The explosion of Time Series (TS) data, driven by advancements in technology, necessitates sophisticated analytical methods. Modern management systems increasingly rely on analyzing this data, highlighting the importance of effcient processing techniques. State-of-the-art Machine Learning (ML) approaches for TS analysis and forecasting are becoming prevalent. This paper briefly describes and compiles suitable algorithms for TS regression task. We compare these algorithms against each other and the classic ARIMA method using diverse datasets: complete data, data with outliers, and data with missing values. The focus is on forecasting accuracy, particularly for long-term predictions. This research aids in selecting the most appropriate algorithm based on forecasting needs and data characteristics.

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles to enhance predictions when dealing with sparse, noisy, or incomplete data? Physics-Informed Neural Networks (PINNs) put this idea into practice by incorporating physical equations, such as Partial Differential Equations (PDEs), as soft constraints. This guidance helps the networks find solutions that align with established laws. Recently, researchers have expanded this framework to include Bayesian NNs (BNNs), which allow for uncertainty quantification while still adhering to physical principles. But what happens when the governing equations of a system are not known? In this work, we introduce methods to automatically extract PDEs from historical data. We then integrate these learned equations into three different modeling approaches: PINNs, Bayesian-PINNs (B-PINNs), and Bayesian Linear Regression (BLR). To assess these frameworks, we evaluate them on a real-world Multivariate Time Series (MTS) dataset. We compare their effectiveness in forecasting future states under different scenarios: with and without PDE constraints and accuracy considerations. This research aims to bridge the gap between data-driven discovery and physics-guided learning, providing valuable insights for practical applications.

The recent DeepSeek-R1 demonstrated how reinforcement learning with simple rule-based reward can enable autonomous development of complex reasoning in large language models, characterized by the "aha moment", in which the model manifest self-reflection and increased response length during training. However, attempts to extend this success to multimodal reasoning often failed to reproduce these key characteristics. In this report, we present the first successful replication of these emergent characteristics for multimodal reasoning on only a non-SFT 2B model. Starting with Qwen2-VL-2B and applying reinforcement learning directly on the SAT dataset, our model achieves 59.47% accuracy on CVBench, outperforming the base model by approximately ~30% and exceeding both SFT setting by ~2%. In addition, we share our failed attempts and insights in attempting to achieve R1-like reasoning using RL with instruct models, aiming to shed light on the challenges involved. Our key observations include: (1) applying RL on instruct model often results in trivial reasoning trajectories, and (2) naive length reward are ineffective in eliciting reasoning capabilities.

Dataset Distillation has emerged as a technique for compressing large datasets into smaller synthetic counterparts, facilitating downstream training tasks. In this paper, we study the impact of bias inside the original dataset on the performance of dataset distillation. With a comprehensive empirical evaluation on canonical datasets with color, corruption and background biases, we found that color and background biases in the original dataset will be amplified through the distillation process, resulting in a notable decline in the performance of models trained on the distilled dataset, while corruption bias is suppressed through the distillation process. To reduce bias amplification in dataset distillation, we introduce a simple yet highly effective approach based on a sample reweighting scheme utilizing kernel density estimation. Empirical results on multiple real-world and synthetic datasets demonstrate the effectiveness of the proposed method. Notably, on CMNIST with 5% bias-conflict ratio and IPC 50, our method achieves 91.5% test accuracy compared to 23.8% from vanilla DM, boosting the performance by 67.7%, whereas applying state-of-the-art debiasing method on the same dataset only achieves 53.7% accuracy. Our findings highlight the importance of addressing biases in dataset distillation and provide a promising avenue to address bias amplification in the process.

Large Language Models (LLMs) have demonstrated remarkable performance in solving math problems, a hallmark of human intelligence. Despite high success rates on current benchmarks; however, these often feature simple problems with only one or two unknowns, which do not sufficiently challenge their reasoning capacities. This paper introduces a novel benchmark, BeyondX, designed to address these limitations by incorporating problems with multiple unknowns. Recognizing the challenges in proposing multi-unknown problems from scratch, we developed BeyondX using an innovative automated pipeline that progressively increases complexity by expanding the number of unknowns in simpler problems. Empirical study on BeyondX reveals that the performance of existing LLMs, even those fine-tuned specifically on math tasks, significantly decreases as the number of unknowns increases - with a performance drop of up to 70\% observed in GPT-4. To tackle these challenges, we propose the Formulate-and-Solve strategy, a generalized prompting approach that effectively handles problems with an arbitrary number of unknowns. Our findings reveal that this strategy not only enhances LLM performance on the BeyondX benchmark but also provides deeper insights into the computational limits of LLMs when faced with more complex mathematical challenges.

