Diversified recommendation has attracted increasing attention from both researchers and practitioners, which can effectively address the homogeneity of recommended items. Existing approaches predominantly aim to infer the diversity of user preferences from observed user feedback. Nonetheless, due to inherent data biases, the observed data may not fully reflect user interests, where underexplored preferences can be overwhelmed or remain unmanifested. Failing to capture these preferences can lead to suboptimal diversity in recommendations. To fill this gap, this work aims to study diversified recommendation from a data-bias perspective.

Dynamic 3D scene reconstruction from multi-view videos demands representation to model complex deformations at scale. Current Gaussian Splatting based methods often either suffer from significant computation cost due to dense MLP-based modeling or explicit modeling deformation of each Gaussian independently. However, the dynamics of objects within a scene are typically hierarchical and exhibit structural correlations. To leverage these structural priors into the representation, we introduce TreeSplat, a Tree data structure for deformable Gaussian Splatting. In TreeSplat, as the name suggests, motions of Gaussian are represented hierarchically within a tree.

Tabular data have been playing a vital role in diverse real-world fields, including healthcare, finance, etc. With the recent success of Large Language Models (LLMs), early explorations of extending LLMs to the domain of tabular data have been developed. Most of these LLM-based methods typically first serialize tabular data into natural language descriptions, and then tune LLMs or directly infer on these serialized data. However, these methods suffer from two key inherent issues: (i) data perspective: existing data serialization methods lack universal applicability for structured tabular data, and may pose privacy risks through direct textual exposure, and (ii) model perspective: LLM fine-tuning methods struggle with tabular data, and in-context learning scalability is bottle-necked by input length constraints (suitable for few-shot learning). This work explores a novel direction of integrating LLMs into tabular data through logical decision tree rules as intermediaries, proposing a decision tree enhancer with LLM-derived rule for tabular prediction, DeLTa. The proposed DeLTa avoids tabular data serialization, and can be applied to full data learning setting without LLM fine-tuning. Specifically, we leverage the reasoning ability of LLMs to redesign an improved rule given a set of decision tree rules. Furthermore, we provide a calibration method for original decision trees via new generated rule by LLM, which approximates the error correction vector to steer the original decision tree predictions in the direction of "errors" reducing. Finally, extensive experiments on diverse tabular benchmarks show that our method achieves state-of-the-art performance.

Ordering-based approaches to causal discovery identify topological orders of causal graphs, providing scalable alternatives to combinatorial search methods. Under the Additive Noise Model (ANM) assumption, recent causal ordering methods based on score matching require an accurate estimation of the Hessian diagonal of the log-densities. In this paper, we aim to improve the approximation of the Hessian diagonal of the log-densities, thereby enhancing the performance of orderingbased causal discovery algorithms. Existing approaches that rely on Stein gradient estimators are computationally expensive and memory-intensive, while diffusionmodel-based methods remain unstable due to the second-order derivatives of score models. To alleviate these problems, we propose Score-informed Neural Operator (SciNO), a probabilistic generative model in smooth function spaces designed to stably approximate the Hessian diagonal and to preserve structural information during the score modeling. Empirical results show that SciNO reduces order divergence by 42.7% on synthetic graphs and by 31.5% on real-world datasets on average compared to DiffAN, while maintaining memory efficiency and scalability. Furthermore, we propose a probabilistic control algorithm for causal reasoning with autoregressive models that integrates SciNO's probability estimates with autoregressive model priors, enabling reliable data-driven causal ordering informed by semantic information. Consequently, the proposed method enhances causal reasoning abilities of LLMs without additional fine-tuning or prompt engineering.

