A growing trend in the database and system communities is to augment conventional index structures, such as B+-trees, with machine learning (ML) models. Among these, error-bounded Piecewise Linear Approximation ($ε$-PLA) has emerged as a popular choice due to its simplicity and effectiveness. Despite its central role in many learned indexes, the design and analysis of $ε$-PLA fitting algorithms remain underexplored. In this paper, we revisit $ε$-PLA from both theoretical and empirical perspectives, with a focus on its application in learned index structures. We first establish a fundamentally improved lower bound of $Ω(κ\cdot ε^2)$ on the expected segment coverage for existing $ε$-PLA fitting algorithms, where $κ$ is a data-dependent constant. We then present a comprehensive benchmark of state-of-the-art $ε$-PLA algorithms when used in different learned data structures. Our results highlight key trade-offs among model accuracy, model size, and query performance, providing actionable guidelines for the principled design of future learned data structures.

--Existing multi-media retrieval models either rely on creating a common subspace with modality-specific representation models or require schema mapping among modalities to measure similarities among multi-media data. Our goal is to avoid the annotation overhead incurred from considering retrieval as a supervised classification task and re-use the pre-trained encoders in large language models and vision tasks. We propose "FemmIR", a framework to retrieve multimodal results relevant to information needs expressed with multimodal queries by example without any similarity label. Such identification is necessary for real-world applications where data annotations are scarce and satisfactory performance is required without fine-tuning with a common framework across applications. We curate a new dataset called MuQNOL for benchmarking progress on this task. Our technique is based on weak supervision introduced through edit distance between samples: graph edit distance can be modified to consider the cost of replacing a data sample in terms of its properties, and relevance can be measured through the implicit signal from the amount of edit cost among the objects. Unlike metric learning or encoding networks, FemmIR re-uses the high-level properties and maintains the property-value and relationship constraints with a multi-level interaction score between data samples and the query example provided by the user . We also proposed a novel attribute recognition model from unstructured text "HART" that can identify attributes without finetuning or large language models. We empirically evaluate FemmIR and HART on a missing person use-case with MuQNOL. HART successfully identifies human attributes from large unstructured text without additional training, while FemmIR performs comparably to similar retrieval systems in delivering on-demand retrieval results with exact and approximate similarities while using the existing property identifiers in the system. With the influx of multimedia data sources, comparing data from different modalities to grasp a more informed decision for any phenomenon has become increasingly difficult.

Heuristic algorithms play a vital role in solving combinatorial optimization (CO) problems, yet traditional designs depend heavily on manual expertise and struggle to generalize across diverse instances. We introduce \textbf{HeurAgenix}, a two-stage hyper-heuristic framework powered by large language models (LLMs) that first evolves heuristics and then selects among them automatically. In the heuristic evolution phase, HeurAgenix leverages an LLM to compare seed heuristic solutions with higher-quality solutions and extract reusable evolution strategies. During problem solving, it dynamically picks the most promising heuristic for each problem state, guided by the LLM's perception ability. For flexibility, this selector can be either a state-of-the-art LLM or a fine-tuned lightweight model with lower inference cost. To mitigate the scarcity of reliable supervision caused by CO complexity, we fine-tune the lightweight heuristic selector with a dual-reward mechanism that jointly exploits singals from selection preferences and state perception, enabling robust selection under noisy annotations. Extensive experiments on canonical benchmarks show that HeurAgenix not only outperforms existing LLM-based hyper-heuristics but also matches or exceeds specialized solvers. Code is available at https://github.com/microsoft/HeurAgenix.

Hyperparameter optimization (HPO) aims to identify an optimal hyperparameter configuration (HPC) such that the resulting model generalizes well to unseen data. As the expected generalization error cannot be optimized directly, it is estimated with a resampling strategy, such as holdout or cross-validation. This approach implicitly assumes that minimizing the validation error leads to improved generalization. However, since validation error estimates are inherently stochastic and depend on the resampling strategy, a natural question arises: Can excessive optimization of the validation error lead to overfitting at the HPO level, akin to overfitting in model training based on empirical risk minimization? In this paper, we investigate this phenomenon, which we term overtuning, a form of overfitting specific to HPO. Despite its practical relevance, overtuning has received limited attention in the HPO and AutoML literature. We provide a formal definition of overtuning and distinguish it from related concepts such as meta-overfitting. We then conduct a large-scale reanalysis of HPO benchmark data to assess the prevalence and severity of overtuning. Our results show that overtuning is more common than previously assumed, typically mild but occasionally severe. In approximately 10% of cases, overtuning leads to the selection of a seemingly optimal HPC with worse generalization error than the default or first configuration tried. We further analyze how factors such as performance metric, resampling strategy, dataset size, learning algorithm, and HPO method affect overtuning and discuss mitigation strategies. Our results highlight the need to raise awareness of overtuning, particularly in the small-data regime, indicating that further mitigation strategies should be studied.

