Large language models (LLMs) can solve an increasing number of complex reasoning tasks while making surprising mistakes in basic numerical understanding and processing (such as 9.11 > 9.9). The latter ability is essential for tackling complex arithmetic and mathematical problems and serves as a foundation for most reasoning tasks, but previous work paid little attention to it or only discussed several restricted tasks (like integer addition). In this paper, we comprehensively investigate the numerical understanding and processing ability (NUPA) of LLMs. Firstly, we introduce a benchmark covering four common numerical representations and 17 distinct numerical tasks in four major categories, resulting in 41 meaningful combinations in total. These tasks are derived from primary and secondary education curricula, encompassing nearly all everyday numerical understanding and processing scenarios, and the rules of these tasks are very simple and clear. Through the benchmark, we find that current LLMs fail frequently in many of the tasks. To study the problem, we train small models with existing and potential techniques for enhancing NUPA (such as tokenizers, PEs, and number formats), comprehensively evaluating their effectiveness using our testbed. We also finetune practical-scale LLMs on our proposed NUPA tasks and find that 1) naive finetuning can improve NUPA a lot on many but not all tasks, and 2) surprisingly, techniques designed to enhance NUPA prove ineffective for finetuning pretrained models. We further explore the impact of chain-of-thought techniques on NUPA. Our work provides a more detailed and comprehensive understanding of NUPA in LLMs. Our benchmark and code are released at https://github.com/GraphPKU/number_cookbook.

Reinforcement Learning from Human Feedback (RLHF) has proven highly effective in aligning Large Language Models (LLMs) with human preferences. However, the original RLHF typically optimizes under an overall reward, which can lead to a suboptimal learning process. This limitation stems from RLHF's lack of awareness regarding which specific tokens should be reinforced or suppressed. Moreover, conflicts in supervision can arise, for instance, when a chosen response includes erroneous tokens, while a rejected response contains accurate elements. To rectify these shortcomings, increasing dense reward methods, such as step-wise and token-wise RLHF, have been proposed. However, these existing methods are limited to specific tasks (like mathematics). In this paper, we propose the "Adaptive Message-wise RLHF" method, which robustly applies to various tasks. By defining pivot tokens as key indicators, our approach adaptively identifies essential information and converts sequence-level supervision into finegrained, subsequence-level supervision. Experiments demonstrate that our method can be integrated into various training methods, significantly mitigating hallucinations and catastrophic forgetting problems, while outperforming other methods on multiple evaluation metrics. Our method improves the success rate on adversarial samples by 10% compared to the samplewise approach, and achieves a 1.3% improvement on evaluation benchmarks such as MMLU, GSM8K, HumanEval, etc. In recent years, generative AI models have made significant achievements, with preference alignment by reinforcement learning playing an essential role in this progress (Ouyang et al., 2022; Touvron et al., 2023; Rafailov et al., 2024; Dubey et al., 2024; Yang et al., 2024a; OpenAI et al., 2024).

Recent work in language modeling has raised the possibility of self-improvement, where a language models evaluates and refines its own generations to achieve higher performance without external feedback. It is impossible for this self-improvement to create information that is not already in the model, so why should we expect that this will lead to improved capabilities? We offer a new perspective on the capabilities of self-improvement through a lens we refer to as sharpening. Motivated by the observation that language models are often better at verifying response quality than they are at generating correct responses, we formalize self-improvement as using the model itself as a verifier during post-training in order to ``sharpen'' the model to one placing large mass on high-quality sequences, thereby amortizing the expensive inference-time computation of generating good sequences. We begin by introducing a new statistical framework for sharpening in which the learner aims to sharpen a pre-trained base policy via sample access, and establish fundamental limits. Then we analyze two natural families of self-improvement algorithms based on SFT and RLHF. We find that (i) the SFT-based approach is minimax optimal whenever the initial model has sufficient coverage, but (ii) the RLHF-based approach can improve over SFT-based self-improvement by leveraging online exploration, bypassing the need for coverage. Finally, we empirically validate the sharpening mechanism via inference-time and amortization experiments. We view these findings as a starting point toward a foundational understanding that can guide the design and evaluation of self-improvement algorithms.