Deep Neural Networks (DNN) have emerged as an effective approach to implementing challenging subproblems. They are increasingly being used as components in critical transportation, medical, and military systems. However, like human-written software, DNNs may have flaws that can lead to unsafe system performance. To confidently deploy DNNs in such systems, strong evidence is needed that they do not contain such flaws. This has led researchers to explore the adaptation and customization of software verification approaches to the problem of neural network verification (NNV). Many dozens of NNV tools have been developed in recent years and as a field these techniques have matured to the point where realistic networks can be analyzed to detect flaws and to prove conformance with specifications. NNV tools are highly-engineered and complex may harbor flaws that cause them to produce unsound results. We identify commonalities in algorithmic approaches taken by NNV tools to define a verifier independent proof format--activation pattern tree proofs (APTP)--and design an algorithm for checking those proofs that is proven correct and optimized to enable scalable checking. We demonstrate that existing verifiers can efficiently generate APTP proofs, and that an APTPcheckersignificantly outperforms prior work on a benchmark of 16 neural networks and 400 NNV problems, and that it is robust to variation in APTP proof structure arising from different NNV tools.

Local search is a powerful clustering technique that provides high-quality solutions with theoretical guarantees. With distance-based sampling strategies, local search methods can achieve constant approximations for clustering with linear running time in data size. Despite their effectiveness, existing algorithms still face scalability issues as they require scanning the entire dataset for iterative center swaps. This typically leads to an O(ndk) running time, where nis the data size, dis the dimension, k is the number of clusters. To further improve the efficiency of local search algorithms, we propose new methods based on adaptive sampling and bandit strategies.

Transformers and their attention mechanism have been revolutionary in the field of Machine Learning. While originally proposed for the language data, they quickly found their way to the image, video, graph, etc. data modalities with various signal geometries. Despite this versatility, generalizing the attention mechanism to scenarios where data is presented at different scales from potentially different modalities is not straightforward. The attempts to incorporate hierarchy and multimodality within transformers are largely based on ad hoc heuristics, which are not seamlessly generalizable to similar problems with potentially different structures. To address this problem, in this paper, we take a fundamentally different approach: we first propose a mathematical construct to represent multi-modal, multi-scale data. We then mathematically derive the neural attention mechanics for the proposed construct from the first principle of entropy minimization. We show that the derived formulation is optimal in the sense of being the closest to the standard Softmax attention while incorporating the inductive biases originating from the hierarchical/geometric information of the problem. We further propose an efficient algorithm based on dynamic programming to compute our derived attention mechanism. By incorporating it within transformers, we show that the proposed hierarchical attention mechanism not only can be employed to train transformer models in hierarchical/multi-modal settings from scratch, but it can also be used to inject hierarchical information into classical, pre-trained transformer models post training, resulting in more efficient models in zero-shot manner.

Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and adaptively employing a mixture of global exploration and local exploitation, this method has been used for optimization in many fields including machine learning, automotive engineering and reinforcement learning. However, the standard method suffers from two problems: 1) with cubic computational complexity in the training-set size it eventually becomes computationally infeasible to train the model, and 2) globally modeling the objective function is not necessarily optimal given the local nature of minimization. Using flexible and recursive binary partitioning of the search space, we adapt both the modeling and acquisitive aspects of standard Bayesian optimization to work harmoniously with the partitioning scheme, thereby ameliorating both standard shortcomings. We compare our method against a commonly used Bayesian optimization library on seven challenging test functions, ranging in dimensionality from $6$ to $124$, and show that our method achieves superior optimization performance in all tests. In addition our method has linear computational complexity.

Contents2 ADeriving Eq. 2. 23 BThe hyperplane set generated by the oblique tree is a superset of that created by the4 ReLU-activated plain DNN 35 CProof of Theorem 1 46 DProof of Theorem 2 57 EProof of Theorem 3 68 FProof of Theorem 4 79 GImplementation Detail 810 We consider a L-layer (L 2) ReLU activated plain DNN module f: Rn0 RnL with input12 x Rp. Eq. 2 in the main text can be30 obtained by rewriting P An oblique tree is a binary tree where each node splits the space by a hyperplane rather than by34 thresholding a single feature. The tree starts with the root of the full input space S, and by recursively35 splitting S, the tree grows deeper. For a D-depth (D 3) binary tree, there are 2D 1 1 internal36 nodes and 2D 1 leaf nodes. As shown in Figure 1, each internal and leaf node maintains a sub-space37 representing a polyhedron in S, and each layer of the tree corresponds to a partition of the input38 space into polyhedrons.