We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of neural networks, results beyond the single-index setting remain elusive. In this work, we introduce spectral algorithms based on the linearization of a message passing scheme tailored to this problem. Our main contribution is to show that the proposed methods achieve the optimal reconstruction threshold. Leveraging a high-dimensional characterization of the algorithms, we show that above the critical threshold the leading eigenvector correlates with the relevant index subspace, a phenomenon reminiscent of the Baik-Ben Arous-Peche (BBP) transition in spiked models arising in random matrix theory. Supported by numerical experiments and a rigorous theoretical framework, our work bridges critical gaps in the computational limits of weak learnability in multi-index model.

Recent advances in CV and NLP have inspired researchers to develop general-purpose graph foundation models through pre-training across diverse domains. However, a fundamental challenge arises from the substantial differences in graph topologies across domains. Additionally, real-world graphs are often sparse and prone to noisy connections and adversarial attacks. To address these issues, we propose the Multi-Domain Graph Foundation Model (MDGFM), a unified framework that aligns and leverages cross-domain topological information to facilitate robust knowledge transfer. MDGFM bridges different domains by adaptively balancing features and topology while refining original graphs to eliminate noise and align topological structures. To further enhance knowledge transfer, we introduce an efficient prompt-tuning approach. By aligning topologies, MDGFM not only improves multi-domain pre-training but also enables robust knowledge transfer to unseen domains. Theoretical analyses provide guarantees of MDGFM's effectiveness and domain generalization capabilities. Extensive experiments on both homophilic and heterophilic graph datasets validate the robustness and efficacy of our method.

We examine an approval-based model of Liquid Democracy with a budget constraint on voting and delegating costs, aiming to centrally select casting voters ensuring complete representation of the electorate. From a computational complexity perspective, we focus on minimizing overall costs, maintaining short delegation paths, and preventing excessive concentration of voting power. Furthermore, we explore computational aspects of strategic control, specifically, whether external agents can change election components to influence the voting power of certain voters.

High-definition maps (HD maps) are detailed and informative maps capturing lane centerlines and road elements. Although very useful for autonomous driving, HD maps are costly to build and maintain. Furthermore, access to these high-quality maps is usually limited to the firms that build them. On the other hand, standard definition (SD) maps provide road centerlines with an accuracy of a few meters. In this paper, we explore the possibility of enhancing SD maps by incorporating information from road manuals using LLMs. We develop SD++, an end-to-end pipeline to enhance SD maps with location-dependent road information obtained from a road manual. We suggest and compare several ways of using LLMs for such a task. Furthermore, we show the generalization ability of SD++ by showing results from both California and Japan.

Large Language Models (LLMs), such as ChatGPT, allow researchers to analyze extensive text corpora with efficiency (Bail, 2024). However, human and algorithmic biases can influence their outputs, reflecting ideological or cultural skewness in the training data (Bender et al., 2021; Kroon et al., 2023). With the growing adoption of LLM-Assisted Content Analysis (LACA)--a method replacing manual coding with LLM-generated datasets (Chew et al., 2023)--the scientific community must ensure these tools enhance understanding rather than reinforce existing biases (Messeri and Crockett, 2024). Human bias is a long-standing issue in content analysis, which traditionally depends on a consensus-oriented research practice. Intercoder agreement is used to ensure reliability, aiming for shared interpretations of text that can be statistically validated (Krippendorff, 1999). However, this emphasis on consensus may inadvertently neglect diverse perspectives, favoring uniform interpretations that risk simplifying the sociocultural complexities embedded in textual connotations.

Nine-degrees-of-freedom (9-DoF) object pose and size estimation is crucial for enabling augmented reality and robotic manipulation. Category-level methods have received extensive research attention due to their potential for generalization to intra-class unknown objects. However, these methods require manual collection and labeling of large-scale real-world training data. To address this problem, we introduce a diffusion-based paradigm for domain-generalized category-level 9-DoF object pose estimation. Our motivation is to leverage the latent generalization ability of the diffusion model to address the domain generalization challenge in object pose estimation. This entails training the model exclusively on rendered synthetic data to achieve generalization to real-world scenes. We propose an effective diffusion model to redefine 9-DoF object pose estimation from a generative perspective. Our model does not require any 3D shape priors during training or inference. By employing the Denoising Diffusion Implicit Model, we demonstrate that the reverse diffusion process can be executed in as few as 3 steps, achieving near real-time performance. Finally, we design a robotic grasping system comprising both hardware and software components. Through comprehensive experiments on two benchmark datasets and the real-world robotic system, we show that our method achieves state-of-the-art domain generalization performance. Our code will be made public at https://github.com/CNJianLiu/Diff9D.

