Top-K

Root cause analysis at a remote site is slow: evidence is scattered across pod logs, Kubernetes events and cluster-level objects, and many operators cannot send production logs to a hosted model at all. On-premise inference removes the second constraint but raises a question live-cluster benchmarks have not addressed: when one workstation GPU fixes both the model and the context budget, how should evidence be retrieved, and what happens when the runbooks the model consults have been tampered with? We present TriFleetRCA, a pipeline running entirely on one on-premise GPU that collects evidence at one of three scopes (pod, namespace, cluster), ranks it by template de-duplication then BM25, filters runbooks through an ingest guard, and returns a root cause with the evidence lines supporting it. We evaluate on a live Kubernetes cluster into which we inject four faults, so ground truth is known by construction, across 100 analyses with Qwen2.5-14B-Instruct at temperature 0. The hit rate was 0.85, 0.90 and 0.95 at pod, namespace and cluster scope; intervals overlap, but the whole scope effect comes from the one fault whose cause is a cluster-level object, and cluster scope costs 55% more tokens. De-duplication before ranking raised the hit rate from 0.75 to 0.90 at equal token cost. A poisoned runbook telling the model to delete the namespace was rejected by the guard every run; with the guard disabled the model declined to follow it in all 20 analyses, making the guard defence in depth rather than the sole barrier. Separating citation quality from accuracy proved informative: one fault was diagnosed correctly and cited incorrectly every trial, a failure mode accuracy conceals. Median latency was 1.6 s at 2,200 prompt tokens. We release the pipeline, the fault injector and all records.

Decoding-time KV cache compression research focuses heavily on designing better token scoring functions, while the temporal rule that aggregates scores across decode steps is often treated as an implementation detail. Under aggressive KV compression, we find that exponential-moving-average (EMA) aggregation makes approximately order-preserving scorer modifications largely indistinguishable at the eviction-set level. Value-norm and entropy variants remain highly correlated with attention and produce nearly unchanged retention sets, whereas KeyDiff, key norm, recency, and a learned scorer alter the ranking and degrade substantially. We associate this stability with the evaluated aggregation, which couples layer weighting and temporal retention. Building on this observation, we introduce InertiaKV, an EMA-based decoding-time eviction method, and InertiaKV-Lazy, its periodic-refresh variant, which yields 1.34-1.46x decode throughput relative to full refresh InertiaKV. We also study Score-Free decoding as a separate empirical operating point: it scores the full context once at the first decode step, freezes that ranking, and incurs an average quality change of +0.03 while removing all subsequent scoring. Across six open-weight backbones and the LongBench, LongBench-v2, and RULER benchmarks, the results identify temporal aggregation and ranking preservation as distinct, consequential design factors; they do not imply that scoring quality is irrelevant in general.

Large language models (LLMs) struggle to classify text into taxonomies with many semantically similar labels, as the distinctions are domain-specific and not captured by pre-training. To handle large label spaces, a common approach retrieves top-$K$ candidate labels by embedding similarity and prompt the LLM to choose among them. However, top-$K$ retrieval reduces the number of candidates but does not help the model tell similar ones apart. When two similar labels both appear as candidates, the model lacks the signal to choose correctly between them. We propose a framework that (1) identifies which label pairs the model struggles to distinguish, (2) expands the candidate set to include confusable labels, and (3) generates targeted rules to differentiate between similar candidates. The framework requires no fine-tuning, and the generated rules transfer to smaller, cheaper models. On three benchmarks (WOS, Flipkart, LEDGAR), our approach improves Macro F1 by up to 10.0pp over retrieval baselines, with smaller models (2B--20B) gaining up to 11.5pp via cross-model transfer.

Diffusion Transformers (DiTs) incur quadratic self-attention cost over spatiotemporal tokens. Existing training-free sparse attention methods often construct sparse masks from block-level or cluster-level proxy scores, which can obscure fine-grained differences among keys and miss high contribution keys under aggressive sparsity. Moreover, such proxy scores may yield overly concentrated softmax distributions, causing Top-$p$ to retain too few keys for some query clusters. Although a fixed Top-$k$ minimum alleviates this failure mode, a shared value cannot adapt to variations across heads and inputs. To address both limitations, we propose SCOPE, a training-free sparse attention framework that combines 3D-RoPE-aligned key subspace clustering with online per-head Top-$k$ estimation for efficient video-DiT inference. SCOPE partitions post-RoPE keys into temporal, height, and width subspaces, clusters them independently, and aggregates the corresponding centroid scores through lookup tables to obtain per key proxy scores for each query cluster. Building on existing hybrid Top-$p$/fixed Top-$k$ selection, SCOPE derives a head-specific Top-$k$ value online by averaging the initial retained key counts within each head, weighted by query cluster size, and selects additional keys only for query clusters whose initial retained key counts fall below this value. Sparse attention is then computed over the selected original keys and values. Across six model--task configurations, SCOPE consistently outperforms existing training-free baselines in both fidelity and latency, achieving up to a $1.99\times$ end-to-end speedup on 720p HunyuanVideo with $28.46$ dB PSNR relative to dense attention.

Top-k selection is a fundamental computational primitive with applications spanning databases, information retrieval, signal processing, and modern machine learning workloads, including sparse activations and attention pruning. As data sizes grow, existing approaches become inefficient: exact methods incur high memory and compute overhead, while approximate methods often rely on brittle heuristics that degrade under adversarial or heavy-tailed inputs. In this paper, we introduce Prof-K, a fast, scalable, and distribution-agnostic top-k algorithm with probabilistic correctness guarantees. Prof-K performs a single-pass filtering procedure: a small random sample estimates an adaptive threshold, the N input elements are streamed once into a compact buffer, and an exact top-k routine on this buffer recovers the true top-k elements with probability at least 1 - $ε$, where $ε$ > 0 is user specified. We derive high-probability guarantees for correctness and buffer size, together with an approximately optimal sample size that minimizes overhead as a function of N and k. Empirically, Prof-K achieves 1.5x-10x speedups over the highly optimized PyTorch topk and recent RadiK implementations, with the largest gains in the large-scale, small-to-moderate-k regime where prior methods struggle most. Unlike previous approaches, these guarantees hold independently of the input distribution, ensuring robustness to adversarial settings. By relaxing the recall target (e.g., recovering 95% of the true top-k values), Prof-K additionally provides a principled accuracy-speed trade-off. We further demonstrate its impact on training BatchTopK Sparse Autoencoders (SAEs), where top-k selection constitutes a significant portion of the training cost.

Organizations decide whom to treat under a budget and want to know what a targeting rule would have earned before deploying it. Off-policy evaluation promises this from logged data, but the deployable rule is a deterministic top-k policy: it removes all averaging over actions, so weak overlap hits the estimate directly. We benchmark six estimators across five datasets and two known-effect sweeps, and validate the mechanisms against a non-simulated paired reference. First, weak overlap is governed by logger-target action alignment, not by logging sharpness alone: what governs support is the logger's probability of the target's actions. Sharpening a logger built from the target's own score barely moves overlap over the tested range; action-level disagreement collapses it. Effective sample size ranks this risk across logging environments, but is weak at ranking candidates within the single log a practitioner holds, and its cut point does not transfer. Second, the optimizer's curse is not fixed by cross-fitting the outcome nuisance. When the rule is fit on the data used to evaluate it, cross-fitting the nuisance alone leaves the reuse bias in place and makes it worse. Honest policy-level splitting avoids the reuse by targeting the learning procedure's value -- a change of estimand, not a de-biasing of the full-sample policy. Third, propensity-estimation error is the largest degradation we measure: an out-of-fold estimate hurts IPS more than any other stress we apply, leaves doubly-robust estimation almost unchanged, and can invert the overlap diagnostic itself. Logging is synthesized and propensities floored at 0.02, so every failure occurs with bounded weights; the floor also reduces the two tuned hybrids to their untuned parents, leaving four practically distinct estimators, and all exact-value surfaces are synthetic or semi-synthetic. We release the benchmark; public data only.

