Miracle-dz/UniFAR-FTUs huggingface dataset:
The Expected Loss of Preconditioned Langevin Dynamics Reveals the Hessian Rank

Langevin dynamics (LD) is widely used for sampling from distributions and for optimization. In this work, we derive a closed-form expression for the expected loss of preconditioned LD near stationary points of the objective function. We use the fact that at the vicinity of such points, LD reduces to an Ornstein–Uhlenbeck process, which is amenable to convenient mathematical treatment. Our analysis reveals that when the preconditioning matrix satisfies a particular relation with respect to the noise covariance, LD's expected loss becomes proportional to the rank of the objective's Hessian. We illustrate the applicability of this result in the context of neural networks, where the Hessian rank has been shown to capture the complexity of the predictor function but is usually computationally hard to probe. Finally, we use our analysis to compare SGD-like and Adam-like preconditioners and identify the regimes under which each of them leads to a lower expected loss.
An adaptive lattice Green's function method for external flows with two unbounded and one homogeneous directions

We solve the incompressible Navier-Stokes equations using a lattice Green's function (LGF) approach, including immersed boundaries (IB) and adaptive mesh refinement (AMR), for external flows with one homogeneous direction (e.g. infinite cylinders of arbitrary cross-section). We hybridize a Fourier collocation (pseudo-spectral) method for the homogeneous direction with a specially designed, staggered-grid finite-volume scheme on an AMR grid. The Fourier series is also truncated variably according to the refinement level in the other directions. We derive new algorithms to tabulate the LGF of the screened Poisson operator and viscous integrating factor. After adapting other algorithmic details from the fully inhomogeneous case, we validate and demonstrate the new method with transitional and turbulent flows over a circular cylinder at $Re=300$ and $Re=12,000$, respectively.
Clifford circuits over non-cyclic abelian groups

We present a discussion of the generalized Clifford group over non-cyclic finite abelian groups. These Clifford groups appear naturally in the theory of topological error correction and abelian anyon models. We demonstrate a generalized Gottesman-Knill theorem, stating that every Clifford circuit can be efficiently classically simulated. We additionally provide circuits for a universal quantum computing scheme based on local two-qudit Clifford gates and magic states.
Dealing with unbounded gradients in stochastic saddle-point optimization

We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may result in instability and divergence. In this paper, we propose a simple and effective regularization technique that stabilizes the iterates and yields meaningful performance guarantees even if the domain and the gradient noise scales linearly with the size of the iterates (and is thus potentially unbounded). Besides providing a set of general results, we also apply our algorithm to a specific problem in reinforcement learning, where it leads to performance guarantees for finding near-optimal policies in an average-reward MDP without prior knowledge of the bias span.
Factual Consistency Evaluation of Summarisation in the Era of Large Language Models

Factual inconsistency with source documents in automatically generated summaries can lead to misinformation or pose risks. Existing factual consistency(FC) metrics are constrained by their performance, efficiency, and explainability. Recent advances in Large language models (LLMs) have demonstrated remarkable potential in text evaluation but their effectiveness in assessing FC in summarisation remains underexplored. Prior research has mostly focused on proprietary LLMs, leaving essential factors that affect their assessment capabilities unexplored. Additionally, current FC evaluation benchmarks are restricted to news articles, casting doubt on the generality of the FC methods tested on them. In this paper, we first address the gap by introducing TreatFact a dataset of LLM-generated summaries of clinical texts, annotated for FC by domain experts. Moreover, we benchmark 11 LLMs for FC evaluation across news and clinical domains and analyse the impact of model size, prompts, pre-training and fine-tuning data. Our findings reveal that despite proprietary models prevailing on the task, open-source LLMs lag behind. Nevertheless, there is potential for enhancing the performance of open-source LLMs through increasing model size, expanding pre-training data, and developing well-curated fine-tuning data. Experiments on TreatFact suggest that both previous methods and LLM-based evaluators are unable to capture factual inconsistencies in clinical summaries, posing a new challenge for FC evaluation.
Mechanism Design with Sequential-Move Games: Revelation Principle

Traditionally, mechanism design focuses on simultaneous-move games (e.g., Myerson (1981)). In this paper, we study mechanism design with sequential-move games, and provide two results on revelation principles for general solution concepts (e.g., perfect Bayesian equilibrium, obvious dominance, strong-obvious dominance). First, if a solution concept is additive, implementation in sequential-move games is equivalent to implementation in simultaneous-move games. Second, for any solution concept \r{ho} and any social choice function f, we identify a canonical operator {\gamma}^{(\r{ho},f)}, which is defined on primitives. We prove that, if \r{ho} is monotonic, f can be implemented by a sequential-move game if and only if {\gamma}^{(\r{ho},f)} is achievable, which translates a complicated mechanism design problem into checking some conditions defined on primitives. Most of the existing solution concepts are either additive or monotonic.
∞Bench: Extending Long Context Evaluation Beyond 100K Tokens

