We study online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed subsets of the $d$-dimensional unit cube. The best known constructive offline approximation factor is $0.401$ under the corresponding meta-solvability assumptions, whereas comparable adversarial online guarantees had remained at $1/e$. We show that this factor is also achievable online. In the post-decision full-information value-oracle model, our algorithm attains factor $0.401$ with sublinear approximate regret when oracle feedback is conditionally unbiased and bounded. The online algorithm does not run the offline construction on a changing objective. Instead, it replaces the offline objective-dependent box step by a weighted online learner that controls the required residual terms cumulatively. An exact asymmetric balance theorem preserves the offline coefficients despite adversarial variation. The direct implementation has $O(T^{3/4})$ regret and uses $O(dT^{1/4})$ oracle calls per round. More generally, for every $δ\in[0,1/4]$, batching gives $O(T^δ)$ calls per round and $O(T^{4/5-δ/5})$ regret, including a one-call $O(T^{4/5})$ endpoint. Under a positive-anchor condition, randomized blocking retains factor $0.401$ with $O(T^{5/6})$ one-point bandit regret.
Loading reusable skill documents into a bounded context window is now the primary way large language model (LLM) agents acquire task-specific capabilities, which makes skill selection a first-order determinant of task performance and token cost. Yet current agents score skills independently by semantic relevance and assemble the set by top-$k$ or greedy packing, with no quality guarantee or cost awareness on the selected set. As a result, redundant or poorly chosen skills waste scarce context tokens and can even degrade performance. We give the first model of how the selected skill set shapes execution outcomes and cast skill selection as an optimization problem: choose a skill set under a hard token budget to maximize a monotone submodular benefit minus context penalty. For this problem, we develop Best Prefix Selection (BPS), a polynomial-time algorithm, and prove, to our knowledge, the first performance guarantee for skill selection: a bicriteria $(1-1/e,1)$ approximation whose benefit coefficient is optimal in polynomial time. On a contamination-controlled BigCodeBench variant, BPS outperforms all the baselines, reaching $0.73$ measured task success versus $0.20$--$0.52$ for released skill routers, text retrievers, and the executor's own selection, on $28\%$ fewer tokens than the strongest released router.
Vision-Language Models (VLMs) are highly effective in retrieving semantically relevant images. However, in practice, relevance alone is often insufficient. Systems must also achieve Result Diversification (RD) across composite attributes such as geography and time, a task for which precise control remains challenging. Current re-ranking methods, such as Multi-Source Determinantal Point Processes (MS-DPP), address this using manifold-based repulsion over similarity representations. Although this strategy is effective for broad exploration, it exposes a key limitation in manifold-based models: when subjected to diversity-decrease tasks on discrete metadata, they suffer substantial degradation in early-rank recall. To bridge this gap, we introduce MASCOT (Model-Aware Submodular Coverage for Composite-Attribute Text-to-Image Retrieval). Instead of relying on manifold repulsion, MASCOT formulates multi-attribute diversity as a resource allocation problem, projecting attributes into a soft-binning space weighted by query-driven importance. Averaged across the three PixelProse diversity-decrease tasks, MASCOT preserves an early-rank recall (R@10) of 88.58%, while MS-DPP retains 67.63%. The margin widens under composite constraints: on PP_geo_hour, where temporal and geographic diversity must be suppressed simultaneously, MS-DPP's recall collapses from 0.9737 to 0.4931 and its top-ranked result degrades to R@1 = 0.23, while MASCOT holds R@10 = 0.9410 and R@1 = 0.7202 at a diversity metric above the unconstrained baseline. We do not claim uniform superiority: on aggregate diversity-relevance scores our own simpler ablations attain higher harmonic means on all three decrease tasks, and MASCOT's advantage is specific to recall beyond rank 1 under composite constraints.