Investigating the marginal causal effect of an intervention on an outcome from complex data remains challenging due to the inflexibility of employed models and the lack of complexity in causal benchmark datasets, which often fail to reproduce intricate real-world data patterns. In this paper we introduce Frugal Flows, a novel likelihood-based machine learning model that uses normalising flows to flexibly learn the data-generating process, while also directly inferring the marginal causal quantities from observational data. We propose that these models are exceptionally well suited for generating synthetic data to validate causal methods. They can create synthetic datasets that closely resemble the empirical dataset, while automatically and exactly satisfying a user-defined average treatment effect. To our knowledge, Frugal Flows are the first generative model to both learn flexible data representations and also exactly parameterise quantities such as the average treatment effect and the degree of unobserved confounding. We demonstrate the above with experiments on both simulated and real-world datasets.

FedProx is a simple yet effective federated learning method that enables model personalization via regularization. Despite remarkable success in practice, a rigorous analysis of how such a regularization provably improves the statistical accuracy of each client's local model hasn't been fully established. Setting the regularization strength heuristically presents a risk, as an inappropriate choice may even degrade accuracy. This work fills in the gap by analyzing the effect of regularization on statistical accuracy, thereby providing a theoretical guideline for setting the regularization strength for achieving personalization. We prove that by adaptively choosing the regularization strength under different statistical heterogeneity, FedProx can consistently outperform pure local training and achieve a minimaxoptimal statistical rate. In addition, to shed light on resource allocation, we design an algorithm, provably showing that stronger personalization reduces communication complexity without increasing the computation cost overhead. Finally, our theory is validated on both synthetic and real-world datasets and its generalizability is verified in a non-convex setting. Federated Learning (FL) has emerged as an attractive framework for aggregating distributed data, enabling clients to collaboratively train a shared global model while preserving data privacy. In the currently prevalent paradigm (McMahan et al., 2017), FL is formulated as a finite sum minimization problem focusing on a single shared model. Nevertheless, it has been well recognized that one of the key challenges in FL is the statistical heterogeneity of the client datasets. As the participants collect their own local data, it often reflects client-specific characteristics and is not identically distributed. With high statistical heterogeneity, training a single model for all clients by minimizing their average in-sample loss becomes questionable. To address this challenge, one solution is to relax the common model constraint and solve alternatively the following objective in FedProx (Li et al., 2020a): ( min p The smaller λ is, the weaker the coupling of the local models the formulation would enforce thus the higher personalization is.

Large language models have emerged as powerful instruments that can automate reasoning process in a host of domains ranging from Olympiad level math problem solving [1] to code generation [2] and financial planning [3]. LLMs have seen widespread adoption among people to automate and refine tasks involving decision making, logical thinking and critical reasoning. However, despite such promising results on numerous benchmarks, LLMs still possess surprising knowledge gaps caused due to a host of reasons varying from engineering heuristics such as tokenization [4] to limitations in the training data itself, such as data bias or a lack of up-to-date information. Furthermore, due to being trained on extensive data accumulated and refined by humans over the years, these LLMs present grounds for inherent cognitive bias as characterized in humans [5]. While there have been promising demonstrations of GPT-based models on tasks involving creativity [6] and critical thinking [7], slight variations in input prompt requests can lead to vastly different output responses[8]. Furthermore, due to being next token predictors scaled to a huge text, the world models formed by language models possess knowledge gaps unapparent on the surface level.

