Token Budgets

Per-instance algorithm selection (PIAS) takes advantage of complementarity between a set of algorithms by deciding which algorithm to run on a given instance. This decision is based on features of the instances, which, in the context of black-box optimization (BBO), require a part of the optimization budget to be computed. This raises two questions: (a) from which fraction of the budget spent on feature computation does PIAS become worth it for BBO, and (b) which fraction of the budget optimizes the tradeoff between feature accuracy and PIAS performance. To this end, we perform a broad study where PIAS with varying sampling budgets for feature computation is compared to the single best algorithm on a broad range of algorithm selection scenarios. These scenarios consist of two portfolio sizes, three problem sets, 4 dimensionalities, and 10 target budgets. We find that PIAS is viable for the majority of tested scenarios, even when as much as a quarter of the total budget is spent on feature computation. The tradeoff for the fraction of the budget spent on feature computation to maximize the benefit of PIAS is highly dependent on the specific AS scenario. Further, on average 20 percent of PIAS loss to the virtual best solver is explained by the budget spent on feature computation, highlighting the importance of properly accounting for the feature budget.

Optimizer states occupy massive GPU memory in large-scale model training. However, gradients in different network blocks exhibit distinct behaviors, such as varying directional stability and scale anisotropy, implying that expensive optimizer states are not universally necessary and using a global optimizer is often memory-inefficient. We propose the Budget-Aware Optimizer Configurator (BAOC) to reduce memory cost by assigning suitable optimizer configurations to individual blocks under given budgets. Specifically, BAOC samples gradient streams to derive statistical metrics that quantify the potential performance risk of applying cheaper configurations (e.g., low precision or removing momentum). It then solves a constrained allocation problem to minimize total risk under memory and time budgets, selecting a budget-feasible configuration for each block. Experiments across vision, language, and diffusion workloads demonstrate that BAOC maintains training quality while significantly reducing the memory usage of optimizer states. The code is available at https://anonymous.4open.science/r/BAOC-45C6.

Large Language Model ensembles improve reasoning accuracy, but only up to a performance boundary beyond which additional deliberation degrades accuracy. We introduce DASE (Deliberative Adaptive Stopping Ensemble), a stopping heuristic for iterative ensemble deliberation that commits early on genuine consensus and applies a global-frequency fallback on fragmented evidence. We make three contributions. (1) DASE produces a commit-type routing partition that generalises across benchmarks and is complementary to verbalized single-call confidence. On GPQA-Extended (N=546, 70B ensemble), the partition yields a 39.5 pp routing gap (right-wall 81.1% vs. left-wall 41.5%). On AIME 2010-2023 (N=261, 120B ensemble, 3 seeds), right-wall commits reach 98.3% accuracy vs. left-wall 72.8% (25.5 pp gap), statistically equivalent to Opus 4.6 Standard verbalized confidence at matched coverage (25.7 pp gap; bootstrap p=0.873); the two mechanisms disagree on 37% of routing assignments. (2) Adaptive stopping, not injection bandwidth, drives accuracy. On AIME-300, bandwidth accounts for only 0.3 pp (ns). On GPQA-Extended at the 120B tier, sparse injection ($\approx15$ tokens/worker/round) achieves 70.9% with a 30.7 pp routing gap; dense injection ($\approx600$ chars/worker/round) achieves 72.2% but with halved right-wall coverage and a narrower 18.9 pp gap. (3) Injection-based methods exhibit an inverted-U accuracy-vs-inference trajectory; this pattern is hypothesis-generating.

Backdoor attacks threaten the deep learning supply chain by poisoning a small fraction of the training data so that a model behaves normally on clean inputs but misclassifies trigger-carrying inputs to an attacker-chosen target class. Clean-label backdoor attacks are especially dangerous because poisoned samples remain label-consistent and are therefore harder to detect. Yet existing clean-label attacks typically rely on expensive optimization, surrogate-model training, or nontrivial data access. We present Checkerboard, a theoretically grounded, learning-free clean-label backdoor attack that is effective, efficient, and simple to implement. From a linear separability formulation, we derive a checkerboard trigger in closed form, removing the need for surrogate-model training and trigger optimization. For texture-rich datasets, we introduce Complexity-driven Sample Selection, which uses only target-class data to improve trigger-to-background contrast by selecting low-complexity images for poisoning. Across four benchmark datasets, Checkerboard outperforms 8 baseline attacks and achieves state-of-the-art performance under low poisoning budgets. For example, on CIFAR-10, under a trigger perturbation budget of $10/255$, poisoning 20 training samples achieves $99.99\%$ Attack Success Rate (ASR). On ImageNet-100, a poisoning rate of only $0.46\%$ yields over $94\%$ ASR without degrading clean accuracy. The proposed attack also remains effective against state-of-the-art backdoor defenses and shows strong resistance to adaptive defenses.