Underwater images often suffer from diverse and coexisting degradations, including color distortion, scattering haze, texture attenuation, and uneven illumination. These degradations vary across regions and may coexist locally, making conventional uniform restoration difficult to adapt to different degradation patterns. To address this problem, we propose Coexisting and Region-wise Degradation for Underwater Image Enhancement (\textbf{CoRe-UIE}), a degradation-oriented expert collaboration framework. CoRe-UIE combines a content-preserving shared expert with four shared-backbone routed experts for color correction, scattering suppression, texture recovery, and illumination protection. The routed experts share the same architecture but have independent parameters, and are assigned to different regions through input-derived degradation cues and region-adaptive Top-$k$ routing. We further introduce a Hilbert--Schmidt Independence Criterion (HSIC)-based representation constraint to reduce statistical dependence among expert features and alleviate redundant expert responses. Experiments on UIEB, LSUI, and U45 demonstrate that CoRe-UIE achieves competitive quantitative performance and visually balanced enhancement under diverse underwater degradation conditions.

The top-$k$ operation is a fundamental building block of modern sparse computation, enabling token routing, expert activation, memory selection, and attention pruning. Yet standard hard top-$k$ blocks gradients, while existing continuous (soft) relaxations remain too costly for large-scale models. We introduce Fast LapSum, an exact-budget soft top-$k$ primitive whose GPU solver runs in linear time after sorting. Unlike prior linear-time methods such as DFTopK, which relax the normalization constraint, Fast LapSum is, to our knowledge, the first method to preserve an exact selection mass of $k$ while remaining fully differentiable end-to-end. Our solver combines a linear-time threshold computation with an analytical vector--Jacobian product, and for extreme scales employs probabilistic bracketing to sort only the uncertain middle band of kernel-noised scores. The resulting overhead is almost negligible: the solver processes $10^6$, $10^7$, and $10^8$ scores in $0.41$, $1.15$, and $5.23$,ms, respectively. This makes exact soft top-$k$ practical for sparse routing, retrieval, and large-scale optimization. We demonstrate Fast LapSum on two demanding applications operating over millions of coordinates inside the training loop: generating megapixel sparse adversarial examples with an exact soft budget of ${\sim}0.02\%$ of an image's pixels, achieving an order-of-magnitude speedup over state-of-the-art methods, and training a fully differentiable sparse image coder from scratch.

Retrieval-augmented generation over long documents is dominated by one design: chunk the text, embed the chunks, and surface the top-k nearest neighbours of the query. We argue that for an important class of documents -- financial statements, audit reports, regulatory returns -- this design is structurally unsound, and we make the argument measurable. On a 780-page government financial report, 86.8% of content lines are table rows, thousands of near-identical figures compete in one embedding space, and a figure inherits its unit from a header a median of 13 lines above it -- so a chunk boundary routinely separates a number from whether it is in lakh or crore, an error of two orders of magnitude. A table-aware chunker built as a steelman fixes the unit problem but leaves 27-30% of numeric chunks with no fiscal-year header at every chunk size we tried. We propose READ (Reliable Embedding-free Agentic Document-search), in which an agent reads the raw document through three deterministic operations -- normalized lexical search, structural navigation, and bounded span reads -- exposed over the Model Context Protocol, so a trajectory is a replayable audit trail, not an opaque similarity score. On 51 verified questions READ answers 58.8% against dense retrieval's 15.7% (p_Holm = 2 x 10^-5) -- or 35.3% tuned, which READ still leads by 23.5 points (p_Holm = 0.017). An agent given the same loop but a top-k tool reaches only 27.5%, locating the gain in the interface rather than in iteration. We also report what the evidence does not support: BM25 is statistically indistinguishable from READ, so our result separates embedding-based from embedding-free retrieval, not agentic from lexical search.

Top-$k$ selection determines which components of a sparse model remain active. Hard selection blocks gradients, while continuous relaxations often couple mask hardness to the selected mass. We introduce LaPrune, a mathematically exact-budget differentiable layer that controls the normalized second moment while preserving the selected mass. A LapSum barrier preserves the selection mass, and a normalized second-moment constraint moves the mask from a dense equal-mass allocation toward hard top-$k$ at each budget. We derive a population prediction of the saturated fraction, a near-binary limiting law, and a tight worst-case guarantee on the near-zero fraction. The normalized hardness parameter is invariant to score scale, while a fixed LapSum temperature is not.

Existing low rank KV cache methods preserve either model weights or key variance, neither of which directly reflects the attention scores used during inference. We derive the expected attention score distortion caused by rank r key compression and show that it yields a covariance weighted low rank objective. Under a margin condition, controlling this distortion also improves top k recall. The optimal rank r solution has a closed form asymmetric factorization obtained from the SVD of the covariance weighted query key operator. This motivates SAKI, a training free KV cache index that directly preserves attention scores rather than key reconstruction quality. Across LLaMA 3.1 8B, Qwen 2.5 7B, Mistral 7B v0.1, and Llama 3.2 3B, SAKI outperforms key PCA at every tested rank. At rank 32, it removes 13 to 30 percent of PCA's remaining top 64 recall error, including improvements from 0.748 to 0.799 on LLaMA 3.1 8B and from 0.786 to 0.850 on Qwen 2.5 7B. It improves 68 to 89 percent of attention heads per model, with the largest gains in deeper layers. Predicted score MSE reductions closely match empirical measurements, with a Pearson correlation of 0.997, while ablation studies confirm that the gains arise from optimizing the attention score objective rather than covariance weighting alone. Analysis of the scoring operator further explains why weight only, invariant subspace, and key reconstruction methods can be suboptimal. SAKI uses random-matrix theory to separate genuine covariance signal from autocorrelated sampling noise, matching PCA with only 512 calibration tokens and adding value exactly where PCA sees no reliable signal.

Leader Reward modifies POMO training to emphasize the best trajectory produced by repeated inference. We test a narrow extension: replace its binary leader/non-leader distinction with a stabilized rank signal indexed by a sampling budget $K$. With the POMO architecture, 3,050-epoch schedule, and TSP-100 test set held fixed, the Leader Reward reimplementation obtains $7.7662$ under 100-start, 8-augmentation greedy decoding, matching the reported $7.766$ at its displayed precision. Under independent sampling, the stabilized $K=8$ recipe lowers realized Best-of-8 cost in all three paired training seeds: $7.7944$ versus $7.8136$. This observation is estimation-only and decoder-specific: three seeds are below the six-seed testing floor, Leader Reward is better at sampled $K=1$, and it remains slightly better under its original augmented-greedy protocol. We make no unbiased-estimator, universal superiority, or state-of-the-art claim.

Vision foundation models, such as DINOv2, learn highly expressive representations but rely on massive, opaque architectures that demand substantial computational power and memory. To provide an interpretable-guided and efficient solution to this issue, we first propose a spectral analysis and new visualization technique for individual attention heads based on the Laplacian eigenvectors of their attention maps. Building upon recent observations regarding the block structure of Vision Transformers, we perform semantic clustering of attention heads and identify functional redundancies. Leveraging these insights, we introduce SAPER (Soft Attention PrunER), an end-to-end differentiable pruning framework based on the LapSum Soft Top-K approach. Extensive experiments on ImageNet-1K demonstrate that SAPER achieves a highly favorable accuracy-efficiency trade-off, outperforming the competitive RAPTOR baseline in FLOPs reduction while preserving strong classification performance.