Streaming VideoLLMs process frames causally while visual tokens grow continuously, making compression essential for controlling prefilling latency and memory. Existing training-free methods independently rank tokens, ignoring marginal-gain interactions among retained tokens. We argue that streaming video token compression should instead be formulated as set selection, where each candidate is valued by what it adds beyond the tokens already retained. Unlike existing set-wise methods designed for offline tasks, streaming makes causal, frame-by-frame pruning decisions, so modeling cross-frame interactions requires an explicit historical reference. This creates a reference-set dilemma: the reference must adequately represent previously conveyed content while remaining bounded for real-time inference. We introduce NovaCov, to our knowledge the first training-free, plug-and-play set-wise token compressor designed for streaming video. NovaCov maintains a capacity-bounded, recency-weighted Historical Reference Bank and optimizes a dual-branch submodular coverage objective that preserves representative current-frame content while prioritizing information insufficiently covered by history. Both branches are facility-location functions, so greedy selection retains the classical (1-1/e) approximation guarantee. Across streaming and offline benchmarks, NovaCov outperforms existing training-free compression methods, retaining 99.6% of ReKV accuracy while reducing LLM prefilling latency by 46%.
Each WSI slide contains thousands of candidate tissue patches, while supervision is usually available only at slide level. Existing bag-construction strategies like Uniform extraction and handcrafted heuristics do not control redundancy while attention-based multiple-instance models couple patch importance to a particular downstream classifier, and coreset methods optimise embedding-space coverage without modelling task-relevant patch quality. We introduce InfoDPP-PAC, a principled patch-selection framework that combines teacher-seeded Gaussian process relevance modelling, determinantal log-determinant diversity,submodular greedy optimisation, and a concentration-based adaptive stopping rule. The main theoretical result shows that the log-determinant diversity term used in DPP-style selection is the Gaussian process mutual information between a selected subset and the latent relevance function. We further derive a PAC-style certificate for residual information gain, allowing the number of retained patches to vary by slide rather than being fixed a priori. The empirical study evaluates whether the selected subset is diverse, spatially and morphologically covering, non-redundant, and enriched for the teacher-derived relevance signal. It does not claim end-to-end diagnostic improvement after retraining a downstream MIL model. On 202 HISTAI gastrointestinal whole-slide images, the adaptive rule uses 83.7% fewer patches on average than a fixed full budget while retaining 97.9% of full-budget composite selection quality. At a matched budget, InfoDPP-PAC achieves the highest mean teacher-derived relevance score among fourteen baselines, with diversity and composite scores close to the strongest coreset methods. The results support InfoDPP-PAC as a controlled quality-diversity-cardinality selection framework, rather than as a downstream clinical predictor.
Submodular maximization is an important building block for developing algorithms in many areas such as machine learning and data mining. Due to the NP-hardness of the problem, analysis of submodular maximization algorithms typically provides pessimistic worst-case approximation factors only. It is not easy to evaluate how close a produced solution is to an optimal one for a given problem instance. In this paper, we develop new data-dependent upper bounds for submodular maximization with a knapsack constraint. We theoretically prove that they dominate the optimal solution and empirically demonstrate their advantages in certifying how close to optimal a solution is through experiments with real-world datasets.
Retrieval-augmented generation (RAG) under a fixed reader-context budget forces a selection problem: of the evidence retrieved, only a fraction can be shown to the reader. We argue that document recall -- the standard retrieval metric -- is the wrong quantity to optimize in this regime, and we make two contributions. First, as a general contribution, we introduce answer-in-context, a diagnostic that measures whether a gold answer survives as a contiguous span in the packed reader context (not the retrieved set). It predicts answer F1 better than recall (r=0.39-0.55 vs. about 0.31), separates answer quality roughly five-fold (0.60 vs. 0.12 on HotpotQA), and carries information beyond retrieval: it adds Delta R squared=0.17 over recall and shows a 4.6x EM gap even among questions where all gold was retrieved. We also confirm it interventionally: on 2WikiMultiHopQA a packing change that raises coverage but not answer-in-context yields no accuracy gain. Second, as a conditional contribution, we cast reader-context construction as budgeted monotone submodular maximization and build a packer that jointly optimizes relevance, query coverage, representativeness, and diversity. On HotpotQA with a 160-token budget and a 3B reader it beats a strong focused heuristic, MMR, and naive packing -- by up to +5.1 F1 at equal-or-lower token cost, across three seeds. Crucially, we map the scope of this win honestly: it requires the conjunction of (i) multi-hop complementary structure, (ii) retrieval that surfaces the evidence, (iii) a binding but not extreme budget, and (iv) a reader weak enough that evidence density, not reading capacity, is the bottleneck. A quantization-controlled reader-scale ladder (3B to 7B to 14B) shows the edge over the heuristic is absorbed by 7B and significantly reverses by 14B, while the diagnostic explains every boundary with a single variable.