Assigning one of K options to each of N groups under a total cost budget is a recurring problem in efficient AI, including mixed-precision quantization, non-uniform pruning, and expert selection. The objective, typically model loss, depends jointly on all assignments and does not decompose across groups, preventing combinatorial solvers from directly optimizing the true objective and forcing reliance on proxy formulations. Methods such as evolutionary search evaluate the actual loss but lack gradient information, while penalty-based approaches enforce the budget only approximately and often require extensive hyperparameter tuning. We present a new approach by showing that, under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with unusually simple geometry. The normal vector admits a closed-form expression, shifting logits along the cost vector changes expected cost monotonically, and vector transport reduces to a single inner product. Building on these properties, we propose Riemannian Constrained Optimization (RCO), which augments a standard Adam step with tangent projection, binary-search retraction, and momentum transport. Combined with Gumbel straight-through estimation and budget-constrained dynamic programming for discrete feasibility, RCO enables first-order optimization of the actual loss under exact budget enforcement without introducing constraint-specific hyperparameters. Across both synthetic benchmarks and realistic LLM compression settings, RCO matches or exceeds state-of-the-art methods while often requiring substantially less wall-clock time. Source code is available at https://github.com/IST-DASLab/RCO.

A key challenge for large language models is token cost per query and overall deployment cost. Clinical inputs are long, heterogeneous, and often redundant, while downstream tasks are short and high stakes. We study budgeted context selection, where a subset of document units is chosen under a strict token budget so an off-the-shelf generator can meet fixed cost and latency constraints. We cast this as a knapsack-constrained subset selection problem with two design choices, unitization that defines document segmentation and selection that determines which units are kept. We propose \textbf{RCD}, a monotone submodular objective that balances relevance, coverage, and diversity. We compare sentence, section, window, and cluster-based unitization, and introduce a routing heuristic that adapts to the budget regime. Experiments on MIMIC discharge notes, Cochrane abstracts, and L-Eval show that optimal strategies depend on the evaluation setting. Positional heuristics perform best at low budgets in extractive tasks, while diversity-aware methods such as MMR improve LLM generation. Selector choice matters more than unitization, with cluster-based grouping reducing performance and other schemes behaving similarly. ROUGE saturates for LLM summaries, while BERTScore better reflects quality differences. We release our code at https://github.com/stone-technologies/ACL_budget_paper.

In black-box large language model (LLM) services, response reliability is often only partially observable at decision time, while stronger inference pathways incur substantial computational cost, inducing a budgeted sequential decision problem: for each request, the system should decide whether the default low-cost response is sufficiently reliable or whether additional computation should be allocated to improve response quality. In this paper, we propose \textbf{Ver}ifiable \textbf{O}bservations for Risk-aware \textbf{I}nference \textbf{C}ontrol (\textsc{Veroic}), a framework for adaptive inference control in black-box LLM settings, which formulates request-time control as a \textit{partially observable Markov decision process} to capture partial observability and sequential budget coupling. It constructs a lightweight verifiable observation channel from the input-output pair by aggregating heterogeneous quality signals into a belief state over latent response reliability, which is then used by a budget-aware policy to decide whether to return the default output or trigger a higher-cost inference pathway. Experiments on diverse tasks show that \textsc{Veroic} achieves improved quality-cost trade-offs, stronger risk estimation and calibration, and more robust long-horizon inference control than competitive baselines.

