Solving nonlinear partial differential equations (PDEs) with multiple solutions is essential in various fields, including physics, biology, and engineering.

We introduce r-loopy Weisfeiler-Leman (r-lWL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, r-lMPNN, that can count cycles up to length r+2. Most notably, we show that r-lWL can count homomorphisms of cactus graphs. This extends 1-WL, which can only count homomorphisms of trees and, in fact, we prove that r-lWL is incomparable to k-WL for any fixed k. We empirically validate the expressive and counting power of r-lMPNN on several synthetic datasets and demonstrate the scalability and strong performance on various real-world datasets, particularly on sparse graphs. Our code is available on GitHub.

Recently powerful Large Language Models (LLMs) have become easily accessible to hundreds of millions of users world-wide. However, their strong capabilities and vast world knowledge do not come without associated privacy risks. In this work, we focus on the emerging privacy threat LLMs pose - the ability to accurately infer personal information from online texts. Despite the growing importance of LLM-based author profiling, research in this area has been hampered by a lack of suitable public datasets, largely due to ethical and privacy concerns associated with real personal data. We take two steps to address this problem: (i) we construct a simulation framework for the popular social media platform Reddit using LLM agents seeded with synthetic personal profiles; (ii) using this framework, we generate SynthPAI, a diverse synthetic dataset of over 7800 comments manually labeled for personal attributes. We validate our dataset with a human study showing that humans barely outperform random guessing on the task of distinguishing our synthetic comments from real ones. Further, we verify that our dataset enables meaningful personal attribute inference research by showing across 18 state-of-theart LLMs that our synthetic comments allow us to draw the same conclusions as real-world data. Combined, our experimental results, dataset and pipeline form a strong basis for future privacy-preserving research geared towards understanding and mitigating inference-based privacy threats that LLMs pose.

Recent text-to-image personalization methods have shown great promise in teaching a diffusion model user-specified concepts given a few images for reusing the acquired concepts in a novel context. With massive efforts being dedicated to personalized generation, a promising extension is personalized editing, namely to edit an image using personalized concepts, which can provide a more precise guidance signal than traditional textual guidance. To address this, a straightforward solution is to incorporate a personalized diffusion model with a text-driven editing framework. However, such a solution often shows unsatisfactory editability on the source image. To address this, we propose DreamSteerer, a plug-in method for augmenting existing T2I personalization methods. Specifically, we enhance the source image conditioned editability of a personalized diffusion model via a novel Editability Driven Score Distillation (EDSD) objective. Moreover, we identify a mode trapping issue with EDSD, and propose a mode shifting regularization with spatial feature guided sampling to avoid such an issue. We further employ two key modifications to the Delta Denoising Score framework that enable high-fidelity local editing with personalized concepts. Extensive experiments validate that DreamSteerer can significantly improve the editability of several T2I personalization baselines while being computationally efficient.

We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of the magnitude of the projection of the data onto a given subspace, and enables us to develop inference procedures for a broad class of group-sparse selection methods, including the group lasso, iterative hard thresholding, and forward stepwise regression. We give numerical results to illustrate these tools on simulated data and on health record data.

This rate is unavoidable when the distribution is isotropic, namely, when the covariance is a multiple of the identity matrix. Yet, real-world data is often highly anisotropic, with signals concentrated on a small number of principal components. We develop estimators that are appropriate for such signals--our estimators are (ε, δ)-differentially private and have sample complexity that is dimension-independent for anisotropic subgaussian distributions.

Imitation learning (IL) aims to mimic the behavior of an expert in a sequential decision making task by learning from demonstrations, and has been widely applied to robotics, autonomous driving, and autoregressive text generation. The simplest approach to IL, behavior cloning (BC), is thought to incur sample complexity with unfavorable quadratic dependence on the problem horizon, motivating a variety of different online algorithms that attain improved linear horizon dependence under stronger assumptions on the data and the learner's access to the expert. We revisit the apparent gap between offline and online IL from a learning-theoretic perspective, with a focus on the realizable/well-specified setting with general policy classes up to and including deep neural networks. Through a new analysis of behavior cloning with the logarithmic loss, we show that it is possible to achieve horizon-independent sample complexity in offline IL whenever (i) the range of the cumulative payoffs is controlled, and (ii) an appropriate notion of supervised learning complexity for the policy class is controlled. Specializing our results to deterministic, stationary policies, we show that the gap between offline and online IL is smaller than previously thought: (i) it is possible to achieve linear dependence on horizon in offline IL under dense rewards (matching what was previously only known to be achievable in online IL); and (ii) without further assumptions on the policy class, online IL cannot improve over offline IL with the logarithmic loss, even in benign MDPs. We complement our theoretical results with experiments on standard RL tasks and autoregressive language generation to validate the practical relevance of our findings.

The Multi-modal Large Language Model (MLLM) based Referring Expression Generation (REG) task has gained increasing popularity, which aims to generate an unambiguous text description that applies to exactly one object or region in the image by leveraging foundation models. We empirically found that there exists a potential trade-off between the detailedness and the correctness of the descriptions for the referring objects. On the one hand, generating sentences with more details is usually required in order to provide more precise object descriptions. On the other hand, complicated sentences could easily increase the probability of hallucinations. To address this issue, we propose a training-free framework, named as "unleash-then-eliminate", which first elicits the latent information in the intermediate layers, and then adopts a cycle-consistency-based decoding method to alleviate the production of hallucinations. Furthermore, to reduce the computational load of cycle-consistency-based decoding, we devise a Probing-based Importance Estimation method to statistically estimate the importance weights of intermediate layers within a subset. These importance weights are then incorporated into the decoding process over the entire dataset, intervening in the next token prediction from intermediate layers. Extensive experiments conducted on the RefCOCOg and PHD benchmarks show that our proposed framework could outperform existing methods on both semantic and hallucination-related metrics.

In label-noise learning, the noise transition matrix reveals how an instance transitions from its clean label to its noisy label. Accurately estimating an instance's noise transition matrix is crucial for estimating its clean label. However, when only a noisy dataset is available, noise transition matrices can be estimated only for some "special" instances. To leverage these estimated transition matrices to help estimate the transition matrices of other instances, it is essential to explore relations between the matrices of these "special" instances and those of others. Existing studies typically build the relation by explicitly defining the similarity between the estimated noise transition matrices of "special" instances and those of other instances.

Event cameras provide exceptionally high temporal resolution in dynamic vision systems due to their unique event-driven mechanism. However, the sparse and asynchronous nature of event data makes frame-based visual processing methods inappropriate. This study proposes a novel framework, Event-based Graph Spatiotemporal Sensitive Transformer (EGSST), for the exploitation of spatial and temporal properties of event data. Firstly, a well-designed graph structure is employed to model event data, which not only preserves the original temporal data but also captures spatial details. Furthermore, inspired by the phenomenon that human eyes pay more attention to objects that produce significant dynamic changes, we design a Spatiotemporal Sensitivity Module (SSM) and an adaptive Temporal Activation Controller (TAC).