Processing and reasoning over long contexts is crucial for many practical applications of Large Language Models (LLMs), such as document comprehension and agent construction. Despite recent strides in making LLMs process contexts with more than 100K tokens, there is currently a lack of a standardized benchmark to evaluate this long-context capability. Existing public benchmarks typically focus on contexts around 10K tokens, limiting the assessment and comparison of LLMs in processing longer contexts. In this paper, we propose $\infty$Bench, the first LLM benchmark featuring an average data length surpassing 100K tokens. $\infty$Bench comprises synthetic and realistic tasks spanning diverse domains, presented in both English and Chinese. The tasks in $\infty$Bench are designed to require well understanding of long dependencies in contexts, and make simply retrieving a limited number of passages from contexts not sufficient for these tasks. In our experiments, based on $\infty$Bench, we evaluate the state-of-the-art proprietary and open-source LLMs tailored for processing long contexts. The results indicate that existing long context LLMs still require significant advancements to effectively process 100K+ context. We further present three intriguing analyses regarding the behavior of LLMs processing long context.
TransGOP: Transformer-Based Gaze Object Prediction

Gaze object prediction aims to predict the location and category of the object that is watched by a human. Previous gaze object prediction works use CNN-based object detectors to predict the object's location. However, we find that Transformer-based object detectors can predict more accurate object location for dense objects in retail scenarios. Moreover, the long-distance modeling capability of the Transformer can help to build relationships between the human head and the gaze object, which is important for the GOP task. To this end, this paper introduces Transformer into the fields of gaze object prediction and proposes an end-to-end Transformer-based gaze object prediction method named TransGOP. Specifically, TransGOP uses an off-the-shelf Transformer-based object detector to detect the location of objects and designs a Transformer-based gaze autoencoder in the gaze regressor to establish long-distance gaze relationships. Moreover, to improve gaze heatmap regression, we propose an object-to-gaze cross-attention mechanism to let the queries of the gaze autoencoder learn the global-memory position knowledge from the object detector. Finally, to make the whole framework end-to-end trained, we propose a Gaze Box loss to jointly optimize the object detector and gaze regressor by enhancing the gaze heatmap energy in the box of the gaze object. Extensive experiments on the GOO-Synth and GOO-Real datasets demonstrate that our TransGOP achieves state-of-the-art performance on all tracks, i.e., object detection, gaze estimation, and gaze object prediction. Our code will be available at https://github.com/chenxi-Guo/TransGOP.git.
Retrieval Helps or Hurts? A Deeper Dive into the Efficacy of Retrieval Augmentation to Language Models

While large language models (LMs) demonstrate remarkable performance, they encounter challenges in providing accurate responses when queried for information beyond their pre-trained memorization. Although augmenting them with relevant external information can mitigate these issues, failure to consider the necessity of retrieval may adversely affect overall performance. Previous research has primarily focused on examining how entities influence retrieval models and knowledge recall in LMs, leaving other aspects relatively unexplored. In this work, our goal is to offer a more detailed, fact-centric analysis by exploring the effects of combinations of entities and relations. To facilitate this, we construct a new question answering (QA) dataset called WiTQA (Wikipedia Triple Question Answers). This dataset includes questions about entities and relations of various popularity levels, each accompanied by a supporting passage. Our extensive experiments with diverse LMs and retrievers reveal when retrieval does not consistently enhance LMs from the viewpoints of fact-centric popularity. Confirming earlier findings, we observe that larger LMs excel in recalling popular facts. However, they notably encounter difficulty with infrequent entity-relation pairs compared to retrievers. Interestingly, they can effectively retain popular relations of less common entities. We demonstrate the efficacy of our finer-grained metric and insights through an adaptive retrieval system that selectively employs retrieval and recall based on the frequencies of entities and relations in the question.
Privacy-Preserving Instructions for Aligning Large Language Models