We make two closely related theoretical contributions to the use of importance sampling schemes. First, for independent sampling, we prove that the minimax optimal trial distribution coincides with the target if and only if the target distribution has no atom with probability greater than $1/2$, where "minimax" means that the worst-case asymptotic variance of the self-normalized importance sampling estimator is minimized. When a large atom exists, it should be downweighted by the trial distribution. A similar phenomenon holds for a continuous target distribution concentrated on a small set. Second, we argue that it is often advantageous to run the Metropolis--Hastings algorithm with a tempered stationary distribution, $π(x)^β$, and correct for the bias by importance weighting. The dynamics of this "importance-tempered" sampling scheme can be described by a continuous-time Markov chain. We prove that for one-dimensional targets with polynomial tails, $π(x) \propto (1 + |x|)^{-γ}$, this chain is uniformly ergodic if and only if $1/γ< β< (γ- 2)/γ$. These results suggest that for target distributions with light or polynomial tails of order $γ> 3$, importance tempering can improve the precision of time-average estimators and essentially eliminate the need for burn-in.

In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable function that makes small prediction errors. This additional goal largely rules out the standard approach used in regression, that is, reducing the learning problem to learning parameters of an expansion of basis functions by optimization. Instead, symbolic regression methods search for a good solution in a space of symbolic expressions. To cope with the typically vast search space, most symbolic regression methods make implicit, or sometimes even explicit, assumptions about its structure. Here, we argue that the only obvious structure of the search space is that it contains small expressions, that is, expressions that can be decomposed into a few subexpressions. We show that systematically searching spaces of small expressions finds solutions that are more accurate and more robust against noise than those obtained by state-of-the-art symbolic regression methods. In particular, systematic search outperforms state-of-the-art symbolic regressors in terms of its ability to recover the true underlying symbolic expressions on established benchmark data sets.

Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems. Computer algebra systems (CASs) provide support for solving ODEs by first simplifying them, in particular through the use of Lie point symmetries. Finding these symmetries is, however, itself a difficult problem for CASs. Recent works in symbolic regression have shown promising results for recovering symbolic expressions from data. Here, we adapt search-based symbolic regression to the task of finding generators of Lie point symmetries. With this approach, we can find symmetries of ODEs that existing CASs cannot find.

Solutions of symbolic regression problems are expressions that are composed of input variables and operators from a finite set of function symbols. One measure for evaluating symbolic regression algorithms is their ability to recover formulae, up to symbolic equivalence, from finite samples. Not unexpectedly, the recovery problem becomes harder when the formula gets more complex, that is, when the number of variables and operators gets larger. Variables in naturally occurring symbolic formulas often appear only in fixed combinations. This can be exploited in symbolic regression by substituting one new variable for the combination, effectively reducing the number of variables. However, finding valid substitutions is challenging. Here, we address this challenge by searching over the expression space of small substitutions and testing for validity. The validity test is reduced to a test of functional dependence. The resulting iterative dimension reduction procedure can be used with any symbolic regression approach. We show that it reliably identifies valid substitutions and significantly boosts the performance of different types of state-of-the-art symbolic regression algorithms.

Tokens are fundamental processing units of generative AI (GenAI) and large language models (LLMs), and token communication (TC) is essential for enabling remote AI-generate content (AIGC) and wireless LLM applications. Unlike traditional bits, each of which is independently treated, the semantics of each token depends on its surrounding context tokens. This inter-token dependency makes TC vulnerable to outage channels, where the loss of a single token can significantly distort the original message semantics. Motivated by this, this paper focuses on optimizing token packetization to maximize the average token similarity (ATS) between the original and received token messages under outage channels. Due to inter-token dependency, this token grouping problem is combinatorial, with complexity growing exponentially with message length. To address this, we propose a novel framework of semantic packet aggregation with lookahead search (SemPA-Look), built on two core ideas. First, it introduces the residual semantic score (RSS) as a token-level surrogate for the message-level ATS, allowing robust semantic preservation even when a certain token packet is lost. Second, instead of full search, SemPA-Look applies a lookahead search-inspired algorithm that samples intra-packet token candidates without replacement (fixed depth), conditioned on inter-packet token candidates sampled with replacement (fixed width), thereby achieving linear complexity. Experiments on a remote AIGC task with the MS-COCO dataset (text captioned images) demonstrate that SemPA-Look achieves high ATS and LPIPS scores comparable to exhaustive search, while reducing computational complexity by up to 40$\times$. Compared to other linear-complexity algorithms such as the genetic algorithm (GA), SemPA-Look achieves 10$\times$ lower complexity, demonstrating its practicality for remote AIGC and other TC applications.

Electromagnetic structure (EMS) design plays a critical role in developing advanced antennas and materials, but remains challenging due to high-dimensional design spaces and expensive evaluations. While existing methods commonly employ high-quality predictors or generators to alleviate evaluations, they are often data-intensive and struggle with real-world scale and budget constraints. To address this, we propose a novel method called Progressive Quadtree-based Search (PQS). Rather than exhaustively exploring the high-dimensional space, PQS converts the conventional image-like layout into a quadtree-based hierarchical representation, enabling a progressive search from global patterns to local details. Furthermore, to lessen reliance on highly accurate predictors, we introduce a consistency-driven sample selection mechanism. This mechanism quantifies the reliability of predictions, balancing exploitation and exploration when selecting candidate designs. We evaluate PQS on two real-world engineering tasks, i.e., Dual-layer Frequency Selective Surface and High-gain Antenna. Experimental results show that our method can achieve satisfactory designs under limited computational budgets, outperforming baseline methods. In particular, compared to generative approaches, it cuts evaluation costs by 75-85%, effectively saving 20.27-38.80 days of product designing cycle.