arXiv subjects
Publications and source records attributed to Lei Song.
We propose a conjecture relevant to Galkin's lower bound conjecture, and verify it for the blow-ups of a four-dimensional quadric at a point or along a projective plane. We also show that Conjecture $\mathcal{O}$ holds in these two cases.
Bayesian optimization (BO) is a popular method for computationally expensive black-box optimization. However, traditional BO methods need to solve new problems from scratch, leading to slow convergence. Recent studies try to extend BO to a transfer learning setup to speed up the optimization, where search space transfer is one of the most promising approaches and has shown impressive performance on many tasks. However, existing search space transfer methods either lack an adaptive mechanism or are not flexible enough, making it difficult to efficiently identify promising search space during the optimization process. In this paper, we propose a search space transfer learning method based on Monte Carlo tree search (MCTS), called MCTS-transfer, to iteratively divide, select, and optimize in a learned subspace. MCTS-transfer can not only provide a well-performing search space for warm-start but also adaptively identify and leverage the information of similar source tasks to reconstruct the search space during the optimization process. Experiments on synthetic functions, real-world problems, Design-Bench and hyper-parameter optimization show that MCTS-transfer can demonstrate superior performance compared to other search space transfer methods under different settings. Our code is available at \url{https://github.com/lamda-bbo/mcts-transfer}.
Black-Box Optimization (BBO) has found successful applications in many fields of science and engineering. Recently, there has been a growing interest in meta-learning particular components of BBO algorithms to speed up optimization and get rid of tedious hand-crafted heuristics. As an extension, learning the entire algorithm from data requires the least labor from experts and can provide the most flexibility. In this paper, we propose RIBBO, a method to reinforce-learn a BBO algorithm from offline data in an end-to-end fashion. RIBBO employs expressive sequence models to learn the optimization histories produced by multiple behavior algorithms and tasks, leveraging the in-context learning ability of large models to extract task information and make decisions accordingly. Central to our method is to augment the optimization histories with \textit{regret-to-go} tokens, which are designed to represent the performance of an algorithm based on cumulative regret over the future part of the histories. The integration of regret-to-go tokens enables RIBBO to automatically generate sequences of query points that satisfy the user-desired regret, which is verified by its universally good empirical performance on diverse problems, including BBO benchmark functions, hyper-parameter optimization and robot control problems.
Retrieval augmented generation has revolutionized large language model (LLM) outputs by providing factual supports. Nevertheless, it struggles to capture all the necessary knowledge for complex reasoning questions. Existing retrieval methods typically divide reference documents into passages, treating them in isolation. These passages, however, are often interrelated, such as passages that are contiguous or share the same keywords. Therefore, it is crucial to recognize such relatedness for enhancing the retrieval process. In this paper, we propose a novel retrieval method, called GNN-Ret, which leverages graph neural networks (GNNs) to enhance retrieval by exploiting the relatedness between passages. Specifically, we first construct a graph of passages by connecting passages that are structure-related or keyword-related. A graph neural network (GNN) is then leveraged to exploit the relationships between passages and improve the retrieval of supporting passages. Furthermore, we extend our method to handle multi-hop reasoning questions using a recurrent graph neural network (RGNN), named RGNN-Ret. At each step, RGNN-Ret integrates the graphs of passages from previous steps, thereby enhancing the retrieval of supporting passages. Extensive experiments on benchmark datasets demonstrate that GNN-Ret achieves higher accuracy for question answering with a single query of LLMs than strong baselines that require multiple queries, and RGNN-Ret further improves accuracy and achieves state-of-the-art performance, with up to 10.4% accuracy improvement on the 2WikiMQA dataset.
The advent of large language models (LLMs) has revolutionized the field of natural language processing, yet they might be attacked to produce harmful content. Despite efforts to ethically align LLMs, these are often fragile and can be circumvented by jailbreaking attacks through optimized or manual adversarial prompts. To address this, we introduce the Information Bottleneck Protector (IBProtector), a defense mechanism grounded in the information bottleneck principle, and we modify the objective to avoid trivial solutions. The IBProtector selectively compresses and perturbs prompts, facilitated by a lightweight and trainable extractor, preserving only essential information for the target LLMs to respond with the expected answer. Moreover, we further consider a situation where the gradient is not visible to be compatible with any LLM. Our empirical evaluations show that IBProtector outperforms current defense methods in mitigating jailbreak attempts, without overly affecting response quality or inference speed. Its effectiveness and adaptability across various attack methods and target LLMs underscore the potential of IBProtector as a novel, transferable defense that bolsters the security of LLMs without requiring modifications to the underlying models.