Service providers of large language model (LLM) applications collect user instructions in the wild and use them in further aligning LLMs with users' intentions. These instructions, which potentially contain sensitive information, are annotated by human workers in the process. This poses a new privacy risk not addressed by the typical private optimization. To this end, we propose using synthetic instructions to replace real instructions in data annotation and model fine-tuning. Formal differential privacy is guaranteed by generating those synthetic instructions using privately fine-tuned generators. Crucial in achieving the desired utility is our novel filtering algorithm that matches the distribution of the synthetic instructions to that of the real ones. In both supervised fine-tuning and reinforcement learning from human feedback, our extensive experiments demonstrate the high utility of the final set of synthetic instructions by showing comparable results to real instructions. In supervised fine-tuning, models trained with private synthetic instructions outperform leading open-source models such as Vicuna.
A quadratically convergent semismooth Newton method for nonlinear semidefinite programming without the subdifferential regularity

We introduce a quadratically convergent semismooth Newton method for nonlinear semidefinite programming that eliminates the need for the subdifferential regularity, a common yet stringent requirement in existing approaches. Our strategy revolves around identifying a single nonsingular element within the B(ouligand)-subdifferential, thus avoiding the standard requirement for nonsingularity across the entire subdifferential set, which is often too restrictive for practical applications. The theoretical framework is supported by the introduction of the weak second order condition (W-SOC) and the weak strict Robinson constraint qualification (W-SRCQ). These conditions not only guarantee the existence of a nonsingular element in the subdifferential but also forge a primal-dual connection in linearly constrained convex quadratic programming. The theoretical advancements further lay the foundation for the algorithmic designing of a novel semismooth Newton method, which integrates a correction step to address degenerate issues. Particularly, this correction step ensures the local convergence as well as a superlinear/quadratic convergence rate of the proposed method. Preliminary numerical experiments corroborate our theoretical findings and underscore the practical effectiveness of our method.
DSLR: Diversity Enhancement and Structure Learning for Rehearsal-based Graph Continual Learning

We investigate the replay buffer in rehearsal-based approaches for graph continual learning (GCL) methods. Existing rehearsal-based GCL methods select the most representative nodes for each class and store them in a replay buffer for later use in training subsequent tasks. However, we discovered that considering only the class representativeness of each replayed node makes the replayed nodes to be concentrated around the center of each class, incurring a potential risk of overfitting to nodes residing in those regions, which aggravates catastrophic forgetting. Moreover, as the rehearsal-based approach heavily relies on a few replayed nodes to retain knowledge obtained from previous tasks, involving the replayed nodes that have irrelevant neighbors in the model training may have a significant detrimental impact on model performance. In this paper, we propose a GCL model named DSLR, specifically, we devise a coverage-based diversity (CD) approach to consider both the class representativeness and the diversity within each class of the replayed nodes. Moreover, we adopt graph structure learning (GSL) to ensure that the replayed nodes are connected to truly informative neighbors. Extensive experimental results demonstrate the effectiveness and efficiency of DSLR. Our source code is available at https://github.com/seungyoon-Choi/DSLR_official.
Replicable Learning of Large-Margin Halfspaces

We provide efficient replicable algorithms for the problem of learning large-margin halfspaces. Our results improve upon the algorithms provided by Impagliazzo, Lei, Pitassi, and Sorrell [STOC, 2022]. We design the first dimension-independent replicable algorithms for this task which runs in polynomial time, is proper, and has strictly improved sample complexity compared to the one achieved by Impagliazzo et al. [2022] with respect to all the relevant parameters. Moreover, our first algorithm has sample complexity that is optimal with respect to the accuracy parameter $\epsilon$. We also design an SGD-based replicable algorithm that, in some parameters' regimes, achieves better sample and time complexity than our first algorithm. Departing from the requirement of polynomial time algorithms, using the DP-to-Replicability reduction of Bun, Gaboardi, Hopkins, Impagliazzo, Lei, Pitassi, Sorrell, and Sivakumar [STOC, 2023], we show how to obtain a replicable algorithm for large-margin halfspaces with improved sample complexity with respect to the margin parameter $\tau$, but running time doubly exponential in $1/\tau^2$ and worse sample complexity dependence on $\epsilon$ than one of our previous algorithms. We then design an improved algorithm with better sample complexity than all three of our previous algorithms and running time exponential in $1/\tau^{2}$.
The Uncanny Valley: A Comprehensive Analysis of Diffusion Models