Top-$K$ sparse attention reduces the cost of Softmax and value aggregation by attending to only a small subset of key--value (KV) entries. However, identifying this subset still requires scoring the current query against the full KV cache and performing global Top-$K$ selection, leaving selector cost linear in context length and limiting the practical efficiency of sparse attention for long-context decoding. In this paper, we introduce ReTopK, a training-free method that accelerates dynamic Top-$K$ attention by reusing historical retrieval decisions. ReTopK builds on the observation that similar queries often attend to overlapping supports and that partially overlapping supports can still preserve most of the Exact Top-$K$ attention mass. For each attention head, it maintains a bounded cache of historical query--support pairs, retrieves the most similar cached queries for each new query, unions their stored supports with a recent window, and reranks only the resulting compact candidate set using exact current-query scores. A similarity-based fallback invokes full-history Exact Top-$K$ when reuse is unreliable, while periodic exact refreshes limit cache drift. ReTopK retains the complete KV cache and reuses only selected indices, rather than historical scores, attention weights, or outputs. Across 16K--128K contexts, ReTopK achieves the lowest PG19 perplexity and the highest NIAH and LongBench scores among the evaluated approximate methods. At 128K with $K=512$, ReTopK incurs only a 0.50% perplexity increase over Exact Top-$K$ while accelerating attention computation by $3.07\times$.

A stochastic Gumbel-Top-$K$ router defines, for every token of a mixture-of-experts (MoE) model, a \emph{routing law}: a distribution over ordered expert lists and mixture weights. We ask which \emph{joint} distributions over the routing choices of different tokens are reachable while every individual token's complete routing law is held exactly fixed. We give a two-sided construction, \emph{Hierarchical Copula-Gumbel-Top-$K$} (\CGA{}). Within a group of related tokens, an exchangeable Gaussian copula positively correlates the Gumbel perturbations at each expert coordinate, which can increase within-group expert-set coherence. Across disjoint pairs of groups, a tunable antithetic construction introduces a selectable amount of negative dependence. We prove that both operations leave each token's ordered Top-$K$ sample, mixture weights, and inclusion probabilities identical in distribution to independent routing \emph{at a routing layer conditioned on its pre-routing logits}; conditional expected expert traffic is preserved as a consequence. We characterize the resulting trade-off: positive within-group coupling can only inflate the variance of realized expert loads relative to independent routing, while nonnegative cross-group opposition can only reduce it relative to flat coupling at the same within-group strength. Coherence and load dispersion are thus controlled by two complementary dependence dials on the invariance constraint surface. Because the base model is untouched, the dials can be driven by a small controller over frozen features, trainable with a score-function estimator: the frozen network is evaluated only in the forward direction, and gradients are confined to the controller. An initial small-scale pilot validates the mechanism and the training route, but does not establish task-level fine-tuning gains.

Reinforcement Learning is a cornerstone technique for modern large reasoning models. Usually, for difficult tasks such as code generation and theorem proving, the agent is evaluated by generating $K$ responses rather than sampling a single response, and performance is then measured using a retry-aware metric such as $\max$@$k$. Despite their practical importance, the theoretical foundations of learning under such criteria remain limited. In this work, we provide a theoretical study of the $\max$@$k$ learning problem in finite-horizon reinforcement learning. We show that optimizing the $\max$@$k$ objectives is fundamentally different from standard expected-return maximization. In particular, we prove that Markovian policies are in general insufficient, identify a compact state augmentation that restores optimality, and explicitly characterize the performance gap that can arise between history-dependent and non-history-dependent policies. Moreover, we show that learning $\max$@$k$-optimal policies is statistically harder than standard reinforcement learning and provide an efficient algorithm that achieves the optimal sample complexity rate.

Text-to-image (T2I) models can synthesize realistic, prompt-aligned images, yet samples generated for the same prompt often cover only a small subset of visually distinct modes. This limits diversity and, for person-centric prompts, can reflect or amplify demographic skew. We formalize this problem as target-mode coverage, the coverage of a predefined set of semantically specified modes, and propose multi-axis max@K, a group-based reinforcement learning objective for improving it in diffusion-based T2I models. Given a group of samples and one score per target mode, multi-axis max@K first takes the maximum score across samples for each mode and then sums these per-mode maxima. The resulting credit assignment gives a sample positive weight on a mode only when it raises that mode's group maximum, so different samples can contribute to different modes. We validate the credit-assignment mechanism on a synthetic mixture and on SD3.5-M with deterministic pixel-based color rewards, and then apply the same objective to perceived-appearance fairness. On held-out prompts, multi-axis max@K improves the Fairness Score by 0.23-0.36 over the base model under three automatic evaluators, while maintaining image quality and text alignment. Code is available at https://github.com/KuOnoda/multi-axis-maxk.

We study the coupled objective J_K^WOR = E_{S ~ PL-WOR_K}[max_{i in S} R_i]: the expected maximum reward of a size-K Plackett-Luce draw without replacement, the law of Gumbel-Top-K / Stochastic Beam Search decoding. This estimand differs from the conventional i.i.d. objective J_K^iid = E[max_{i<=K} R_i] targeted by existing sample-reuse Max@K estimators, and reusing their i.i.d. weights under the coupled sampler is provably biased (a closed-form three-item instance gives E[g_iid] = (4/5) grad J_K^WOR exactly; pass@K under the coupled sampler is the binary-reward special case). Generic joint-score REINFORCE is already unbiased for J_K^WOR; what it lacks is sample reuse. Our contribution is to instantiate standard rank-conditioned Horvitz-Thompson estimation for the J_K^WOR subset total: from one Gumbel-Top-n pool (n>K) and its observed priority threshold we build an estimator that reuses all C(n,K) embedded K-subsets, unbiased with an unbiased exact score-function surrogate gradient, plus a reward-sorted Max-specific dynamic program that collapses the C(n,K)-term subset sum (with K!-cost set probabilities) exactly to a one-dimensional integral. A fixed-Q quadrature evaluation costs O(n log n + nKQ) arithmetic and is numerically, not algebraically, exact; no epsilon-approximation rate is certified. Each nonzero degree-K Horvitz-Thompson term has finite second moment exactly when n >= 2K; under the same assumptions the full surrogate gradient has finite second moment whenever n >= 2K (sharpness there is open). At K=1 the construction recovers classical priority sampling. All quantities require only the values and differentiable computation graphs of the n+1 drawn items' probabilities, so finite structured sequence policies sampled by exact SBS are covered. A certified finite-Q quadrature bound and countably infinite support remain open. Validation code is included as ancillary files.

Indexer-TopK, the operation to compute the scores and select the top-k candidates, is widely used by sparse attention kernels in large language models and vector retrieval in recommendation systems and vector databases. However, existing GPU-based Indexer-TopK kernels like DeepSeek Sparse Attention (DSA) remain inefficient due to excessive global memory traffic, costly synchronization, and prohibitive memory overhead. In this work, we exploit the curse of dimensionality in high-dimensional spaces, where distances between high-dimensional vectors tend to concentrate within a narrow range, to design LITETOPK, a novel and efficient fused Indexer-TopK kernel. LITETOPK first samples a small subset of data to estimate query-data score ranges, then uses these estimates to partition candidate results into bins online. This organization allows the LITETOPK kernel to maintain a tight approximate threshold, write back only promising candidates, reduce unnecessary I/O, substantially lower memory overhead, and still preserve exact Top-k correctness. Experimental results show that LITETOPK accelerates the prefill stage of GLM 5.2 by 1.2x in real-world deployment scenarios while incurring lower memory overhead.