We study the singularities of secant varieties of smooth projective varieties using methods from birational geometry when the embedding line bundle is sufficiently positive. More precisely, we study the Du Bois complex of secant varieties and its relationship with the sheaves of differential forms. Through this analysis, we give a necessary and sufficient condition for these varieties to have $p$-Du Bois singularities (in a sense that was proposed in [SVV23]). In addition, we show that the singularities of these varieties are never higher rational, by giving a classification of the cases when they are pre-1-rational. From these results, we deduce several consequences, including a Kodaira-Akizuki-Nakano type vanishing result for the reflexive differential forms of the secant varieties.
The accuracy of mapping agricultural fields across large areas is steadily improving with high-resolution satellite imagery and deep learning (DL) models, even in regions where fields are small and geometrically irregular. However, developing effective DL models often requires large, expensive label datasets, typically available only for specific years or locations. This limits the ability to create annual maps essential for agricultural monitoring, as domain shifts occur between years and regions due to changes in farming practices and environmental conditions. The challenge is to design a model flexible enough to account for these shifts without needing yearly labels. While domain adaptation techniques or semi-supervised training are common solutions, we explored enhancing the model's generalization power. Our results indicate that a holistic approach is essential, combining methods to improve generalization. Specifically, using an area-based loss function, such as Tversky-focal loss (TFL), significantly improved predictions across multiple years. The use of different augmentation techniques helped to encode different types of invariance, particularly photometric augmentations encoded invariance to brightness changes, though they increased false positives. The combination of photometric augmentation, TFL loss, and MC-dropout produced the best results, although dropout alone led to more false negatives in subsequent year predictions. Additionally, the choice of input normalization had a significant impact, with the best results obtained when statistics were calculated either locally or across the entire dataset over all bands (lab and gab). We developed a workflow that enabled a U-Net model to generate effective multi-year crop maps over large areas. Our code, available at: https://github.com/agroimpacts/cnn-generalization-enhancement, will be regularly updated with improvements.
With the advent of foundation models, prompt tuning has positioned itself as an important technique for directing model behaviors and eliciting desired responses. Prompt tuning regards selecting appropriate keywords included into the input, thereby adapting to the downstream task without adjusting or fine-tuning the model parameters. There is a wide range of work in prompt tuning, from approaches that directly harness the backpropagated gradient signals from the model, to those employing black-box optimization such as reinforcement learning (RL) methods. Our primary focus is on RLPrompt, which aims to find optimal prompt tokens leveraging soft Q-learning. While the results show promise, we have observed that the prompts frequently appear unnatural, which impedes their interpretability. We address this limitation by using sparse Tsallis entropy regularization, a principled approach to filtering out unlikely tokens from consideration. We extensively evaluate our approach across various tasks, including few-shot text classification, unsupervised text style transfer, and textual inversion from images. The results indicate a notable improvement over baselines, highlighting the efficacy of our approach in addressing the challenges of prompt tuning. Moreover, we show that the prompts discovered using our method are more natural and interpretable compared to those from other baselines.
Offline reinforcement learning (RL) methodologies enforce constraints on the policy to adhere closely to the behavior policy, thereby stabilizing value learning and mitigating the selection of out-of-distribution (OOD) actions during test time. Conventional approaches apply identical constraints for both value learning and test time inference. However, our findings indicate that the constraints suitable for value estimation may in fact be excessively restrictive for action selection during test time. To address this issue, we propose a \textit{Mildly Constrained Evaluation Policy (MCEP)} for test time inference with a more constrained \textit{target policy} for value estimation. Since the \textit{target policy} has been adopted in various prior approaches, MCEP can be seamlessly integrated with them as a plug-in. We instantiate MCEP based on TD3BC (Fujimoto & Gu, 2021), AWAC (Nair et al., 2020) and DQL (Wang et al., 2023) algorithms. The empirical results on D4RL MuJoCo locomotion, high-dimensional humanoid and a set of 16 robotic manipulation tasks show that the MCEP brought significant performance improvement on classic offline RL methods and can further improve SOTA methods. The codes are open-sourced at \url{https://github.com/egg-west/MCEP.git}.