We study finite-horizon budget allocation as a closed-loop economic control problem and evaluate receding-horizon Model Predictive Control (MPC) relative to reactive budgeting policies. Budgets are allocated periodically under execution noise and operational constraints, while return efficiency may evolve over time. Using a controlled simulation framework motivated by digital marketing, we compare reactive pacing to MPC across environments with increasing degrees of non-stationarity. Our results show that non-stationarity alone does not justify predictive control. When return dynamics are stationary or evolve through unpredictable stochastic drift, MPC offers no systematic advantage over reactive baselines. By contrast, when return efficiency exhibits predictable structure over the planning horizon, that is captured through an underlying model, MPC consistently outperforms reactive budgeting by exploiting intertemporal trade-offs.

Autonomous LLM agents increasingly operate in long-horizon, interactive settings where success depends on reusing experience accumulated over extended histories. However, existing agent memory systems are fundamentally constrained by text-context budgets: storing or revisiting raw trajectories is prohibitively token-expensive, while summarization and text-only retrieval trade token savings for information loss and fragmented evidence. To address this limitation, we propose Optical Context Retrieval Memory (OCR-Memory), a memory framework that leverages the visual modality as a high-density representation of agent experience, enabling retention of arbitrarily long histories with minimal prompt overhead at retrieval time. Specifically, OCR-Memory renders historical trajectories into images annotated with unique visual identifiers. OCR-Memory retrieves stored experience via a \emph{locate-and-transcribe} paradigm that selects relevant regions through visual anchors and retrieves the corresponding verbatim text, avoiding free-form generation and reducing hallucination. Experiments on long-horizon agent benchmarks show consistent gains under strict context limits, demonstrating that optical encoding increases effective memory capacity while preserving faithful evidence recovery.

Treatment allocation under budget constraints is a central challenge in digital advertising: advertisers must decide which users to show ads to while spending a limited budget wisely. The standard approach follows a two-stage offline pipeline - first collect historical data to estimate heterogeneous treatment effects (HTE), then solve a constrained optimization to allocate the budget. This works well with abundant data, but fails in cold-start settings such as new campaigns, new markets, or new customer segments where little historical data exists. We propose Budget-Constrained Causal Bandits (BCCB), an online framework that learns which users respond to ads while simultaneously spending the budget, making treatment decisions one user at a time. BCCB unifies three components into a single sequential process: learning individual-level ad effectiveness, exploring users whose response is uncertain, and pacing the budget over time. We evaluated on the Criteo Uplift dataset, a large-scale advertising dataset from a real randomized controlled trial. Our key finding is a data-efficiency crossover: offline methods require approximately 10,000 historical observations to produce reliable results, while BCCB operates effectively from the very first user. Furthermore, BCCB exhibits 3-5x lower performance variance between runs, making it more practical for real campaign planning. Among purely online methods, BCCB consistently outperforms standard Thompson Sampling, budgeted Thompson Sampling, and greedy HTE estimation across all budget levels tested.

Organizations routinely make strategic budget allocations under operational constraints, but often lack a principled way to assess whether realized allocations were close to the best feasible choices in hindsight. We present a retrospective auditing framework based on hindsight regret, defined as the opportunity cost of the realized allocation relative to a constraint-faithful benchmark under the same budget and stability guardrails. The framework estimates regime-specific spend--response functions from historical logs, computes feasible hindsight allocations via constrained optimization, and propagates uncertainty through Monte Carlo evaluation to produce regret distributions, expected lift, and probability-of-improvement summaries. This separates allocation inefficiency from uncertainty in the estimated response surfaces. Experiments on real marketing allocation logs show that the framework yields interpretable post-hoc diagnostics and reveals a practical trade-off between allocation flexibility and detectability: moderate feasible reallocations often capture most measurable gain, while larger shifts move into weak-support regions with higher uncertainty. The result is a practical method for auditing historical budget decisions when online experimentation is costly or infeasible.

Large Language Models (LLMs) solve many reasoning tasks via chain-of-thought (CoT) prompting, but smaller models (about 7 to 8B parameters) still struggle with multi-step reasoning under tight compute and token budgets. Existing test time reasoning methods such as self consistency (sampling multiple rationales and voting), Tree-of-Thoughts (search over intermediate thoughts), and critique revise loops improve performance, but often at high token cost and without fine-grained step-level control. This project1 aims to address that gap: can Small Language Models (SLMs) reason reliably using the same or fewer tokens? This question is both scientific and practical. Scientifically, it probes whether process supervision and simple test-time controls (such as token budgets and rejection of redundant steps) can substitute for model scale or large sampling counts. Practically, many deployments (on-device, low-latency, or cost-constrained settings) cannot afford huge models or dozens of sampled rationales per query. A method that improves SLM reasoning at fixed cost would therefore be directly useful.