Large Language Models (LLMs) exhibit strong generalization capabilities to novel tasks when prompted with language instructions and in-context demos. Since this ability sensitively depends on the quality of prompts, various methods have been explored to automate the instruction design. While these methods demonstrated promising results, they also restricted the searched prompt to one instruction. Such simplification significantly limits their capacity, as a single demo-free instruction might not be able to cover the entire complex problem space of the targeted task. To alleviate this issue, we adopt the Mixture-of-Expert paradigm and divide the problem space into a set of sub-regions; Each sub-region is governed by a specialized expert, equipped with both an instruction and a set of demos. A two-phase process is developed to construct the specialized expert for each region: (1) demo assignment: Inspired by the theoretical connection between in-context learning and kernel regression, we group demos into experts based on their semantic similarity; (2) instruction assignment: A region-based joint search of an instruction per expert complements the demos assigned to it, yielding a synergistic effect. The resulting method, codenamed Mixture-of-Prompts (MoP), achieves an average win rate of 81% against prior arts across several major benchmarks.

This paper introduces the first gradient-based framework for prompt optimization in text-to-image diffusion models. We formulate prompt engineering as a discrete optimization problem over the language space. Two major challenges arise in efficiently finding a solution to this problem: (1) Enormous Domain Space: Setting the domain to the entire language space poses significant difficulty to the optimization process. (2) Text Gradient: Efficiently computing the text gradient is challenging, as it requires backpropagating through the inference steps of the diffusion model and a non-differentiable embedding lookup table. Beyond the problem formulation, our main technical contributions lie in solving the above challenges. First, we design a family of dynamically generated compact subspaces comprised of only the most relevant words to user input, substantially restricting the domain space. Second, we introduce "Shortcut Text Gradient" -- an effective replacement for the text gradient that can be obtained with constant memory and runtime. Empirical evaluation on prompts collected from diverse sources (DiffusionDB, ChatGPT, COCO) suggests that our method can discover prompts that substantially improve (prompt enhancement) or destroy (adversarial attack) the faithfulness of images generated by the text-to-image diffusion model.

Diffusion models have achieved remarkable success in text-to-image generation tasks; however, the role of initial noise has been rarely explored. In this study, we identify specific regions within the initial noise image, termed trigger patches, that play a key role for object generation in the resulting images. Notably, these patches are ``universal'' and can be generalized across various positions, seeds, and prompts. To be specific, extracting these patches from one noise and injecting them into another noise leads to object generation in targeted areas. We identify these patches by analyzing the dispersion of object bounding boxes across generated images, leading to the development of a posterior analysis technique. Furthermore, we create a dataset consisting of Gaussian noises labeled with bounding boxes corresponding to the objects appearing in the generated images and train a detector that identifies these patches from the initial noise. To explain the formation of these patches, we reveal that they are outliers in Gaussian noise, and follow distinct distributions through two-sample tests. Finally, we find the misalignment between prompts and the trigger patch patterns can result in unsuccessful image generations. The study proposes a reject-sampling strategy to obtain optimal noise, aiming to improve prompt adherence and positional diversity in image generation.

The safety alignment of Large Language Models (LLMs) is vulnerable to both manual and automated jailbreak attacks, which adversarially trigger LLMs to output harmful content. However, current methods for jailbreaking LLMs, which nest entire harmful prompts, are not effective at concealing malicious intent and can be easily identified and rejected by well-aligned LLMs. This paper discovers that decomposing a malicious prompt into separated sub-prompts can effectively obscure its underlying malicious intent by presenting it in a fragmented, less detectable form, thereby addressing these limitations. We introduce an automatic prompt \textbf{D}ecomposition and \textbf{R}econstruction framework for jailbreak \textbf{Attack} (DrAttack). DrAttack includes three key components: (a) `Decomposition' of the original prompt into sub-prompts, (b) `Reconstruction' of these sub-prompts implicitly by in-context learning with semantically similar but harmless reassembling demo, and (c) a `Synonym Search' of sub-prompts, aiming to find sub-prompts' synonyms that maintain the original intent while jailbreaking LLMs. An extensive empirical study across multiple open-source and closed-source LLMs demonstrates that, with a significantly reduced number of queries, DrAttack obtains a substantial gain of success rate over prior SOTA prompt-only attackers. Notably, the success rate of 78.0\% on GPT-4 with merely 15 queries surpassed previous art by 33.1\%. The project is available at https://github.com/xirui-li/DrAttack.

Federated learning~(FL) has recently attracted increasing attention from academia and industry, with the ultimate goal of achieving collaborative training under privacy and communication constraints. Existing iterative model averaging based FL algorithms require a large number of communication rounds to obtain a well-performed model due to extremely unbalanced and non-i.i.d data partitioning among different clients. Thus, we propose FedDM to build the global training objective from multiple local surrogate functions, which enables the server to gain a more global view of the loss landscape. In detail, we construct synthetic sets of data on each client to locally match the loss landscape from original data through distribution matching. FedDM reduces communication rounds and improves model quality by transmitting more informative and smaller synthesized data compared with unwieldy model weights. We conduct extensive experiments on three image classification datasets, and results show that our method can outperform other FL counterparts in terms of efficiency and model performance. Moreover, we demonstrate that FedDM can be adapted to preserve differential privacy with Gaussian mechanism and train a better model under the same privacy budget.