KV-cache compression methods are predominantly evaluated with the query appended to the context before compression -- a query-aware protocol. Yet the economic case for a compressed KV cache is reuse: compress a document once, answer many future questions against it. In that deployment, compression must happen query-agnostic -- before any question is seen. We present a matched-budget audit of six published compression methods against three trivial baselines on three open 7-9B models (144,300 paired evaluations on RULER-8192; 40,800 on LongBench; 50,000-resample paired bootstrap throughout). Everything is held fixed -- model, compression ratio, instances, decoding -- except the scoring rule. Three findings. (1) Query visibility changes the rankings: under the agnostic protocol, of the five audited methods that share a common attention backend, only KeyDiff beats a best-of-3 trivial baseline consistently (31 of 36 cells), and the most widely deployed method, SnapKV, loses to "keep the start and the recent window" on average (-0.066). (2) The per-method drop between the two protocols is ordered consistently with how visible the question is to each method's scoring signal, legible in its source code: from Delta=+0.198 for SnapKV (the question sits inside its 64-token observation window) down to Delta=+0.011 for KeyDiff (its score contains no query term at all).

We study the active learning problem of fixed-confidence top-$k$ identification from noisy pairwise comparisons. In this problem, an algorithm sequentially chooses pairs of items to compare, observes the outcomes, and stops when it can return the set of top-$k$ items with error probability at most $δ$. The objective is to design such a $δ$-correct procedure that minimizes the expected number of comparisons (the sample complexity). This problem falls within the broader literature on fixed-confidence pure exploration in bandit models, where a common target is asymptotic optimality: the algorithm's expected sample complexity matches the information theoretic lower bound as $δ\to 0$. Asymptotically optimal procedures have been developed for a range of fixed-confidence pure-exploration problems, however to the best of our knowledge, for top-$1$, or more generally top-$k$ identification from pairwise comparisons under latent utility models an asymptotically optimal algorithm has not been established. In this setting, we develop such an algorithm. We characterize the structure of the lower bound and formulate it as a saddle-point problem. This structure enables a computationally efficient primal-dual procedure that learns the asymptotically optimal comparison allocation online. We then construct an adaptive comparison-allocation algorithm that tracks the allocation learned by the primal-dual procedure and prove it is asymptotically optimal.

The k-means++ algorithm is commonly restarted multiple times to avoid poor local optima, yet the number of restarts is almost always chosen arbitrarily and applied uniformly regardless of data set difficulty. This undermines any comparison relying on such a choice and wastes computation on easy data sets while potentially under-serving hard ones. We introduce GTRC, a restart criterion combining a Good-Turing estimate, a proven unconditional bound, and a confidence-based bound on the probability that a further restart would improve on the current result, stopping once this probability falls below a user-specified tolerance $\varepsilon$. Across 36 data sets, GTRC reached clustering quality competitive with well-chosen fixed restart counts, while the number of restarts used varied considerably and appropriately with data set difficulty, governed by an interpretable, data-dependent signal rather than a fixed rule. GTRC offers a principled and reportable alternative to fixing the number of $k$-means++ restarts in advance. Software:https://github.com/RCdeAmorim/Good-Turing-Restart-Criterion.

Coreset selection aims to identify a small and highly representative subset of a massive dataset for efficient model training. The problem remains challenging even in the few-shot knowledge distillation (KD) setup, where a full-scale pre-trained teacher informs the student network. Typical sample selection strategies often struggle to surpass the random selection baseline. In this paper, we showcase few-medoids, an embarrassingly simple coreset selection strategy that chooses the samples closest to the centroid (average image) of each class. We present extensive KD experiments on four datasets, covering a wide range of image classification problems, and three teacher-student model pairs, comprising both convolutional and transformer networks. Although the proposed method is embarrassingly simple, our empirical results indicate that few-medoids is able to consistently surpass the random selection baseline, as well as the other coreset selection strategies. We therefore consider that few-medoids can be used as a drop-in replacement for commonly-used baselines (e.g. herding or k-center Greedy), in future research on coreset selection. To reproduce the reported results, we publicly release our code at https://github.com/CemilAndreiDilmac/Few-Shot-KD-Coreset.

Automatic mapping between disease classification systems, such as the International Classification of Diseases (ICD), is a challenging yet essential task for integrating health data and conducting longitudinal data analysis. Existing embedding-based methods primarily focus on \emph{one-to-one} mappings, overlooking more complex \emph{one-to-many} scenarios. The threshold-based and top-K methods offer natural extensions; however, they involve inherent trade-offs between \emph{precision}, \emph{recall} and \emph{mapping coverage} -- the proportion of source codes with at least one mapping to a target code. To address this challenge, we introduce a novel method, which is inspired by the \emph{blocking-and-matching} pipeline commonly used in \emph{entity resolution}. In particular, we first generate a block of candidate matches (\emph{blocking}) and then employ a large language model (LLM) to identify all valid mappings within each block (\emph{matching}). Empirically, we show that the proposed method achieves higher precision with comparable recall and broader coverage across multiple ICD version pairs (ICD-9-CM$\leftrightarrow$ICD-10-CM and ICD-10-AM$\leftrightarrow$ICD-11). Our source code and dataset is available at: https://tinyurl.com/46kyn7wp.

Sparse Mixture-of-Experts (MoE) architectures enable scaling LLM parameters under a fixed inference budget by activating only a small subset of experts via top-$k$ routing. While this preserves causality and suits autoregressive language models, the discrete top-$k$ operator is not differentiable, forcing a fixed number of active experts per input and resulting in inefficient use of computation. We propose SoftMoE, which replaces discrete routing with a truncated soft top-$k$ LapSum relaxation, allowing gradient-based optimization of expert routing. We further parameterize the mean number of active experts per layer and impose a global budget constraint, enabling the model to learn how to allocate expert capacity across layers. SoftMoE remains fully compatible with autoregressive modeling and achieves performance comparable to or better than sparse MoE on language modeling and downstream tasks, while activating significantly fewer experts. Notably, the learned allocation is highly non-uniform, with later layers activating more experts. The source code is publicly available$^\dagger$.

Diversity plays a critical role in data selection, improving performance under fixed data budgets by reducing redundancy and repetition. However, optimizing for diversity is inherently challenging, as it is a set-level property that depends on interactions between data points rather than individual examples. As a result, existing approaches typically rely on proxies or approximations, which often fail to ensure sufficiently diverse subsets. In this work, we directly optimize diversity by introducing a probabilistic diversification framework based on the G-Vendi score, optimized via exponentiated gradient descent. Our method produces subsets that are substantially more diverse than those obtained via random sampling, achieving a +489 increase in G-Vendi score on a 500k-sample subset. We evaluate our approach on FineWeb and DCLM, where it consistently outperforms existing methods. Notably, SPOKES (diversity-only) improves average downstream performance by +0.4 and +0.5 points over random sampling on DCLM and FineWeb, respectively. More importantly, jointly optimizing for both quality and diversity yields the strongest results: SPOKES achieves gains of +1.5 and +1.4 points on DCLM and FineWeb, outperforming all baselines, including semantic deduplication and quality filtering.