Budget-constrained micro-pretraining often requires triaging many candidate recipes on a shared accelerator before larger search budgets are spent. We study whether a staged fractional-factorial workflow can recover stable early effect structure in this setting. On a fixed autoresearch-derived single-GPU training loop, we run 613 experiments across pilot and follow-up screens at 2, 5, and 10 minutes; full 16-condition seeded reruns at 5 and 10 minutes; targeted seeded anchor checks; same-host greedy and matched-cost random baselines; a 60-minute bridge package; and bounded Windows A100 and Linux L40S anchor continuations through 24 hours. Main penalties from total batch, depth, and width are largest at short budgets and relax as budget increases. Within the predeclared seeded full-screen families, D, A, B, and C retain non-zero estimates at 5 and 10 minutes after within-budget Benjamini-Hochberg correction, while E does not. Random search can reach strong incumbents in this 32-condition space, but repeatedly in the same low-penalty region and without factor attribution. The 60-minute bridge anchor has the lowest mean, although that package does not separate workflow refinement from the larger bridge model's capacity advantage. In bounded 12-hour and 24-hour three-anchor continuations on both hosts, the bridge has the lowest sample mean while the non-bridge ordering stays host-sensitive. We therefore present a bounded methods result: use short designed screens to identify high-penalty directions, confirm promising anchors under repeated runs, and refine locally inside the reduced space. The evidence supports a bridge-centered recommendation through 24 hours on two hosts, not hardware-invariant ranking or general hyperparameter-optimization superiority.

Scaling laws are used to plan multi-million-dollar training runs, but fitting those laws can itself cost millions. In modern large-scale workflows, assembling a sufficiently informative set of pilot experiments is already a major budget-allocation problem rather than a routine preprocessing step. We formulate scaling-law fitting as budget-aware sequential experimental design: given a finite pool of runnable experiments with heterogeneous costs, choose which runs to execute so as to maximize extrapolation accuracy in a high-cost target region. We then propose an uncertainty-aware method for sequentially allocating experimental budget toward the runs most useful for target-region extrapolation. Across a diverse benchmark of scaling-law tasks, our method consistently outperforms classical design-based baselines, and often approaches the performance of fitting on the full experimental set while using only about 10% of the total training budget. Our code is available at https://github.com/PlanarG/active-sl.

Multi-head attention enables Transformers to capture diverse representations, but all attention heads are typically activated for every input, regardless of task complexity. For coarse-grained tasks such as text classification, where relevant information is often global, this fixed allocation can introduce unnecessary computation. We propose BudgetFormer, a Transformer architecture that dynamically allocates attention heads on a per-input basis. The model learns both a head budget and a relevance distribution to select the most informative heads. To support effective head selection, we introduce a training strategy that balances exploration and exploitation. Experiments on text classification tasks show that BudgetFormer reduces FLOPs and memory usage while matching or surpassing the performance of standard multi-head attention. These results highlight adaptive head allocation as an effective approach to improving Transformer efficiency and performance.

The Model Context Protocol (MCP) has become a common interface for connecting large language model (LLM) agents to external tools, but its reliance on stateless, eager schema injection imposes a hidden per-turn overhead the MCP Tax or Tools Tax that practitioner reports place between roughly 10k and 60k tokens in typical multi-server deployments. This payload inflates the key-value cache, is associated with reasoning degradation as context utilization approaches published fracture points around 70%, and turns token budgets into a recurring operational cost. We introduce Tool Attention, a middleware-layer mechanism that generalizes the "Attention Is All You Need" paradigm from self-attention over tokens to gated attention over tools. Tool Attention combines (i) an Intent Schema Overlap (ISO) score from sentence embeddings, (ii) a state-aware gating function enforcing preconditions and access scopes, and (iii) a two-phase lazy schema loader that keeps a compact summary pool in context and promotes full JSON schemas only for top-k gated tools. We evaluate on a simulated 120-tool, six-server benchmark whose per-server token counts are calibrated to public audits of real MCP deployments. In this simulation, Tool Attention directly reduces measured per-turn tool tokens by 95.0% (47.3k -> 2.4k) and raises effective context utilization (a token-ratio quantity) from 24% to 91%. End-to-end figures for task success, latency, cost, and reasoning quality are reported as projections derived from the measured token counts combined with published deployment telemetry; they are not measured on live LLM agents, and we mark projected values explicitly throughout. Taken together, the results support a simple thesis: protocol-level efficiency, not raw context length, is a binding constraint on scalable gentic systems. The code for this work is accessible at https://github.com/asadani/tool-attention

