Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian inference. We show that for a large class of transport maps $T$, there exists a time-dependent ODE velocity field realizing a straight-line interpolation $(1-t)x + tT(x)$, $t \in [0,1]$, of the displacement induced by the map. Moreover, we show that such velocity fields are minimizers of a training objective containing a specific minimum-energy regularization. We then derive explicit upper bounds for the $C^k$ norm of the velocity field that are polynomial in the $C^k$ norm of the corresponding transport map $T$; in the case of triangular (Knothe--Rosenblatt) maps, we also show that these bounds are polynomial in the $C^k$ norms of the associated source and target densities. Combining these results with stability arguments for distribution approximation via ODEs, we show that Wasserstein or Kullback--Leibler approximation of the target distribution to any desired accuracy $\epsilon > 0$ can be achieved by a deep neural network representation of the velocity field whose size is bounded explicitly in terms of $\epsilon$, the dimension, and the smoothness of the source and target densities. The same neural network ansatz yields guarantees on the value of the regularized training objective.

This paper presents a quantitative approach to studying linguistic and cultural change in China during the first half of the twentieth century, a period that remains understudied in computational humanities research. The dramatic changes in Chinese language and culture during this time call for greater reflection on the tools and methods used for text analysis. This preliminary study offers a framework for analyzing Chinese texts from the late nineteenth and twentieth centuries, demonstrating how established methods such as word counts and word embeddings can provide new historical insights into the complex negotiations between Western modernity and Chinese cultural discourse.

High-quality, large-scale instructions are crucial for aligning large language models (LLMs), however, there is a severe shortage of instruction in the field of natural language understanding (NLU). Previous works on constructing NLU instructions mainly focus on information extraction (IE), neglecting tasks such as machine reading comprehension, question answering, and text classification. Furthermore, the lack of diversity in the data has led to a decreased generalization ability of trained LLMs in other NLU tasks and a noticeable decline in the fundamental model's general capabilities. To address this issue, we propose Hum, a large-scale, high-quality synthetic instruction corpus for NLU tasks, designed to enhance the NLU capabilities of LLMs. Specifically, Hum includes IE (either close IE or open IE), machine reading comprehension, text classification, and instruction generalist tasks, thereby enriching task diversity. Additionally, we introduce a human-LLMs collaborative mechanism to synthesize instructions, which enriches instruction diversity by incorporating guidelines, preference rules, and format variants. We conduct extensive experiments on 5 NLU tasks and 28 general capability evaluation datasets for LLMs. Experimental results show that Hum enhances the NLU capabilities of six LLMs by an average of 3.1\%, with no significant decline observed in other general capabilities.

Do the rich representations of multi-modal diffusion transformers (DiTs) exhibit unique properties that enhance their interpretability? We introduce ConceptAttention, a novel method that leverages the expressive power of DiT attention layers to generate high-quality saliency maps that precisely locate textual concepts within images. Without requiring additional training, ConceptAttention repurposes the parameters of DiT attention layers to produce highly contextualized concept embeddings, contributing the major discovery that performing linear projections in the output space of DiT attention layers yields significantly sharper saliency maps compared to commonly used cross-attention mechanisms. Remarkably, ConceptAttention even achieves state-of-the-art performance on zero-shot image segmentation benchmarks, outperforming 11 other zero-shot interpretability methods on the ImageNet-Segmentation dataset and on a single-class subset of PascalVOC. Our work contributes the first evidence that the representations of multi-modal DiT models like Flux are highly transferable to vision tasks like segmentation, even outperforming multi-modal foundation models like CLIP.

Randomized experiments are the preferred approach for evaluating the effects of interventions, but they are costly and often yield estimates with substantial uncertainty. On the other hand, in silico experiments leveraging foundation models offer a cost-effective alternative that can potentially attain higher statistical precision. However, the benefits of in silico experiments come with a significant risk: statistical inferences are not valid if the models fail to accurately predict experimental responses to interventions. In this paper, we propose a novel approach that integrates the predictions from multiple foundation models with experimental data while preserving valid statistical inference. Our estimator is consistent and asymptotically normal, with asymptotic variance no larger than the standard estimator based on experimental data alone. Importantly, these statistical properties hold even when model predictions are arbitrarily biased. Empirical results across several randomized experiments show that our estimator offers substantial precision gains, equivalent to a reduction of up to 20% in the sample size needed to match the same precision as the standard estimator based on experimental data alone.

While Fourier-based neural operators are best suited to learning mappings between functions on periodic domains, several works have introduced techniques for incorporating non trivial boundary conditions. However, all previously introduced methods have restrictions that limit their applicability. In this work, we introduce an alternative approach to imposing boundary conditions inspired by volume penalization from numerical methods and Mixture of Experts (MoE) from machine learning. By introducing competing experts, the approach additionally allows for model selection. To demonstrate the method, we combine a spatially conditioned MoE with the Fourier based, Modal Operator Regression for Physics (MOR-Physics) neural operator and recover a nonlinear operator on a disk and quarter disk. Next, we extract a large eddy simulation (LES) model from direct numerical simulation of channel flow and show the domain decomposition provided by our approach. Finally, we train our LES model with Bayesian variational inference and obtain posterior predictive samples of flow far past the DNS simulation time horizon.