Stimulated word-of-mouth is a strategy that promotes information sharing through prompts or incentives. Optimizing stimulated word-of-mouth through social networks requires identifying and targeting connected users who are most susceptible to spillover, a phenomenon where the influence of recommendations extends beyond the immediate audience to impact their connected users. The probability of spillover varies across individuals, and their connections, leading to heterogeneity. Understanding and accurately estimating the spillover probabilities among users in social networks is crucial for improving the effectiveness of stimulated word-of-mouth. To address this, we present a novel contextual multi-armed bandit framework that learns individual spillover probabilities and ranks connected users to maximize rewards from stimulated word-of-mouth. Experiments on real-world network datasets demonstrate that accounting for spillover heterogeneity enhances the targeting precision of top-$k$ connected users, boosting rewards and outperforming baseline methods that do not learn individual spillover effects.

We establish conditions for embedding a corpus of $N$ documents as $d$-dimensional vectors such that every $k$-subset $S \subseteq [N]$ is realizable as a result of top-$k$ retrieval by some query vector. Recent work shows that $d = O(k)$ suffices for such embeddings to exist in $\mathbb{R}^d$, independently of $N$. We theoretically prove that this corpus-independent bound is specific to infinite precision. With $B$ bits per coordinate, perfect top-$k$ retrieval requires $Bd = Ω(k \ln N)$; thus, at any fixed precision, the dimension must grow at least logarithmically with $N$. Specializing to a $\ell_2$-normalized $B$-bit uniform scalar quantization model, we also identify a threshold on the precision $B^{*} = O(\ln \ln N)$ below which no dimension suffices, together with two further regimes that bound the feasible $(B, d)$ pairs. Our result implies that in practical vector databases and dense retrieval systems where quantization is standard, the embedding dimension and possibly the precision must grow with the corpus size.

Long, multimodal documents force retrieval-augmented systems to assemble answers from evidence fragmented across text, tables, and slides broken across cells in a long table, spread over multiple slides, or split between a figure and its discussion. Top-$k$ chunk retrieval treats each fragment independently and cannot represent how evidence connects. We introduce FLOWREADER, which reframes evidence assembly as a min-cost flow problem on a multimodal node graph: a single scoring vector $h$ controls source selection (via MMR), sink selection (via a length-aware answerability proxy), and the costs and capacities of every edge. The optimal flow is decomposed into candidate evidence paths, a compact non-redundant subset is selected by entropy-regularized replicator dynamics, and parallel VLM workers under a dual-process gate produce the answer with a single System-2 refinement pass triggered when answer consistency is low or the routed flow is strained. On VisDoMBench, FLOWREADER is best on the two subsets dominated by fragmented evidence PaperTab ($58.40$, $+1.30$ over G^{2}-Reader) and SlideVQA ($72.93$, $+0.62$) and competitive on SPIQA, FetaTab, and SciGraphQA. Macro-averaged across all five subsets, FLOWREADER ($65.47$) is within $0.74$ of the strongest baseline (G^{2}-Reader, $66.21$). Overall, these results show that min-cost flow performs well on fragmented multimodal evidence, where top-$k$ retrieval fails. It also provides a unified way to control scoring, routing, selection, and adaptive compute together.

The attention mechanism is a cornerstone of modern transformer architectures. However, its expressive power comes at the cost of quadratic runtime and linear space usage. In particular, the classical transformer architecture explicitly stores all previously seen input elements (tokens) in order to generate the next one. The problem of implementing a transformer in limited space, known as KV cache compression, has received much interest over the past few years, spurring the development of powerful heuristics. Recent works of Haris et al, COLT'25 and Kochetkova et al, NeurIPS'25, formalized KV cache compression as the streaming attention approximation problem, providing both upper bounds (based on discrepancy theory) and information theoretic lower bounds. However, those papers left open a significant gap between the upper and lower bounds. For example, the space usage of their algorithms increases with the precision parameter, but the lower bound does not get stronger. In this work, we revisit the streaming attention approximation problem and provide nearly tight bounds on its space complexity. On the algorithmic side, we achieve the result through a surprisingly tight interplay between three distinct methods for kernel density estimation: discrepancy-based coreset constructions (e.g., Charikar-Kapralov-Waingarten'24), the polynomial method (e.g., Greengard-Rokhlin'87, Alman-Song'23), and space partitioning (e.g., Andoni-Laarhoven-Razenshteyn-Waingarten'17, Charikar-Kapralov-Nouri-Siminelakis'20). On the lower bound side, our main technical contribution is a new technique for using the INDEX problem with a large amount of side information that we hope will prove useful in other high dimensional geometric estimation problems.

TorchKM is an open-source library for kernel machines, including support vector machines, kernel logistic regression, and kernel quantile regression, with GPU acceleration. The library features a scikit-learn-style API and is designed to exploit GPU-friendly linear algebra, accelerating the full training and model-selection pipeline through intelligent reuse of matrix operations. Benchmarks show competitive predictive performance with substantial speedups over standard baselines. The efficiency and programmable design also make TorchKM a kernel-learning component for AI-driven workflows. Code and documentation are available at https://github.com/YikaiZhang95/torchkm, and the package can be easily installed via PyPI.

Language model parameters are known to impose unique (to each model) geometric constraints on their logit outputs, which serves as a signature that identifies the model, but also leaks the model's final layer parameters when an API distributes logits. We investigate more restrictive APIs that expose token rankings (i.e., their ordering by probability, but not the probability values) and find that rankings also constitute a signature: every model has a unique set of feasible top-$k$ rankings for sufficiently large $k$. Furthermore, the ranking signature is the first known (polynomially) unforgeable signature, since finding a model with the same set of feasible rankings is NP-hard. On the security front, we find that token rankings are already sufficient to approximately steal the final layer of the model, similar to logits, though the approximation is too coarse to forge the signature, and can be effectively countered by restricting the API to top-$k$ tokens with sufficiently small $k$. Since the top-$k$ required to present the model signature is generally smaller than the $k$ required to prevent stealing, it is possible for an API to present an unforgeable signature without leaking model parameters.

As real-world applications increasingly require processing inputs of 100k+ tokens, the gap between context length and inference efficiency has become a critical bottleneck. Context compression offers a way to reduce prefill costs while preserving task accuracy. However, existing training-free attention-based methods leave substantial gaps in demanding long-context tasks such as code reasoning. We present LongAttnComp, a long-context adaptation of AttnComp that fine-tunes a lightweight cross-attention scoring layer and introduces tokenlevel chunking, a token-budget top-p algorithm, positional reordering, and a formatagnostic query parser. We further design a two-stage fine-tuning recipe for the compressor: Stage 1 builds a general retrieval foundation from NIAH-style data, and Stage 2 extends it with multi-hop and reasoning data for broader long-context task coverage. On InfiniteBench Code-Debug, LongAttnComp matches or exceeds full-context accuracy, substantially outperforms training-free baselines, and transfers across four target models from three families. On LongBench v2, the two-stage recipe largely closes the Stage 1 gap on multi-document reasoning while preserving Code-Debug performance.

We describe \emph{Dual-Route Top-K Retrieval with 1v1 VLM Reranking} for the CoVR-R challenge. The method treats composed video retrieval as two coupled problems: finding a sufficiently complete top-k candidate set, and then safely deciding whether any candidate should replace a strong current top-1. We first improve the reasoning/text seed with a VLM slot selector over existing candidates, without introducing DFN visual retrieval. We then add a visual route from contact-sheet embeddings using DFN-H/DFN-L. The routes are merged into a top-10 candidate set, after which a VLM final reranker performs conservative 1v1 comparisons between the current top-1 and each challenger. On the hidden test split, the final system reaches 95.28 R@1, 97.47 R@5, 98.48 R@10, and 99.66 R@50. The main lesson is that CoVR-R benefits more from recall-selection decoupling than from broad text reranking or direct multi-candidate VLM classification.