Through Diffusion Models (DMs), we have made significant advances in generating high-quality images. Our exploration of these models delves deeply into their core operational principles by systematically investigating key aspects across various DM architectures: i) noise schedules, ii) samplers, and iii) guidance. Our comprehensive examination of these models sheds light on their hidden fundamental mechanisms, revealing the concealed foundational elements that are essential for their effectiveness. Our analyses emphasize the hidden key factors that determine model performance, offering insights that contribute to the advancement of DMs. Past findings show that the configuration of noise schedules, samplers, and guidance is vital to the quality of generated images; however, models reach a stable level of quality across different configurations at a remarkably similar point, revealing that the decisive factors for optimal performance predominantly reside in the diffusion process dynamics and the structural design of the model's network, rather than the specifics of configuration details. Our comparative analysis reveals that Denoising Diffusion Probabilistic Model (DDPM)-based diffusion dynamics consistently outperform the Noise Conditioned Score Network (NCSN)-based ones, not only when evaluated in their original forms but also when continuous through Stochastic Differential Equation (SDE)-based implementations.
A Unified Framework and Dataset for Assessing Gender Bias in Vision-Language Models

Large vision-language models (VLMs) are widely getting adopted in industry and academia. In this work we build a unified framework to systematically evaluate gender-profession bias in VLMs. Our evaluation encompasses all supported inference modes of the recent VLMs, including image-to-text, text-to-text, text-to-image, and image-to-image. We construct a synthetic, high-quality dataset of text and images that blurs gender distinctions across professional actions to benchmark gender bias. In our benchmarking of recent vision-language models (VLMs), we observe that different input-output modalities result in distinct bias magnitudes and directions. We hope our work will help guide future progress in improving VLMs to learn socially unbiased representations. We will release our data and code.
The Geography of Information Diffusion in Online Discourse on Europe and Migration

The online diffusion of information related to Europe and migration has been little investigated from an external point of view. However, this is a very relevant topic, especially if users have had no direct contact with Europe and its perception depends solely on information retrieved online. In this work we analyse the information circulating online about Europe and migration after retrieving a large amount of data from social media (Twitter), to gain new insights into topics, magnitude, and dynamics of their diffusion. We combine retweets and hashtags network analysis with geolocation of users, linking thus data to geography and allowing analysis from an"outside Europe"perspective, with a special focus on Africa. We also introduce a novel approach based on cross-lingual quotes, i.e. when content in a language is commented and retweeted in another language, assuming these interactions are a proxy for connections between very distant communities. Results show how the majority of online discussions occurs at a national level, especially when discussing migration. Language (English) is pivotal for information to become transnational and reach far. Transnational information flow is strongly unbalanced, with content mainly produced in Europe and amplified outside. Conversely Europe-based accounts tend to be self-referential when they discuss migration-related topics. Football is the most exported topic from Europe worldwide. Moreover, important nodes in the communities discussing migration-related topics include accounts of official institutions and international agencies, together with journalists, news, commentators and activists.
CriticBench: Evaluating Large Language Models as Critic

Critique ability are crucial in the scalable oversight and self-improvement of Large Language Models (LLMs). While many recent studies explore the critique ability of LLMs to judge and refine flaws in generations, how to comprehensively and reliably measure the critique abilities of LLMs is under-explored. This paper introduces CriticBench, a novel benchmark designed to comprehensively and reliably evaluate four key critique ability dimensions of LLMs: feedback, comparison, refinement and meta-feedback. CriticBench encompasses nine diverse tasks, each assessing the LLMs' ability to critique responses at varying levels of quality granularity. Our extensive evaluations of open-source and closed-source LLMs reveal intriguing relationships between the critique ability and tasks, response qualities, and model scales. Datasets, resources and evaluation toolkit for CriticBench will be publicly released at https://github.com/open-compass/CriticBench.
Exploring Primordial Black Holes and Gravitational Waves with R-Symmetric GUT Higgs Inflation

This study investigates the realization of R-symmetric Higgs inflation within the framework of no-scale-like supergravity, aiming to elucidate the formation of primordial black holes and observable gravitational waves within a class of GUT models. We explore the possibility of an ultra-slow-roll phase in a hybrid inflation framework, where the GUT Higgs field primarily takes on the role of the inflaton. The amplification of the scalar power spectrum gives rise to scalar-induced gravitational waves and the generation of primordial black holes. The predicted stochastic gravitational wave background falls within the sensitivity range of existing and upcoming gravitational wave detectors, while primordial black holes hold the potential to explain the abundance of dark matter. Furthermore, we highlight the significance of the leading-order nonrenormalizable term in the superpotential of achieving inflationary observables consistent with the latest experimental data. Additionally, the predicted range of the tensor-to-scalar ratio, a key measure of primordial gravitational waves, lies within the observational window of future experiments searching for B-mode polarization patterns in cosmic microwave background data.