Advancements in artificial intelligence, machine learning, and deep learning have catalyzed the transformation of big data analytics and management into pivotal domains for research and application. This work explores the theoretical foundations, methodological advancements, and practical implementations of these technologies, emphasizing their role in uncovering actionable insights from massive, high-dimensional datasets. The study presents a systematic overview of data preprocessing techniques, including data cleaning, normalization, integration, and dimensionality reduction, to prepare raw data for analysis. Core analytics methodologies such as classification, clustering, regression, and anomaly detection are examined, with a focus on algorithmic innovation and scalability. Furthermore, the text delves into state-of-the-art frameworks for data mining and predictive modeling, highlighting the role of neural networks, support vector machines, and ensemble methods in tackling complex analytical challenges. Special emphasis is placed on the convergence of big data with distributed computing paradigms, including cloud and edge computing, to address challenges in storage, computation, and real-time analytics. The integration of ethical considerations, including data privacy and compliance with global standards, ensures a holistic perspective on data management. Practical applications across healthcare, finance, marketing, and policy-making illustrate the real-world impact of these technologies. Through comprehensive case studies and Python-based implementations, this work equips researchers, practitioners, and data enthusiasts with the tools to navigate the complexities of modern data analytics. It bridges the gap between theory and practice, fostering the development of innovative solutions for managing and leveraging data in the era of artificial intelligence.

With the wide application of deep neural network models in various computer vision tasks, there has been a proliferation of adversarial example generation strategies aimed at deeply exploring model security. However, existing adversarial training defense models, which rely on single or limited types of attacks under a one-time learning process, struggle to adapt to the dynamic and evolving nature of attack methods. Therefore, to achieve defense performance improvements for models in long-term applications, we propose a novel Sustainable Self-Evolution Adversarial Training (SSEAT) framework. Specifically, we introduce a continual adversarial defense pipeline to realize learning from various kinds of adversarial examples across multiple stages. Additionally, to address the issue of model catastrophic forgetting caused by continual learning from ongoing novel attacks, we propose an adversarial data replay module to better select more diverse and key relearning data. Furthermore, we design a consistency regularization strategy to encourage current defense models to learn more from previously trained ones, guiding them to retain more past knowledge and maintain accuracy on clean samples. Extensive experiments have been conducted to verify the efficacy of the proposed SSEAT defense method, which demonstrates superior defense performance and classification accuracy compared to competitors.

In self-supervised robot learning, robots actively explore their environments and generate data by acting on entities in the environment. Therefore, an exploration policy is desired that ensures sample efficiency to minimize robot execution costs while still providing accurate learning. For this purpose, the robotic community has adopted Intrinsic Motivation (IM)-based approaches such as Learning Progress (LP). On the machine learning front, Active Learning (AL) has been used successfully, especially for classification tasks. In this work, we develop a novel AL framework geared towards robotics regression tasks, such as action-effect prediction and, more generally, for world model learning, which we call MUSEL - Model Uncertainty for Sample Efficient Learning. MUSEL aims to extract model uncertainty from the total uncertainty estimate given by a suitable learning engine by making use of earning progress and input diversity and use it to improve sample efficiency beyond the state-of-the-art action-effect prediction methods. We demonstrate the feasibility of our model by using a Stochastic Variational Gaussian Process (SVGP) as the learning engine and testing the system on a set of robotic experiments in simulation. The efficacy of MUSEL is demonstrated by comparing its performance to standard methods used in robot action-effect learning. In a robotic tabletop environment in which a robot manipulator is tasked with learning the effect of its actions, the experiments show that MUSEL facilitates higher accuracy in learning action effects while ensuring sample efficiency.

Multimodal large language models (LLMs) have demonstrated impressive capabilities in generating high-quality images from textual instructions. However, their performance in generating scientific images--a critical application for accelerating scientific progress--remains underexplored. In this work, we address this gap by introducing ScImage, a benchmark designed to evaluate the multimodal capabilities of LLMs in generating scientific images from textual descriptions. ScImage assesses three key dimensions of understanding: spatial, numeric, and attribute comprehension, as well as their combinations, focusing on the relationships between scientific objects (e.g., squares, circles). We evaluate five models, GPT-4o, Llama, AutomaTikZ, Dall-E, and StableDiffusion, using two modes of output generation: code-based outputs (Python, TikZ) and direct raster image generation. Additionally, we examine four different input languages: English, German, Farsi, and Chinese. Our evaluation, conducted with 11 scientists across three criteria (correctness, relevance, and scientific accuracy), reveals that while GPT-4o produces outputs of decent quality for simpler prompts involving individual dimensions such as spatial, numeric, or attribute understanding in isolation, all models face challenges in this task, especially for more complex prompts.