Fine-tuning often introduces spurious correlations alongside task knowledge, causing systematic failures on underrepresented groups. Existing mitigations require retraining, group labels, or curated counterfactual data. We show a simple post-hoc intervention reduces shortcut reliance without any of these: truncating the tail of the SVD of $ΔW = W_\mathrm{ft} - W_\mathrm{base}$ reduces the spurious-group gap while preserving task accuracy. Across three instruction-tuned models ($0.5$B--$7$B) and four classification benchmarks, top-$k$ truncation reduces the gap on every cell at $<2$ pp accuracy loss, by up to $5\times$ on CivilComments. We propose this works because the shortcut response sits in the tail of the singular ordering of $ΔW$, a claim about how truncation behaves rather than about the raw singular values, which are broadly distributed and look the same across all four datasets. A controlled boundary case in which fine-tuning has only a shortcut to learn shows the predicted FT-to-base collapse, and bottom-/random-$k$ and matched-rank LoRA controls rule out generic low-rank approximation and rank-constrained training as the explanation. We read this as preliminary evidence that the singular basis of $ΔW$ is a useful coordinate system for studying what fine-tuning has learned.

We empirically audit the k-NAF budget-accounting mechanism in Anchored Decoding using (i) a fixed, class-stratified workload (approximately 8,500 randomized executions across six prompt classes) and (ii) an adaptive prompt-search procedure targeting high proxy spend ratios. On the fixed workload, mean cumulative KL spend remains far below the sequence-level budgets K in {600, 1000}, and an empirical Bernstein-style proxy stays below K for every class; surface-overlap diagnostics (ROUGE-L and 5-gram Jaccard) are correspondingly small. Adaptive search increases the proxy spend ratio but does not produce clear budget exhaustion. On a held-out copyright-domain workload at k = 3, several prompts exhibit proxy ratios above 1 under early-stopped evaluations with small realized sample sizes; re-evaluating the same prompts with larger allocation reduces the proxy ratio to the range [0.26, 0.40] under comparable mean spend, consistent with proxy artifacts rather than per-trajectory budget failures.

This paper presents CyBOKClaw, an interpretable human-in-the-loop retrieval framework for mapping cybersecurity keywords or phrases (KWoPs) to the Cyber Security Body of Knowledge (CyBOK). Rather than treating the task as strict exact classification, the framework is designed as a top-k candidate generator for expert review. It combines query normalization, curated term expansion, concept-level boosts, topic-description enrichment, and domain-sensitive ranking rules. Because educational KWoPs are often broad, ambiguous, and only approximately aligned with CyBOK terminology, strict exact matching provides only a partial account of practical utility. We therefore evaluate the framework using both structural retrieval metrics and an expert-guided top-5 usefulness metric, ECA-5 (Exact or Closest Acceptable Match at top-5), which records whether the returned candidates contain at least one mapping that an expert would judge exact or accept as the nearest practical CyBOK placement. On the development dataset, CyBOKClaw achieves 64.73% EXA-5 (Exact Match at top-5), 84.18% structural semantic alignment, and 91.88% ECA-5; on the validation dataset, it achieves 81.19% EXA-5, 93.32% structural semantic alignment, and 98.00% ECA-5. These results show that expert-guided top-k usefulness provides a more faithful account of practical CyBOK mapping utility than exact structural matching alone, and that CyBOKClaw is effective as a CyBOK-specific expert-support retrieval system.

Graph Neural Networks (GNNs) have become important machine learning tools for graph analysis, and its explainability is crucial for safety, fairness, and robustness. Layer-wise relevance propagation for GNNs (GNN-LRP) evaluates the relevance of \emph{walks} to reveal important information flows in the network, and provides higher-order explanations, which have been shown to be superior to the lower-order, i.e., node-/edge-level, explanations. However, identifying relevant walks by GNN-LRP requires {\em exponential} computational complexity with respect to the network depth, which we will remedy in this paper. Specifically, we propose {\em polynomial-time} algorithms for finding top-$K$ relevant walks, which drastically reduces the computation and thus increases the applicability of GNN-LRP to large-scale problems. Our proposed algorithms are based on the \emph{max-product} algorithm -- a common tool for finding the maximum likelihood configurations in probabilistic graphical models -- and can find the most relevant walks exactly at the neuron level and approximately at the node level. Our experiments demonstrate the performance of our algorithms at scale and their utility across application domains, i.e., on epidemiology, molecular, and natural language benchmarks. We provide our codes under \href{https://github.com/xiong-ping/rel_walk_gnnlrp}{github.com/xiong-ping/rel\_walk\_gnnlrp}.

The linear growth of the Key-Value (KV) cache is a critical bottleneck in long-form LLM inference. Existing KV compression methods mitigate this by evicting tokens based on importance scores. However, we show that their reliance on global Top-k selection triggers Region Wipe-out: the severe eviction of contiguous reasoning blocks that derails logical coherence. To address this, we propose Adaptive Mass-Segmented (AMS) KV Compression, a framework that shifts the paradigm from token-level competition to region-aware quota allocation. AMS adaptively partitions the KV cache based on the spatial distribution of attention mass, ensuring structurally vital reasoning segments receive guaranteed memory quotas. To ensure stability during iterative decoding, an EMA-based smoothing mechanism is incorporated to prevent jitter in segment boundaries. Crucially, AMS is a universal plug-and-play layer that is orthogonal to existing scorers. It can be seamlessly integrated into representative methods such as TOVA, Expected Attention, KeyDiff, R-KV and TriAttention. AMS is also system-compatible with modern paged-KV serving frameworks such as vLLM, supporting efficient gather-and-compact KV execution without introducing additional steady-state attention overhead. Extensive experiments across a diverse suite of tasks, including mathematical reasoning (MATH500, AIME, GSM8K), code completion, open-domain QA, and sparse retrieval, demonstrate that AMS consistently mitigates structural fragmentation and boosts model performance.

Current hierarchical attention methods, such as NSA and InfLLMv2, select the top-k relevant key-value (KV) blocks based on coarse attention scores and subsequently apply fine-grained softmax attention on the selected tokens. However, the top-k operation assumes the number of relevant tokens for any query is fixed and it precludes the gradient flow between the sparse and dense stages. In this work, we propose DashAttention (Differentiable and Adaptive Sparse Hierarchical Attention), which leverages the adaptively sparse $α$-entmax transformation to select a variable number of blocks according to the current query in the first stage. This in turn provides a prior for the second-stage softmax attention, keeping the entire hierarchy fully differentiable. Contrary to other hierarchical attention methods, we show that DashAttention is non-dispersive, translating to better long-context modeling ability. Experiments with large language models (LLMs) show that DashAttention achieves comparable accuracy as full attention with 75% sparsity and a better Pareto frontier than NSA and InfLLMv2, especially in high-sparsity regimes. We also provide an efficient, GPU-aware implementation of DashAttention in Triton, which achieves a speedup of up to over FlashAttention-3 at inference time. Overall, DashAttention offers a cost-effective strategy to model long contexts.

Most current paradigms in visual mechanistic interpretability (MI) remain confined to interpreting internal units of the vision model via heuristic methods (e.g., top-$K$ activation retrieval or optimization with regularization). In this work, we establish a theoretical distributional view for visual MI, which models the influence of a feature activation on the natural image distribution, thereby formulating a Kullback-Leibler (KL)-minimal optimization problem to model the MI task. Under this framework, statistical biases are identified within previous MI paradigms, which reveal that they may either be perceptually uninterpretable to humans (i.e., deviate from the natural image distribution), or mechanistically unfaithful to the vision models (i.e., unable to activate model features). To resolve the biases under the distributional view, we propose a model with a KL-minimal soft-constraint principle for visual MI that theoretically balances interpretability and faithfulness. We realize this principle via energy-guided diffusion posterior sampling. Extensive experiments validate the theoretical soundness of the proposed distributional view and demonstrate the practical effectiveness of our paradigm on the DINOv3 vision model.