Long-context inference in Large Language Models (LLMs) is bottlenecked by the linear growth of Key-Value (KV) cache memory. Existing KV cache compression paradigms are fundamentally limited by heuristics: heuristic budgeting relies on statistical priors rather than task objectives, causing resource misallocation, while heuristic selection relies on coupled query-key interactions or static inductive biases (e.g., attention sinks). To address this limitation, we introduce LKV (Learned KV Eviction), which formulates KV compression as an end-to-end differentiable optimization problem. LKV integrates LKV-H to learn task-optimized global budgets, and LKV-T to derive intrinsic KV importance without materializing attention matrices. This design bypasses heuristic proxies, strictly aligning compression with task objectives. Extensive evaluations demonstrate that LKV achieves state-of-the-art performance on both LongBench and RULER benchmarks at high compression rates. In particular, on LongBench, LKV achieves near-lossless performance with only 15% KV cache retention. Crucially, our analysis identifies learned budgeting as the dominant driver of fidelity, demonstrating that data-driven allocation is essential to overcome the limitations of hand-crafted heuristics.

We introduce a new budgeted framework for online influence maximization, considering the total cost of an advertising campaign instead of the common cardinality constraint on a chosen influencer set. Our approach better models the real-world setting where the cost of influencers varies and advertisers want to find the best value for their overall social advertising budget. We propose an algorithm assuming an independent cascade diffusion model and edge level semi-bandit feedback, and provide both theoretical and experimental results. Our analysis is also valid for the cardinality constraint setting and improves the state of the art regret bound in this case.

Large language models (LLMs) are expensive to serve because model parameters, attention computation, and KV caches impose substantial memory and latency costs. We present GRASPrune, a structured pruning framework applied after pretraining that jointly prunes FFN channels and KV head groups under a single global budget. Instead of learning importance scores without constraints and applying the budget only after training, GRASPrune learns lightweight gate scores with a projected straight-through estimator that enforces a hard mask satisfying the budget at every step while keeping the backbone weights frozen. After the mask is fixed, we calibrate scaling factors on the retained units to mitigate scale mismatch caused by pruning, and fold these factors into the pruned weights to obtain a smaller dense checkpoint with no extra parameters at inference. On LLaMA-2-7B, GRASPrune removes 50% of parameters and achieves 12.18 perplexity on WikiText-2 while maintaining competitive average zero-shot accuracy on five benchmarks, using four epochs on 512 unlabeled calibration sequences on a single NVIDIA A100 80GB GPU without any full model fine-tuning.

Reach and Frequency (R&F) contract advertising is an important form of widely used brand advertising. Unlike performance advertising, R&F contracts emphasize controllable delivery of UV and PV under given targeting, scheduling, and frequency control constraints. In practical systems, advertisers typically need to view the UV, PV change curves at different budget levels in real time when creating an R&F contract. However, most existing publicly available advertising datasets are based on independent samples, lacking a characterization of the core structure of the "budget-performance curve" (including UV and PV) in R&F contracts.This paper proposes and releases a large-scale R&F contract inventory estimation dataset. This dataset uses the R&F contract context consisting of "targeting-scheduling-frequency control" as the basic context, providing observations of UV and PV corresponding to multiple budget points within the same context, thus forming a complete budget-performance curve. The dataset explicitly includes a time-window-based frequency control mechanism (e.g.,"no more than 3 times within 5 days") and naturally satisfies the monotonicity and diminishing marginal returns characteristics in the budget and scheduling dimensions. We further derive the theoretical maximum exposure ceiling and use it as a consistency check to evaluate data quality and the feasibility of model predictions. Using this data set, this paper defines two standardized benchmark tasks: single-point performance prediction and reconstruction of budget-performance curves, and provides a set of reproducible baseline methods and evaluation protocols. This dataset can support systematic research on problems such as structural constraint learning, monotonic regression, curve consistency modeling, and R&F contract planning.The code for our experiments can be found at https://github.com/pengyunshan/RF-Inventory.