We investigate algorithmic decision problems where agents can respond strategically to the decision maker's (DM) models. The demand for clear and actionable explanations from DMs to (potentially strategic) agents continues to rise. While prior work often treats explanations as full model disclosures, explanations in practice might convey only partial information, which can lead to misinterpretations and harmful responses. When full disclosure of the predictive model is neither feasible nor desirable, a key open question is how DMs can use explanations to maximise their utility without compromising agent welfare. In this work, we explore well-known local and global explanation methods, and establish a necessary condition to prevent explanations from misleading agents into self-harming actions. Moreover, with conditional homogeneity, we establish that action recommendation (AR)-based explanations are sufficient for non-harmful responses, akin to the revelation principle in information design. To operationalise AR-based explanations, we propose a simple algorithm to jointly optimise the predictive model and AR policy to balance DM outcomes with agent welfare. Our empirical results demonstrate the benefits of this approach as a more refined strategy for safe and effective partial model disclosure in algorithmic decision-making.

Data selection has emerged as a crucial downstream application of data valuation. While existing data valuation methods have shown promise in selection tasks, the theoretical foundations and full potential of using data values for selection remain largely unexplored. In this work, we first demonstrate that data values applied for selection can be naturally reformulated as a sequential-decision-making problem, where the optimal data value can be derived through dynamic programming. We show this framework unifies and reinterprets existing methods like Data Shapley through the lens of approximate dynamic programming, specifically as myopic reward function approximations to this sequential problem. Furthermore, we analyze how sequential data selection optimality is affected when the ground-truth utility function exhibits monotonic submodularity with curvature. To address the computational challenges in obtaining optimal data values, we propose an efficient approximation scheme using learned bipartite graphs as surrogate utility models, ensuring greedy selection is still optimal when the surrogate utility is correctly specified and learned. Extensive experiments demonstrate the effectiveness of our approach across diverse datasets.

Large language models (LLMs), such as o1 from OpenAI, have demonstrated remarkable reasoning capabilities. o1 generates a long chain-of-thought (LongCoT) before answering a question. LongCoT allows LLMs to analyze problems, devise plans, reflect, and backtrack effectively. These actions empower LLM to solve complex problems. After the release of o1, many teams have attempted to replicate its LongCoT and reasoning capabilities. In terms of methods, they primarily rely on knowledge distillation with data from existing models with LongCoT capacities (e.g., OpenAI-o1, Qwen-QwQ, DeepSeek-R1-Preview), leaving significant uncertainties on systematically developing such reasoning abilities. In terms of data domains, these works focus narrowly on math while a few others include coding, limiting their generalizability. This paper introduces a novel approach to enable LLM's LongCoT capacity without distillation from o1-like models or expensive human annotations, where we bootstrap LongCoT (BOLT) from a standard instruct model. BOLT involves three stages: 1) LongCoT data bootstrapping with in-context learning on a standard instruct model; 2) LongCoT supervised finetuning; 3) online training to further refine LongCoT capacities. In BOLT, only a few in-context examples need to be constructed during the bootstrapping stage; in our experiments, we created 10 examples, demonstrating the feasibility of this approach. We use Llama-3.1-70B-Instruct to bootstrap LongCoT and apply our method to various model scales (7B, 8B, 70B). We achieve impressive performance on a variety of benchmarks, Arena-Hard, MT-Bench, WildBench, ZebraLogic, MATH500, which evaluate diverse task-solving and reasoning capabilities.

Despite notable advancements in Retrieval-Augmented Generation (RAG) systems that expand large language model (LLM) capabilities through external retrieval, these systems often struggle to meet the complex and diverse needs of real-world industrial applications. The reliance on retrieval alone proves insufficient for extracting deep, domain-specific knowledge performing in logical reasoning from specialized corpora. To address this, we introduce sPecIalized KnowledgE and Rationale Augmentation Generation (PIKE-RAG), focusing on extracting, understanding, and applying specialized knowledge, while constructing coherent rationale to incrementally steer LLMs toward accurate responses. Recognizing the diverse challenges of industrial tasks, we introduce a new paradigm that classifies tasks based on their complexity in knowledge extraction and application, allowing for a systematic evaluation of RAG systems' problem-solving capabilities. This strategic approach offers a roadmap for the phased development and enhancement of RAG systems, tailored to meet the evolving demands of industrial applications. Furthermore, we propose knowledge atomizing and knowledge-aware task decomposition to effectively extract multifaceted knowledge from the data chunks and iteratively construct the rationale based on original query and the accumulated knowledge, respectively, showcasing exceptional performance across various benchmarks.