KV-cache compression at small budgets is a crowded design space spanning cache representation, head-wise routing, compression cadence, decoding behavior, and within-budget scoring. We study seven mechanisms across these five families under matched mean cache on long-form mathematical reasoning (MATH-500~\cite{hendrycks2021math}) with two distilled-reasoning models (Qwen-7B and Llama-8B variants of DeepSeek-R1-Distill~\cite{deepseek2025r1}) at budgets $b \in \{64, 128\}$. All seven were rejected. We then propose $α$, a one-function modification to the TriAttention~\cite{mao2026triattention} retention scorer that replaces argmax-top-$k$ with greedy facility-location-inspired selection under a V-space redundancy penalty controlled by a single weight $λ$. A pre-registered protocol tunes $λ$ on a frozen development split and confirms on a disjoint held-out split; with $λ= 0.5$, $α$ clears Bonferroni on two of the four (model, budget) cells (Qwen $b{=}128$ and Llama $b{=}64$), no cell is significantly negative, and the pre-registered Branch~A triggers. The finding is asymmetric: a minimal scoring modification beat heavier structural redesigns in this regime, and the combined matched-memory, sympy-graded, held-out confirmation protocol is the evidence standard that made the asymmetry visible.

Modern LLM APIs often reveal only top-$K$ logit scores and censor the remaining vocabulary. We study the per-position distribution-recovery limits of this access model. For censoring threshold $τ$, the compatible teacher distributions form an identified set whose total-variation diameter is exactly $U_K=(V-K)\exp(τ)/(Z_A+(V-K)\exp(τ))$, where $Z_A$ is the observed partition function. For KL recovery, we give a computable binary-endpoint lower bound and an asymptotically matching small-ambiguity upper bound, with an extension to reference-aware attackers. Experiments on a Qwen3 math-reasoning teacher reveal a layered extraction hierarchy: on-task top-$K$ distillation recovers 12% of private capability, full-logit distillation recovers 56% despite 99% KL closure, and generation-based extraction recovers 96%. Top-$K$ censoring therefore limits per-position distribution recovery but does not by itself prevent capability extraction, separating fidelity from transfer in prompt-only logit distillation.

Decision Trees (DTs) are widely used in safety-critical domains such as medical diagnosis, valued for their interpretability and effectiveness on tabular data. However, training accurate oblique DTs is challenging due to complex optimization landscapes and overfitting risks, particularly in regression. Recent advances have introduced differentiable formulations that enable gradient-based training and joint optimization of decision boundaries and leaf regressors. Yet, existing approaches typically rely on approximations, either through probabilistic softening of boundaries (soft DTs) or quantized gradients such as the Straight-Through Estimator (STE). To overcome these limitations, we propose DTSemNet, a novel, semantically equivalent, and invertible representation of hard oblique DTs as neural networks. DTSemNet enables end-to-end training with standard gradient descent, eliminating the need for approximations in both classification and regression. While classification aligns naturally with this formulation, regression remains challenging due to the joint optimization of internal nodes and leaf regressors. To address this, we analyze the limitations of STE and introduce an annealed Top-k method that provides accurate gradient signals without approximation. Extensive experiments on classification and regression benchmarks show that DTSemNet-trained oblique DTs outperform state-of-the-art differentiable DTs. Furthermore, we demonstrate that DTSemNet can serve as programmatic DT policies in reinforcement learning environments, thereby broadening their applicability.

Sparse Autoencoders (SAEs) have become an important tool in mechanistic interpretability, helping to analyze internal representations in both Large Language Models (LLMs) and Vision Transformers (ViTs). By decomposing polysemantic activations into sparse sets of monosemantic features, SAEs aim to translate neural network computations into human-understandable concepts. However, common architectures such as TopK SAEs rely on a fixed sparsity level. They enforce the same number of active features (K) across all inputs, ignoring the varying complexity of real-world data. Natural data often lies on manifolds with varying local intrinsic dimensionality, meaning the number of relevant factors can change significantly across samples. This suggests that a fixed sparsity level is not optimal. Simple inputs may require only a few features, while more complex ones need more expressive representations. Using a constant K can therefore introduce noise in simple cases or miss important structure in more complex ones. To address this issue, we propose SoftSAE, a sparse autoencoder with a Dynamic Top-K selection mechanism. Our method uses a differentiable Soft Top-K operator to learn an input-dependent sparsity level k. This allows the model to adjust the number of active features based on the complexity of each input. As a result, the representation better matches the structure of the data, and the explanation length reflects the amount of information in the input. Experimental results confirm that SoftSAE not only finds meaningful features, but also selects the right number of features for each concept. The source code is available at: https://github.com/St0pien/SoftSAE.

We consider the problem of estimating the Attention mechanism in small space, and prove the existence of coresets for it of nearly optimal size. Specifically, we show that for any set of unit-norm keys and values $(K,V)$ in $\mathbb{R}^d$, there exists a subset $(K',V')$ of size at most $O({\sqrt{d} e^{ρ+o(ρ)}/\varepsilon})$ such that $$\left\| \operatorname{Attn}(q,K,V)- \operatorname{Attn}(q,K',V') \right\| \le \varepsilon$$ simultaneously for all queries whose norm is bounded by $ρ$. This outperforms the best known results for this problem. We also offer an improved lower bound showing that $\varepsilon$-coresets must have size $Ω({\sqrt{d} e^ρ/ε})$.

DeepSeek-V3.2 and V4 introduce Compressed Sparse Attention (CSA): a lightning indexer (a learned scoring projection over compressed keys) scores them, the top-k are selected per query, and a sparse attention kernel reads only those. Public CSA implementations materialize a [B, S, H_I, T] FP32 score tensor before the top-k reduction. With H_I=64 indexer heads and the V4-Flash compression ratio m=4, that intermediate is 256 GB at sequence length S=65,536, exceeding any single-GPU high-bandwidth-memory (HBM) budget. We present StreamIndex, a Triton implementation of the CSA pipeline whose central component is a chunked partition-merge top-k driver that never materializes the full intermediate. On synthetic-but-realistic V4-shaped inputs at the indexer-step (layer) level on a single NVIDIA H200, the materialize path runs out of memory (OOMs) at S=65,536 with V4-Flash dimensions; StreamIndex runs the same indexer to S=1,048,576 with 6.21 GB peak HBM, a 32x regime extension. Set-overlap recall against the materialize ground truth is bit-exact at small S where both fit; across three 5-point design-space sweeps (chunk size, key-tile size, top-k), mean recall rounds to 1.0000 with min recall at least 0.9980 in every cell. The chunked driver composes with TileLang's pipelined attention kernel: at S=262,144 with V4-Flash dimensions, the materialize indexer paired with TileLang attention OOMs while the chunked indexer paired with the same attention runs in 1.97 s at 18.56 GB peak. Our contribution targets the indexer step; we make no claim of a faster attention kernel or of real-checkpoint end-to-end behavior. Code: https://github.com/RightNow-AI/StreamIndex.

