In response to the issues of abnormal replication and splitting caused by unstable gradients during the 3D Gaussian splatting process when using Stable Diffusion XL, we propose a pixel-by-pixel gradient clipping method. Extensive experiments show that our model significantly surpasses the state-of-the-art models in terms of visual quality and performance. Code: \url{https://github.com/xingy038/Dreamer-XL}.

Fine-Grained Embedding Dimension Optimization During Training for Recommender Systems

Huge embedding tables in modern Deep Learning Recommender Models (DLRM) require prohibitively large memory during training and inference. Aiming to reduce the memory footprint of training, this paper proposes FIne-grained In-Training Embedding Dimension optimization (FIITED). Given the observation that embedding vectors are not equally important, FIITED adjusts the dimension of each individual embedding vector continuously during training, assigning longer dimensions to more important embeddings while adapting to dynamic changes in data. A novel embedding storage system based on virtually-hashed physically-indexed hash tables is designed to efficiently implement the embedding dimension adjustment and effectively enable memory saving. Experiments on two industry models show that FIITED is able to reduce the size of embeddings by more than 65% while maintaining the trained model's quality, saving significantly more memory than a state-of-the-art in-training embedding pruning method. On public click-through rate prediction datasets, FIITED is able to prune up to 93.75%-99.75% embeddings without significant accuracy loss.

Provably Convergent Policy Optimization via Metric-aware Trust Region Methods

Trust-region methods based on Kullback-Leibler divergence are pervasively used to stabilize policy optimization in reinforcement learning. In this paper, we exploit more flexible metrics and examine two natural extensions of policy optimization with Wasserstein and Sinkhorn trust regions, namely Wasserstein policy optimization (WPO) and Sinkhorn policy optimization (SPO). Instead of restricting the policy to a parametric distribution class, we directly optimize the policy distribution and derive their closed-form policy updates based on the Lagrangian duality. Theoretically, we show that WPO guarantees a monotonic performance improvement, and SPO provably converges to WPO as the entropic regularizer diminishes. Moreover, we prove that with a decaying Lagrangian multiplier to the trust region constraint, both methods converge to global optimality. Experiments across tabular domains, robotic locomotion, and continuous control tasks further demonstrate the performance improvement of both approaches, more robustness of WPO to sample insufficiency, and faster convergence of SPO, over state-of-art policy gradient methods.

Towards Optimal Pricing of Demand Response -- A Nonparametric Constrained Policy Optimization Approach

Demand response (DR) has been demonstrated to be an effective method for reducing peak load and mitigating uncertainties on both the supply and demand sides of the electricity market. One critical question for DR research is how to appropriately adjust electricity prices in order to shift electrical load from peak to off-peak hours. In recent years, reinforcement learning (RL) has been used to address the price-based DR problem because it is a model-free technique that does not necessitate the identification of models for end-use customers. However, the majority of RL methods cannot guarantee the stability and optimality of the learned pricing policy, which is undesirable in safety-critical power systems and may result in high customer bills. In this paper, we propose an innovative nonparametric constrained policy optimization approach that improves optimality while ensuring stability of the policy update, by removing the restrictive assumption on policy representation that the majority of the RL literature adopts: the policy must be parameterized or fall into a certain distribution class. We derive a closed-form expression of optimal policy update for each iteration and develop an efficient on-policy actor-critic algorithm to address the proposed constrained policy optimization problem. The experiments on two DR cases show the superior performance of our proposed nonparametric constrained policy optimization method compared with state-of-the-art RL algorithms.

Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Control

In this paper, we present a Distributionally Robust Markov Decision Process (DRMDP) approach for addressing the dynamic epidemic control problem. The Susceptible-Exposed-Infectious-Recovered (SEIR) model is widely used to represent the stochastic spread of infectious diseases, such as COVID-19. While Markov Decision Processes (MDP) offers a mathematical framework for identifying optimal actions, such as vaccination and transmission-reducing intervention, to combat disease spreading according to the SEIR model. However, uncertainties in these scenarios demand a more robust approach that is less reliant on error-prone assumptions. The primary objective of our study is to introduce a new DRMDP framework that allows for an ambiguous distribution of transition dynamics. Specifically, we consider the worst-case distribution of these transition probabilities within a decision-dependent ambiguity set. To overcome the computational complexities associated with policy determination, we propose an efficient Real-Time Dynamic Programming (RTDP) algorithm that is capable of computing optimal policies based on the reformulated DRMDP model in an accurate, timely, and scalable manner. Comparative analysis against the classic MDP model demonstrates that the DRMDP achieves a lower proportion of infections and susceptibilities at a reduced cost.