Retrieval-augmented generation (RAG) typically treats context selection as ranking chunks against a single query embedding. This assumption breaks down for complex queries, such as multi-hop or ambiguous questions, where top-k selection tends to over-cover one semantic aspect while ignoring critical sub-questions. We propose GeoRAG, which recasts context selection as Information Demand Coverage Optimization. GeoRAG builds a multi-dimensional demand distribution through diverse sub-query generation and reverse-validation weighting, then selects context by minimizing the Sinkhorn-Wasserstein distance between this demand distribution and the coverage of the selected set. The resulting demand-weighted facility-location objective is monotone submodular, giving a $1-1/e$ greedy guarantee, which we approximate with a Sinkhorn-based marginal-gain surrogate. The method is unsupervised, training-free, and retrieval-agnostic. We further show that single-point, query-proximity scorers cannot cover multi-modal demands, exposing a structural limit of ranking-based selection. On six open-domain QA benchmarks, GeoRAG improves exact match (EM) by +6.5 to +7.5 points over top-k truncation (up to +9.7 on HotpotQA and ASQA) and outperforms strong baselines including MMR, DPP, BGE-Reranker, SMART-RAG, and AdaGReS, with stable gains across context budgets and sub-query generators.
Trustworthy AI requires reliable data-processing pipelines, not only robust downstream predictive models. As an upstream component, data summarization determines which information is retained and passed to subsequent learning or decision modules. Therefore, adversarial perturbations to the summarization process can compromise trustworthy AI in an upstream manner: they may alter the selected summary, reduce its representativeness, and further degrade the utility of subsequent learning tasks. In this paper, we study adversarial attacks on continuous data summarization under similarity-level perturbations through DR-submodular optimization. We show that a class of multi-resolution image summarization objectives can be formulated as multilinear extensions of non-negative submodular set functions and satisfy DR-submodularity with $m$-weak monotonicity. We then formulate multi-target attack generation as a min-max problem, where one admissible perturbation of the similarity structure is optimized to degrade multiple target summarization models. To mitigate such perturbations, we formulate robust defense against mixed attack types as a regularized max-min problem. For both problems, we develop approximation algorithms with theoretical guarantees. Experiments on real-data and controlled clustered benchmarks show that the proposed attack is effective in representative low-to-moderate budget regimes and can induce downstream task-performance loss. The proposed defense improves the robustness--mitigation trade-off in structured settings, while also revealing the parameter sensitivity of robust protection on real data.
Few-shot example retrieval is the dominant paradigm for grounding large language models (LLMs) in domain-specific text-to-SQL systems. However, the quality of the annotated example bank directly governs system accuracy, and expert annotation is prohibitively expensive. We formalize the active selection of these examples as a constrained experimental design problem over the intrinsic, low-dimensional manifold of semantic query embeddings. Unlike standard active learning frameworks, our setting introduces three critical challenges: varying, query-dependent annotation reliability (heteroscedasticity), strict requirements for spatial diversity across semantic topics (partition matroid constraints), and the inherent reality that the true covariance structure of the embedding space is unknown (misspecification). To address these, we propose a stratified greedy algorithm that maximizes a heteroscedastic mutual information objective. We prove that this objective remains submodular and approximately monotonic on the intrinsic manifold, yielding a theoretical constant-factor approximation guarantee. We establish a spectral bound demonstrating that this approximation guarantee degrades gracefully, rather than catastrophically, when the assumed surrogate kernel diverges from the true underlying data-generating process. Empirical results demonstrate that the proposed strategy significantly reduces labeling effort while maintaining high text-to-SQL retrieval accuracy.