From extracting features to generating text, the outputs of large language models (LLMs) typically rely on their final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that intermediate layers can encode even richer representations, often improving performance on a wide range of downstream tasks. To explain and quantify these hidden-layer properties, we propose a unified framework of representation quality metrics based on information theory, geometry, and invariance to input perturbations. Our framework highlights how each model layer balances information compression and signal preservation, revealing why mid-depth embeddings can exceed the last layer's performance. Through extensive experiments on 32 text-embedding tasks and comparisons across model architectures (transformers, state-space models) and domains (language, vision), we demonstrate that intermediate layers consistently provide stronger features. These findings challenge the standard focus on final-layer embeddings and open new directions for model analysis and optimization, including strategic use of mid-layer representations for more robust and accurate AI systems.

Large language models (LLMs) have shown impressive capabilities in natural language processing tasks, including dialogue generation. This research aims to conduct a novel comparative analysis of two prominent techniques, fine-tuning with LoRA (Low-Rank Adaptation) and the Retrieval-Augmented Generation (RAG) framework, in the context of doctor-patient chat conversations with multiple datasets of mixed medical domains. The analysis involves three state-of-the-art models: Llama-2, GPT, and the LSTM model. Employing real-world doctor-patient dialogues, we comprehensively evaluate the performance of models, assessing key metrics such as language quality (perplexity, BLEU score), factual accuracy (fact-checking against medical knowledge bases), adherence to medical guidelines, and overall human judgments (coherence, empathy, safety). The findings provide insights into the strengths and limitations of each approach, shedding light on their suitability for healthcare applications. Furthermore, the research investigates the robustness of the models in handling diverse patient queries, ranging from general health inquiries to specific medical conditions. The impact of domain-specific knowledge integration is also explored, highlighting the potential for enhancing LLM performance through targeted data augmentation and retrieval strategies.

We present a novel class of jailbreak adversarial attacks on LLMs, termed Task-in-Prompt (TIP) attacks. Our approach embeds sequence-to-sequence tasks (e.g., cipher decoding, riddles, code execution) into the model's prompt to indirectly generate prohibited inputs. To systematically assess the effectiveness of these attacks, we introduce the PHRYGE benchmark. We demonstrate that our techniques successfully circumvent safeguards in six state-of-the-art language models, including GPT-4o and LLaMA 3.2. Our findings highlight critical weaknesses in current LLM safety alignments and underscore the urgent need for more sophisticated defence strategies. Warning: this paper contains examples of unethical inquiries used solely for research purposes.

ICESat-2 (IS2) by NASA is an Earth-observing satellite that measures high-resolution surface elevation. The IS2's ATL07 and ATL10 sea ice elevation and freeboard products of 10m-200m segments which aggregated 150 signal photons from the raw ATL03 (geolocated photon) data. These aggregated products can potentially overestimate local sea surface height, thus underestimating the calculations of freeboard (sea ice height above sea surface). To achieve a higher resolution of sea surface height and freeboard information, in this work we utilize a 2m window to resample the ATL03 data. Then, we classify these 2m segments into thick sea ice, thin ice, and open water using deep learning methods (Long short-term memory and Multi-layer perceptron models). To obtain labeled training data for our deep learning models, we use segmented Sentinel-2 (S2) multi-spectral imagery overlapping with IS2 tracks in space and time to auto-label IS2 data, followed by some manual corrections in the regions of transition between different ice/water types or cloudy regions. We employ a parallel workflow for this auto-labeling using PySpark to scale, and we achieve 9-fold data loading and 16.25-fold map-reduce speedup. To train our models, we employ a Horovod-based distributed deep-learning workflow on a DGX A100 8 GPU cluster, achieving a 7.25-fold speedup. Next, we calculate the local sea surface heights based on the open water segments. Finally, we scale the freeboard calculation using the derived local sea level and achieve 8.54-fold data loading and 15.7-fold map-reduce speedup. Compared with the ATL07 (local sea level) and ATL10 (freeboard) data products, our results show higher resolutions and accuracy (96.56%).