Constrained Bayesian optimization (CBO) methods have seen significant success in black-box optimization with constraints. One of the most commonly used CBO methods is the constrained expected improvement (CEI) algorithm. CEI is a natural extension of expected improvement (EI) when constraints are incorporated. However, the theoretical convergence rate of CEI has not been established. In this work, we study the convergence rate of CEI by analyzing its simple regret upper bound.

Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

Large Language Models (LLMs) have demonstrated remarkable capabilities, yet their extensive parameter scales pose significant challenges for practical deployment. Unstructured pruning has emerged as an effective model compression strategy with minimal performance loss, which introduces fine-grained sparsity for weight parameters. While existing methods employ a layer-wise pruning strategy to avoid the complexity of global pruning for billion-scale LLMs, they require appropriate sparsity allocation for the layer-wise pruning objectives and often lead to suboptimal solutions for the overall model. In this paper, we propose Lua-LLM (Learning unstructured-sparsity allocation in LLMs), a learning-based global pruning framework that explores the optimal unstructured sparsity allocation. Unlike existing pruning methods, which primarily focus on allocating per-layer sparsity, Lua-LLM achieves flexible allocation for both layer-wise and intra-layer sparsity.

Natural language has long enabled human cooperation, but its lossy, ambiguous, and indirect nature limits the potential of collective intelligence. While machines are not subject to these constraints, most LLM-based multi-agent systems still rely solely on natural language, exchanging tokens or their embeddings. To go beyond language, we introduce a new paradigm, thought communication, which enables agents to interact directly mind-to-mind, akin to telepathy. To uncover these latent thoughts in a principled way, we formalize the process as a general latent variable model, where agent states are generated by an unknown function of underlying thoughts. We prove that, in a nonparametric setting without auxiliary information, both shared and private latent thoughts between any pair of agents can be identified. Moreover, the global structure of thought sharing, including which agents share which thoughts and how these relationships are structured, can also be recovered with theoretical guarantees.

Imputation methods play a critical role in enhancing the quality of practical timeseries data, which often suffer from pervasive missing values. Recently, diffusionbased generative imputation methods have demonstrated remarkable success compared to autoregressive and conventional statistical approaches. Despite their empirical success, the theoretical understanding of how well diffusion-based models capture complex spatial and temporal dependencies between the missing values and observed ones remains limited.

Clinical diagnosis is a highly specialized discipline requiring both domain expertise and strict adherence to rigorous guidelines. While current AI-driven medical research predominantly focuses on knowledge graphs or natural text pretraining paradigms to incorporate medical knowledge, these approaches primarily rely on implicitly encoded knowledge within model parameters, neglecting task-specific knowledge required by diverse downstream tasks. To address this limitation, we propose Retrieval-Augmented Diagnosis (RAD), a novel framework that explicitly injects external knowledge into multimodal models directly on downstream tasks. Specifically, RAD operates through three key mechanisms: retrieval and refinement of disease-centered knowledge from multiple medical sources, a guidelineenhanced contrastive loss that constrains the latent distance between multi-modal features and guideline knowledge, and the dual transformer decoder that employs guidelines as queries to steer cross-modal fusion, aligning the models with clinical diagnostic workflows from guideline acquisition to feature extraction and decision-making. Moreover, recognizing the lack of quantitative evaluation of interpretability for multimodal diagnostic models, we introduce a set of criteria to assess the interpretability from both image and text perspectives. Extensive evaluations across four datasets with different anatomies demonstrate RAD's generalizability, achieving state-of-the-art performance. Furthermore, RAD enables the model to concentrate more precisely on abnormal regions and critical indicators, ensuring evidence-based, trustworthy diagnosis. Our code is available at this repository.

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Our work is motivated by single-cell data which can have very high-dimensionality - exceeding the capabilities of existing methods for point clouds which are mostly tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e., one data set for every patient), necessitating models that can process large, high-dimensional point-clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric and topological information. In contrast, HiPoNet models the point-cloud as a set of higher-order simplicial complexes, with each particular complex being created using a reweighting of features. This method thus generates multiple constructs corresponding to different views of high-dimensional data, which in biology offers the possibility of disentangling distinct cellular processes. It then employs simplicial wavelet transforms to extract multiscale features, capturing both local and global topology from each view. We show that geometric and topological information is preserved in this framework both theoretically and empirically.

We study the selection of agents based on mutual nominations, a theoretical problem with many applications from committee selection to AI alignment. As agents both select and are selected, they may be incentivized to misrepresent their true opinion about the eligibility of others to influence their own chances of selection. Impartial mechanisms circumvent this issue by guaranteeing that the selection of an agent is independent of the nominations cast by that agent. Previous research has established strong bounds on the performance of impartial mechanisms, measured by their ability to approximate the number of nominations for the most highly nominated agents. We study to what extent the performance of impartial mechanisms can be improved if they are given a prediction of a set of agents receiving a maximum number of nominations. Specifically, we provide bounds on the consistency and robustness of such mechanisms, where consistency measures the performance of the mechanisms when the prediction is accurate and robustness its performance when the prediction is inaccurate. For the general setting where up to k agents are to be selected and agents nominate any number of other agents, we give a mechanism with consistency 1 O 1k and robustness 1 1e O 1k .

Pre-trained Large language models (LLMs) have shown impressive advancements in functional magnetic resonance imaging (fMRI) analysis and causal discovery. Considering the unique nature of the causal discovery field, which focuses on extracting causal graphs from observed data, research on LLMs in this field is still at an early exploratory stage. As a subfield of causal discovery, effective connectivity (EC) has received even less attention, and LLM-based approaches in EC remain unexplored. Existing LLM-based approaches for causal discovery typically rely on iterative querying to assess the causal influence between variable pairs, without any model adaptation or fine-tuning, making them ill-suited for handling the cross-modal gap and complex causal structures. To this end, we propose BrainECLLM, the first method to fine-tune LLMs for estimating brain EC from fMRI data. Specifically, multiscale decomposition mixing module decomposes fMRI time series data into short-term and long-term multiscale trends, then mixing them in bottom-up (fine to coarse) and top-down (coarse to fine) manner to extract multiscale temporal variations. And cross attention is applied with pre-trained word embeddings to ensure consistency between the fMRI input and pre-trained natural language. The experimental results on simulated and real resting-state fMRI datasets demonstrate that BrainEC-LLM can achieve superior performance when compared to state-of-the-art baselines. The code is available at https: //github.com/XiongWenXww/BrainEC-LLM.

Greedy Equivalence Search (GES) is a classic score-based algorithm for causal discovery from observational data. In the sample limit, it recovers the Markov equivalence class of graphs that describe the data. Still, it faces two challenges in practice: computational cost and finite-sample accuracy. In this paper, we develop Less Greedy Equivalence Search (LGES), a variant of GES that retains its theoretical guarantees while partially addressing these limitations. LGES modifies the greedy step; rather than always applying the highest-scoring insertion, it avoids edge insertions between variables for which the score implies some conditional independence.