Meher Chaitanya, Sebastian Dalleiger, Luana Ruizcs.LG
Local Hyper-Flow Diffusion (HFD) gives an edge-size-independent Cheeger-type guarantee for seeded clustering in general submodular hypergraphs, but existing HFD solvers do not keep intermediate computation local at every iteration. We introduce Thresholded Local HFD (TL-HFD), a first-order method that maintains an active region around the seeds, performs projected subgradient updates on that region and its immediate boundary, and expands via thresholded (top-k) boundary activation. We prove that the local update is exact: the degree-preconditioned projected subgradient step restricted to the active region and its boundary coincides with the unrestricted global update. We establish finite-time dual suboptimality for both exact and thresholded updates, treating the latter as inexact projected subgradient steps with explicit skipped-boundary error. We further derive an additive activated-volume bound controlled by realized local subgradient norms and the minimum boundary-push among newly activated vertices, and translate approximate dual optimality with localized support into a robust sweep-cut guarantee for early-stopped iterates. For general submodular cut-costs, each iteration is local in the scanned region and oracle-sensitive in the hyperedge primitive. Empirically, TL-HFD often matches or improves over HFD while activating less volume, with the largest gains on noisy instances where diffusion tends to absorb non-target vertices.
Paul Dütting, Federico Fusco, Silvio Lattanzi +3cs.DS cs.LG stat.ML
Consistency is an important property in dynamic submodular maximization and entails maintaining a near-optimal solution at all times, making only a small number of adjustments to the solution in each step. Prior work has explored this question for the insertion-only case, where the algorithm faces a stream of $n$ insertions, and has established lower and upper bounds for the cardinality-constrained version of the problem. We consider this question in the fully dynamic setting, where the stream of operations may contain both insertions and deletions. We develop a general framework for designing algorithms for this setting, and instantiate it to obtain the first constant-factor approximations with sublinear consistency. For cardinality constraints, we propose a $\frac 12 - O(\varepsilon)$ approximation that is $O\left(\frac{1}{\varepsilon^2}\right)$ consistent. For rank-$k$ matroid constraints, we construct a $\frac 14 - O(\varepsilon)$ approximation to the dynamic optimum that is $O\left(\frac{\log k}{\varepsilon^2}\right)$ consistent.
Vision-language models such as CLIP achieve strong visual-textual alignment, but often suffer from overfitting and limited interpretability when adapted through continuous prompt learning. While discrete prompt optimization improves interpretability, it usually depends on large external models, leading to high computational costs and limited scalability. In this paper, we propose Interpretable Prompt Learning (IPL), a hybrid framework that alternates between discrete semantic token selection and continuous prompt optimization. Specifically, IPL formulates semantic token selection as an approximate submodular optimization problem, encouraging tokens that are both human-understandable and semantically diverse. It further adopts an alternating optimization strategy to integrate discrete token selection with continuous prompt tuning, improving interpretability while preserving adaptability to downstream tasks. Our framework is plug-and-play, allowing seamless integration with existing prompt learning methods. Extensive experiments on multiple benchmarks show that IPL consistently improves both interpretability and accuracy across five representative prompt learning methods, providing an effective and scalable extension to existing frameworks.
We consider selective classification with abstention in the fixed-pool (or transductive) setting, where the unlabeled pool is given beforehand and only a subset of points can be queried for labels. Our main insight is to view selective prediction through agreement: given queried labels and Lipschitz margin constraints in an embedding space, the version space of Lipschitz-consistent classification heads is well defined. We obtain upper and lower Lipschitz margin bounds that define, for each pool point, a set of certified valid labels containing the prediction of every head in the version space. The model therefore predicts only when the label is forced (i.e., all consistent heads agree), and abstains otherwise. We also propose a monotone submodular geometric proxy for budgeted querying, and show that a greedy algorithm retains the standard approximation factor.