We consider the problem of diversity maximization from the perspective of individual fairness: given a set P of n points in a metric space, we aim to extract a subset S of size k from P so that (1) the diversity of S is maximized and (2) S is individually fair in the sense that every point in P has at least one of its nk-nearest neighbors as its "representative" in S. We propose (O(1),3)-bicriteria approximation algorithms for the individually fair variants of the three most common diversity maximization problems, namely, max-min diversification, max-sum diversification, and sum-min diversification. Specifically, the proposed algorithms provide a set of points where every point in the dataset finds a point within a distance at most 3 times its distance to its nk-nearest neighbor while achieving a diversity value at most O(1) times lower than the optimal solution. Numerical experiments on real-world and synthetic datasets demonstrate that the proposed algorithms generate solutions that are individually fairer than those produced by unconstrained algorithms and incur only modest losses in diversity.

This work studies a novel subset selection problem called max-min diversification with monotone submodular utility (MDMS), which has a wide range of applications in machine learning, e.g., data sampling and feature selection. Given a set of points in a metric space, the goal of MDMS is to maximize f(S) = g(S)+λ div(S) subject to a cardinality constraint |S| k, where g(S)is a monotone submodular function and div(S) = minu,v S:u =v dist(u,v)is the max-min diversity objective. We propose the GIST algorithm, which gives a 1/2-approximation guarantee for MDMS by approximating a series of maximum independent set problems with a bicriteria greedy algorithm. We also prove that it is NP-hard to approximate within a factor of 0.5584. Finally, we show in our empirical study that GISToutperforms state-of-the-art benchmarks for a single-shot data sampling task on ImageNet.

Proposition 1. Suppose Qφj(s,a) = Q(s,a) and Qφj(s,) is locally linear in the neighborhood of a for all j [N]. Let λmin and wmin be the smallest eigenvalue and the corresponding normalized eigenvector of the matrix Var aQφj(s,a) and > 0 be the value such that mini6=j aQφi(s,a), aQφj(s,a) = 1 . We first prove that the smallest eigenvalue λmin of Var aQφj(s,a) is upper-bounded by some constant multiple of . By Lemma 1, the total variance of the matrix is less or equal to N 1N. Note that, using the fact that the Q-values coincide at the action a and the local linearity of the Q-functions, we have derived Var(Qφj(s,a+ kw)) = k2w|Var aQφj(s,a) w. (2) Plugging w = wmin in Equation (2) and using Equation (1), we have Var(Qφj(s,a+ kwmin)) = k2w|minVar aQφj(s,a) wmin = k2λmin A.2 Relationship between maximizing the total variance and maximizing the smallest eigenvalue As we have shown in Section 4, maximizing the total variance of the matrix Var ( aQφi(s,a)) is equivalent to minimizing the cosine similarity of all distinct pairs of the gradients aQφi(s,a), 2 which makes the gradients uniformly distributed on the unit sphere S|A| 1.

In addition, our algorithm also adapts to scenarios where the repulsion is onlyrequired among nearby fewitems intheresult sequence.

We study timestamped question answering over educational lecture videos under a single-GPU latency/memory budget. Given a natural-language query, the system retrieves relevant timestamped segments and synthesizes a grounded answer. We present CourseTimeQA (52.3 h, 902 queries across six courses) and a lightweight, latency-constrained cross-modal retriever (CrossFusion-RAG) that combines frozen encoders, a learned 512->768 vision projection, shallow query-agnostic cross-attention over ASR and frames with a temporal-consistency regularizer, and a small cross-attentive reranker. On CourseTimeQA, CrossFusion-RAG improves nDCG@10 by 0.10 and MRR by 0.08 over a strong BLIP-2 retriever while achieving approximately 1.55 s median end-to-end latency on a single A100. Closest comparators (zero-shot CLIP multi-frame pooling; CLIP + cross-encoder reranker + MMR; learned late-fusion gating; text-only hybrid with cross-encoder reranking and its MMR variant; caption-augmented text retrieval; non-learned temporal smoothing) are evaluated under matched hardware and indexing. We report robustness across ASR noise (WER quartiles), diagnostics for temporal localization, and full training/tuning details to support reproducible comparison.

This paper introduces a hybrid framework for portfolio optimization that fuses Long Short-Term Memory (LSTM) forecasting with a Proximal Policy Optimization (PPO) reinforcement learning strategy. The proposed system leverages the predictive power of deep recurrent networks to capture temporal dependencies, while the PPO agent adaptively refines portfolio allocations in continuous action spaces, allowing the system to anticipate trends while adjusting dynamically to market shifts. Using multi-asset datasets covering U.S. and Indonesian equities, U.S. Treasuries, and major cryptocurrencies from January 2018 to December 2024, the model is evaluated against several baselines, including equal-weight, index-style, and single-model variants (LSTM-only and PPO-only). The framework's performance is benchmarked against equal-weighted, index-based, and single-model approaches (LSTM-only and PPO-only) using annualized return, volatility, Sharpe ratio, and maximum drawdown metrics, each adjusted for transaction costs. The results indicate that the hybrid architecture delivers higher returns and stronger resilience under non-stationary market regimes, suggesting its promise as a robust, AI-driven framework for dynamic portfolio optimization.

Step-wise explanations can explain logic puzzles and other satisfaction problems by showing how to derive decisions step by step. Each step consists of a set of constraints that derive an assignment to one or more decision variables. However, many candidate explanation steps exist, with different sets of constraints and different decisions they derive. To identify the most comprehensible one, a user-defined objective function is required to quantify the quality of each step. However, defining a good objective function is challenging. Here, interactive preference elicitation methods from the wider machine learning community can offer a way to learn user preferences from pairwise comparisons. We investigate the feasibility of this approach for step-wise explanations and address several limitations that distinguish it from elicitation for standard combinatorial problems. First, because the explanation quality is measured using multiple sub-objectives that can vary a lot in scale, we propose two dynamic normalization techniques to rescale these features and stabilize the learning process. We also observed that many generated comparisons involve similar explanations. For this reason, we introduce MACHOP (Multi-Armed CHOice Perceptron), a novel query generation strategy that integrates non-domination constraints with upper confidence bound-based diversification. We evaluate the elicitation techniques on Sudokus and Logic-Grid puzzles using artificial users, and validate them with a real-user evaluation. In both settings, MACHOP consistently produces higher-quality explanations than the standard approach.

Recent work has emphasized the diversification benefits of combining trend signals across multiple horizons, with the medium-term window-typically six months to one year-long viewed as the "sweet spot" of trend-following. This paper revisits this conventional view by reallocating exposure dynamically across horizons using a Bayesian optimization framework designed to learn the optimal weights assigned to each trend horizon at the asset level. The common practice of equal weighting implicitly assumes that all assets benefit equally from all horizons; we show that this assumption is both theoretically and empirically suboptimal. We first optimize the horizon-level weights at the asset level to maximize the informativeness of trend signals before applying Bayesian graphical models-with sparsity and turnover control-to allocate dynamically across assets. The key finding is that the medium-term band contributes little incremental performance or diversification once short- and long-term components are included. Removing the 125-day layer improves Sharpe ratios and drawdown efficiency while maintaining benchmark correlation. We then rationalize this outcome through a minimum-variance formulation, showing that the medium-term horizon largely overlaps with its neighboring horizons. The resulting "barbell" structure-combining short- and long-term trends-captures most of the performance while reducing model complexity. This result challenges the common belief that more horizons always improve diversification and suggests that some forms of time-scale diversification may conceal unnecessary redundancy in trend premia.