Stock clustering algorithms play a pivotal role in quantitative finance and the asset management industry, serving as a core mechanism for understanding market complexity and conducting asset preselection. Their intrinsic value lies in enabling investors to identify the true underlying structure of the stock market, thereby categorizing stocks with similar return characteristics or risk profiles into distinct groups. This data-driven market segmentation not only significantly reduces the computational dimensionality involved in portfolio construction but also provides a solid foundation for formulating differentiated investment strategies. A review of existing literature reveals that scholars both domestic and international have achieved fruitful results in stock clustering. Traditional clustering research predominantly employs classic machine learning algorithms: Xiaojun (2019) and Wu et al. (2022) utilized the K-means algorithm for stock partitioning; Huang et al. (2010) and Lu et al. (2020) explored the sectoral structures of the SSE 50 Index and other markets based on Agglomerative Hierarchical Clustering (AHC) and Spectral Clustering; Korzeniewski (2018) further introduced the Partitioning Around Medoids (PAM) algorithm to construct portfolios with enhanced risk resistance. In recent years, with the advancement of deep learning, L ucio and Caiado (2022) and Siregar and Yosia (2024) have attempted to incorporate time-series models (such as TGARCH) or specific market features (e.g., Indonesian stock data) into clustering frameworks. However, despite their respective merits in capturing market trends, these methods share a common limitation: traditional stock clustering approaches predominantly rely exclusively on stock-specific information (e.g., price, volatility, or financial metrics), neglecting the heterogeneity of market participants--namely, the "investors". In reality, investors are typically categorized into three distinct types based on their risk preferences: risk-averse, risk-seeking, and risk-neutral. Divergent risk attitudes inevitably lead to fundamentally different asset selection logic.

A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the minimization of the maximum mean discrepancy (MMD) between the true joint measure and its transport-based approximation. To circumvent the non-convexity in the MMD optimization, we introduce a training-free transport filter method via gradient flows, which leads to an analytic computation for the transport map that implies the steepest descent direction of the MMD. The proposed approach accurately approximates non-Gaussian filtering posteriors and avoids particle collapse. We provide a convergence analysis for the expectation of the MMD between the approximated posterior and the truth posterior. Finally, we extend the method to high-dimensional problems through domain localization. Numerical examples demonstrate the superior performance of our approach over conventional filtering methods in nonlinear, non-Gaussian scenarios.

Decision making under uncertainty is commonly modelled as a process of competitive stochastic evidence accumulation to threshold (the drift-diffusion model). However, it is unknown how animals learn these decision thresholds. We examine threshold learning by constructing a reward function that averages over many trials to Wald's cost function that defines decision optimality. These rewards are highly stochastic and hence challenging to optimize, which we address in two ways: first, a simple two-factor reward-modulated learning rule derived from Williams' REINFORCE method for neural networks; and second, Bayesian optimization of the reward function with a Gaussian process. Bayesian optimization converges in fewer trials than REINFORCE but is slower computationally with greater variance. The REINFORCE method is also a better model of acquisition behaviour in animals and a similar learning rule has been proposed for modelling basal ganglia function.

We present the HOH (Human-Object-Human) Handover Dataset, a large object count dataset with 136 objects, to accelerate data-driven research on handover studies, human-robot handover implementation, and artificial intelligence (AI) on handover parameter estimation from 2D and 3D data of two-person interactions. HOH contains multi-view RGB and depth data, skeletons, fused point clouds, grasp type and handedness labels, object, giver hand, and receiver hand 2D and 3D segmentations, giver and receiver comfort ratings, and paired object metadata and aligned 3D models for 2,720 handover interactions spanning 136 objects and 20 giver-receiver pairs--40 with role-reversal--organized from 40 participants. We also show experimental results of neural networks trained using HOH to perform grasp, orientation, and trajectory prediction. As the only fully markerless handover capture dataset, HOH represents natural human-human handover interactions, overcoming challenges with markered datasets that require specific suiting for body tracking, and lack high-resolution hand tracking. To date, HOH is the largest handover dataset in terms of object count, participant count, pairs with role reversal accounted for, and total interactions captured.

Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees. We study the worst-case performance of recent graph-based approximate nearest neighbor search algorithms, such as HNSW, NSG and DiskANN. For DiskANN, we show that its "slow preprocessing" version provably supports approximate nearest neighbor search query with constant approximation ratio and poly-logarithmic query time, on data sets with bounded "intrinsic" dimension. For the other data structure variants studied, including DiskANN with "fast preprocessing", HNSW and NSG, we present a family of instances on which the empirical query time required to achieve a "reasonable" accuracy is linear in instance size. For example, for DiskANN, we show that the query procedure can take at least 0.1n steps on instances of size nbefore it encounters any of the 5nearest neighbors of the query.

Modern neural networks are often quite wide, causing large memory and computation costs. It is thus of great interest to train a narrower network. However, training narrow neural nets remains a challenging task. We ask two theoretical questions: Can narrow networks have as strong expressivity as wide ones? If so, does the loss function exhibit a benign optimization landscape?

We define the Performer architecture formally as follows. V Rdmodel d are trainable parameters (separate for each instance of MultiHead-Att, FFN), "+" is broadcasted rowwise when biases are added and LN is layer normalization [2], which is applied rowwise and depends on additional trainable parameters. GeLU denotes Gaussian error Linear Unit [16], which is applied elementwise. Similarly, U(n) does not affect L(1),...,L(n), so This way, the 3D tensor R RL d M is not stored in memory explicitly, resulting in O(L) time and O(L(d+ M) + dM) memory complexity. In order to have the same memory consumption during back-propagation, [18] propose the following routine.