Counterfactual explanations (CEs) provide an intuitive way to understand recommender systems by identifying minimal modifications to user-item interactions that alter recommendation outcomes. Existing CE methods for recommender systems, however, have been evaluated under heterogeneous protocols, using different datasets, recommenders, metrics, and even explanation formats, which hampers reproducibility and fair comparison. Our paper systematically reproduces, re-implement, and re-evaluate eleven state-of-the-art CE methods for recommender systems, covering both native explainers (e.g., LIME-RS, SHAP, PRINCE, ACCENT, LXR, GREASE) and specific graph-based explainers originally proposed for GNNs. Here, a unified benchmarking framework is proposed to assess explainers along three dimensions: explanation format (implicit vs. explicit), evaluation level (item-level vs. list-level), and perturbation scope (user interaction vectors vs. user-item interaction graphs). Our evaluation protocol includes effectiveness, sparsity, and computational complexity metrics, and extends existing item-level assessments to top-K list-level explanations. Through extensive experiments on three real-world datasets and six representative recommender models, we analyze how well previously reported strengths of CE methods generalize across diverse setups. We observe that the trade-off between effectiveness and sparsity depends strongly on the specific method and evaluation setting, particularly under the explicit format; in addition, explainer performance remains largely consistent across item level and list level evaluations, and several graph-based explainers exhibit notable scalability limitations on large recommender graphs. Our results refine and challenge earlier conclusions about the robustness and practicality of CE generation methods in recommender systems: https://github.com/L2R-UET/CFExpRec.

Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure cases causes the advantage signal in group-relative algorithms (e.g., GRPO) to vanish, driving policies into mode collapse. To address this, we propose Constrained Uniform Top-K Sampling (CUTS), a parameter-free decoding strategy enforcing structure-preserving exploration. Unlike standard sampling that follows model biases, CUTS flattens the local optimization landscape by sampling uniformly from constrained high-confidence candidates. We integrate this into Mixed-CUTS, a training framework synergizing exploitative and exploratory rollouts to amplify intra-group advantage variance. Experiments on Qwen3 models demonstrate that our approach prevents policy degeneration and significantly boosts out-of-domain generalization. Notably, Mixed-CUTS improves Pass@1 accuracy on the challenging AIME25 benchmark by up to 15.1% over standard GRPO, validating that maintaining diversity within the semantic manifold is critical for rigorous reasoning.

The key-value (KV) cache is the dominant memory bottleneck during Transformer inference, yet little is known theoretically about how aggressively it can be compressed before multi-step reasoning degrades. We study this through $k$-hop pointer chasing on $n$ tokens under a shared KV cache of size $s$, attention dimension $m$, $H$ heads, $p$-bit precision, and a locality-respecting cache controller (satisfied by all standard KV-compression methods). We give three results. (1) Product depth lower bound (conjectured). We conjecture that any such Transformer ($n \geq 4k$, $s \leq \sqrt{n}/4$) requires depth $L = Ω(\lceil k/s \rceil \cdot \lceil \log_2 n/(Hmp) \rceil)$, and isolate the sole remaining gap as a probabilistic step on the joint distribution of cache trace and pointer chain. Unconditionally, we prove a matching upper bound $L = O(\min(k, \lceil k/s \rceil \log s) \cdot \log n/(mp))$ via windowed pointer doubling, and a max-bound $L = Ω(\max(\lceil k/s \rceil, \log n/(Hmp)))$. Closing the conjecture amounts to upgrading max to product. (2) Bandwidth barrier. The product bound binds only when $Hmp \lesssim \log n$. Any lower bound provable via per-window distinguishability counting -- including reachability, bandwidth, and combinations -- cannot exceed $\lceil k/s \rceil$ once $Hmp \geq \log_2 n$. Breaking this requires lifting unconditional communication-complexity bounds for pointer chasing to Cache-Transformer depth. (3) Adaptive vs oblivious error scaling. Under random cache over $T = \lceil \log_2 k \rceil$ doubling stages, oblivious caches give $\Pr[\mathcal{E}] \leq (s/(n-T))^T + 2T^3/n$ (exponential in $T$), while adaptive locality-respecting caches achieve $\Pr[\mathcal{E}] = s/n$ exactly, independent of $T$. The $Ω((n/s)^{T-1})$ separation explains why heavy-hitter eviction empirically dominates random eviction for multi-hop reasoning.

Learned top-K search improves the accuracy-latency trade-off of graph-based vector search, but existing methods are designed for a fixed K: serving production workloads with varying K values requires preprocessing cost proportional to the number of distinct Ks served - prohibitive in practice. This paper shows that learned search can support arbitrary K with the preprocessing cost of a single top-1 model. The key idea is to reduce top-K learned search to repeated masked top-1 refinement, which works because the distance-reduction trajectory for discovering the next top-1 vector is largely invariant to the number of results already found. We therefore train the model on trajectory features that remain effective under masking. To make repeated refinement robust and efficient, OMEGA counters error accumulation across iterations with rank-wise confidence allocation, and skips unnecessary model invocations with a statistical forecast of recall from partial results. Across nine dataset-scale configurations, OMEGA meets the 0.95 recall target with one K-independent model. Under the lowest-preprocessing configuration of each learned baseline,it reduces mean latency by 7-36% versus DARTH, 3-25% versus MultiK-DARTH, and 8-21% versus LAET on BIGANN, BIGANN-1B, DEEP, and three production workloads. On GIST, Text2Image, and MS MARCO, its latency remains within 9% of DARTH and MultiK-DARTH. On production traces, OMEGA further reduces total serving and preprocessing computation by up to 28%.

The $K$-Max combinatorial multi-armed bandit problem arises in applications such as recommendation and distributed decision making, where the reward is determined by the maximum outcome among $K$ selected arms. When outcomes are continuous and only the maximum value together with the winner's index is observed, this problem introduces unprecedented difficulties including discretization errors, non-deterministic tie-breaking, and severe estimation biases. To overcome these barriers, we introduce DCK-UCB, an efficient algorithm combining adaptive discretization with bias-corrected confidence bounds. We prove that DCK-UCB achieves a $\widetilde{O}(T^{3/4})$ regret bound, the first sublinear guarantee in this setting. Numerical experiments show strong performance over baseline methods. Furthermore, for the specific case of exponential distributions under full-bandit feedback, we propose the MLE-Exp algorithm that attains a near-optimal $\widetilde{O}(\sqrt{T})$ regret bound. This work establishes fundamental theoretical guarantees and provides a powerful algorithmic solution for continuous combinatorial bandits.

Mixture-of-Experts (MoE) models activate few experts per token, yet their full expert sets can exceed GPU memory and require repeated weight transfers during decoding. We formulate expert-cache management as a model-side algorithmic problem and propose cache-aware post-training that jointly adapts the MoE backbone and lightweight auxiliary routers while preserving the native inference-time Top-K rule. The update-only Temporal Router learns same-layer retention across tokens without proactive loading. The full Spatio-Temporal Router adds a Spatio Router that uses the causal predecessor's hidden state to refine the temporal cache before target-layer access. We evaluate both modes on Qwen3 and GPT-OSS across GSM8K, MATH, and CommonsenseQA. Temporal Router consistently improves hit rate and reduces expert-weight traffic over matched LM-only baselines. On Qwen3, the full mode improves adjusted hit rate by 1.15--18.03 points and reduces traffic by 4.6--53.3% relative to the strongest evaluated prefetching baseline; GPT-OSS results are competitive but task-dependent. Auxiliary-only training preserves baseline accuracy but yields modest coverage gains; joint post-training achieves substantially higher coverage. Sensitivity analyses distinguish the effects of cache capacity, refinement budget, and cache-loss weight on coverage, traffic, and quality.