Recent advancements in solving large-scale traveling salesman problems (TSP) utilize the heatmap-guided Monte Carlo tree search (MCTS) paradigm, where machine learning (ML) models generate heatmaps, indicating the probability distribution of each edge being part of the optimal solution, to guide MCTS in solution finding. However, our theoretical and experimental analysis raises doubts about the effectiveness of ML-based heatmap generation. In support of this, we demonstrate that a simple baseline method can outperform complex ML approaches in heatmap generation. Furthermore, we question the practical value of the heatmap-guided MCTS paradigm. To substantiate this, our findings show its inferiority to the LKH-3 heuristic despite the paradigm's reliance on problem-specific, hand-crafted strategies. For the future, we suggest research directions focused on developing more theoretically sound heatmap generation methods and exploring autonomous, generalizable ML approaches for combinatorial problems. The code is available for review: https://github.com/xyfffff/rethink_mcts_for_tsp.
Multi-agent reinforcement learning (MARL) is employed to develop autonomous agents that can learn to adopt cooperative or competitive strategies within complex environments. However, the linear increase in the number of agents leads to a combinatorial explosion of the action space, which may result in algorithmic instability, difficulty in convergence, or entrapment in local optima. While researchers have designed a variety of effective algorithms to compress the action space, these methods also introduce new challenges, such as the need for manually designed prior knowledge or reliance on the structure of the problem, which diminishes the applicability of these techniques. In this paper, we introduce Evolutionary action SPAce Reduction with Knowledge (eSpark), an exploration function generation framework driven by large language models (LLMs) to boost exploration and prune unnecessary actions in MARL. Using just a basic prompt that outlines the overall task and setting, eSpark is capable of generating exploration functions in a zero-shot manner, identifying and pruning redundant or irrelevant state-action pairs, and then achieving autonomous improvement from policy feedback. In reinforcement learning tasks involving inventory management and traffic light control encompassing a total of 15 scenarios, eSpark consistently outperforms the combined MARL algorithm in all scenarios, achieving an average performance gain of 34.4% and 9.9% in the two types of tasks respectively. Additionally, eSpark has proven to be capable of managing situations with a large number of agents, securing a 29.7% improvement in scalability challenges that featured over 500 agents. The code can be found in https://github.com/LiuZhihao2022/eSpark.git.
Explaining deep learning models operating on time series data is crucial in various applications of interest which require interpretable and transparent insights from time series signals. In this work, we investigate this problem from an information theoretic perspective and show that most existing measures of explainability may suffer from trivial solutions and distributional shift issues. To address these issues, we introduce a simple yet practical objective function for time series explainable learning. The design of the objective function builds upon the principle of information bottleneck (IB), and modifies the IB objective function to avoid trivial solutions and distributional shift issues. We further present TimeX++, a novel explanation framework that leverages a parametric network to produce explanation-embedded instances that are both in-distributed and label-preserving. We evaluate TimeX++ on both synthetic and real-world datasets comparing its performance against leading baselines, and validate its practical efficacy through case studies in a real-world environmental application. Quantitative and qualitative evaluations show that TimeX++ outperforms baselines across all datasets, demonstrating a substantial improvement in explanation quality for time series data. The source code is available at \url{https://github.com/zichuan-liu/TimeXplusplus}.
One of the notorious issues for Reinforcement Learning (RL) is poor sample efficiency. Compared to single agent RL, the sample efficiency for Multi-Agent Reinforcement Learning (MARL) is more challenging because of its inherent partial observability, non-stationary training, and enormous strategy space. Although much effort has been devoted to developing new methods and enhancing sample efficiency, we look at the widely used episodic training mechanism. In each training step, tens of frames are collected, but only one gradient step is made. We argue that this episodic training could be a source of poor sample efficiency. To better exploit the data already collected, we propose to increase the frequency of the gradient updates per environment interaction (a.k.a. Replay Ratio or Update-To-Data ratio). To show its generality, we evaluate $3$ MARL methods on $6$ SMAC tasks. The empirical results validate that a higher replay ratio significantly improves the sample efficiency for MARL algorithms. The codes to reimplement the results presented in this paper are open-sourced at https://anonymous.4open.science/r/rr_for_MARL-0D83/.
Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by context variable in the environment, which is uncontrollable by decision makers. In this paper, we focus on the optimization of functions' expectations over continuous context variable, subject to an unknown distribution. To address this problem, we propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. The first algorithm is simpler, which directly optimizes the expectation under the estimated PDF. Considering that the estimated PDF may have high estimation error when the true distribution is complicated, we further propose the second algorithm that optimizes the distributionally robust objective. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective. Furthermore, we conduct numerical experiments to empirically demonstrate the effectiveness of our algorithms.
The development of very large-scale integration (VLSI) technology has posed new challenges for electronic design automation (EDA) techniques in chip floorplanning. During this process, macro placement is an important subproblem, which tries to determine the positions of all macros with the aim of minimizing half-perimeter wirelength (HPWL) and avoiding overlapping. Previous methods include packing-based, analytical and reinforcement learning methods. In this paper, we propose a new black-box optimization (BBO) framework (called WireMask-BBO) for macro placement, by using a wire-mask-guided greedy procedure for objective evaluation. Equipped with different BBO algorithms, WireMask-BBO empirically achieves significant improvements over previous methods, i.e., achieves significantly shorter HPWL by using much less time. Furthermore, it can fine-tune existing placements by treating them as initial solutions, which can bring up to 50% improvement in HPWL. WireMask-BBO has the potential to significantly improve the quality and efficiency of chip floorplanning, which makes it appealing to researchers and practitioners in EDA and will also promote the application of BBO. Our code is available at https://github.com/lamda-bbo/WireMask-BBO.
For industrial control, developing high-performance controllers with few samples and low technical debt is appealing. Foundation models, possessing rich prior knowledge obtained from pre-training with Internet-scale corpus, have the potential to be a good controller with proper prompts. In this paper, we take HVAC (Heating, Ventilation, and Air Conditioning) building control as an example to examine the ability of GPT-4 (one of the first-tier foundation models) as the controller. To control HVAC, we wrap the task as a language game by providing text including a short description for the task, several selected demonstrations, and the current observation to GPT-4 on each step and execute the actions responded by GPT-4. We conduct series of experiments to answer the following questions: 1)~How well can GPT-4 control HVAC? 2)~How well can GPT-4 generalize to different scenarios for HVAC control? 3) How different parts of the text context affect the performance? In general, we found GPT-4 achieves the performance comparable to RL methods with few samples and low technical debt, indicating the potential of directly applying foundation models to industrial control tasks.
Multi-agent reinforcement learning (MARL) models multiple agents that interact and learn within a shared environment. This paradigm is applicable to various industrial scenarios such as autonomous driving, quantitative trading, and inventory management. However, applying MARL to these real-world scenarios is impeded by many challenges such as scaling up, complex agent interactions, and non-stationary dynamics. To incentivize the research of MARL on these challenges, we develop MABIM (Multi-Agent Benchmark for Inventory Management) which is a multi-echelon, multi-commodity inventory management simulator that can generate versatile tasks with these different challenging properties. Based on MABIM, we evaluate the performance of classic operations research (OR) methods and popular MARL algorithms on these challenging tasks to highlight their weaknesses and potential.
The Swin transformer has recently attracted attention in medical image analysis due to its computational efficiency and long-range modeling capability. Owing to these properties, the Swin Transformer is suitable for establishing more distant relationships between corresponding voxels in different positions in complex abdominal image registration tasks. However, the registration models based on transformers combine multiple voxels into a single semantic token. This merging process limits the transformers to model and generate coarse-grained spatial information. To address this issue, we propose Recovery Feature Resolution Network (RFRNet), which allows the transformer to contribute fine-grained spatial information and rich semantic correspondences to higher resolution levels. Furthermore, shifted window partitioning operations are inflexible, indicating that they cannot perceive the semantic information over uncertain distances and automatically bridge the global connections between windows. Therefore, we present a Weighted Window Attention (WWA) to build global interactions between windows automatically. It is implemented after the regular and cyclic shift window partitioning operations within the Swin transformer block. The proposed unsupervised deformable image registration model, named RFR-WWANet, detects the long-range correlations, and facilitates meaningful semantic relevance of anatomical structures. Qualitative and quantitative results show that RFR-WWANet achieves significant improvements over the current state-of-the-art methods. Ablation experiments demonstrate the effectiveness of the RFRNet and WWA designs. Our code is available at \url{https://github.com/MingR-Ma/RFR-WWANet}.