Visual token pruning methods effectively mitigate the quadratic computational growth caused by processing high-resolution images and video frames in vision-language models (VLMs). However, existing approaches rely on predefined pruning configurations without determining whether they achieve computation-performance optimality. In this work, we introduce , a novel framework that formulates visual token pruning as a Pareto configuration optimization problem to automatically identify optimal configurations. Our approach employs continuous relaxation and straight-through estimators to enable gradient-based search, solved via the Augmented Lagrangian method. Extensive experiments across 8 visual benchmarks demonstrate that effectively approximates the empirical Pareto frontier obtained through grid search and generalizes well across various pruning methods and VLM architectures. Furthermore, through learnable kernel functions, we investigate layer-wise pruning patterns and reveal that multi-step progressive pruning captures VLMs' hierarchical compression structure, achieving superior accuracy-efficiency trade-offs compared to single-layer approaches.

Software supply chain security compromises often stem from cascaded interactions of vulnerabilities, for example, between multiple vulnerable components. Yet, Software Bill of Materials (SBOM)-based pipelines for security analysis typically treat scanner findings as independent per-CVE (Common Vulnerabilities and Exposures) records. We propose a new research direction based on learning multi-vulnerability attack chains through a novel SBOM-driven graph-learning approach. This treats SBOM structure and scanner outputs as a dependency-constrained evidence graph rather than a flat list of vulnerabilities. We represent vulnerability-enriched CycloneDX SBOMs as heterogeneous graphs whose nodes capture software components and known vulnerabilities (i.e, CVEs), connected by typed relations, such as dependency and vulnerability links. We train a Heterogeneous Graph Attention Network (HGAT) to predict whether a component is associated with at least one known vulnerability as a feasibility check for learning over this structure. Additionally, we frame the discovery of cascading vulnerabilities as CVE-pair link prediction using a lightweight Multi-Layer Perceptron (MLP) neural network trained on documented multi-vulnerability chains. Validated on 200 real-world SBOMs from the Wild SBOMs public dataset, the HGAT component classifier achieves 91.03% Accuracy and 74.02% F1-score, while the cascade predictor model (MLP) achieves a Receiver Operating Characteristic - Area Under Curve (ROC-AUC) of 0.93 on a seed set of 35 documented attack chains.

Vision Transformers require significant computational resources and memory bandwidth, severely limiting their deployment on resource-constraint hardware. Most structured pruning methods reduce theoretical cost effectively, yet they typically operate at a single structural granularity and depend on multi-stage pipelines with importance ranking, auxiliary solvers or post-hoc magnitude thresholding, followed by a separate fine-tuning phase to recover accuracy. We propose Hierarchical Auto-Pruning (HiAP), which casts ViT pruning as a single budget-aware learning problem and jointly allocates sparsity across four granularities in one end-to-end phase. HiAP introduces stochastic Gumbel-Sigmoid gates at macro level (attention heads and FFN blocks) and micro level (intra-head dimensions and FFN neurons), and optimizes them against the task loss together with an analytical MAC cost term. The budget coefficient steers the network to a target compute level while the gates gradually harden into a dense, smaller sub-network at convergence. It does not require importance heuristics, ranking metrics, auxillary solvers or secondary fine-tuning. On ImageNet with DeiT small, HiAP automatically discovers hetergenous architectures, pruning depths, heads, and width by different amount across layers, and reaches competitive accuracies against substantially more complex pruning pipelines at comparable compute from a single training run.

Agentic systems accumulate persistent memory across sessions, tools, and tasks, and a later request must retrieve from it under two distinct constraints: which memories it is permitted to access, and which are relevant under a limited search budget. Existing memory systems handle access scope in two flawed ways: applying scope after retrieval wastes probe budget on inadmissible memories, while treating scope as a learned ranking feature makes a hard constraint depend on router quality. We present SHARD-MEMO, an agentic memory system built on scope-before-routing: metadata predicates first identify the admissible shards, and a learned router then selects a small number of them for shard-local approximate nearest neighbor retrieval. Given the supplied scope predicate and metadata, this separates hard admissibility from learned relevance ranking, so inadmissible shards cannot consume shard-probe budget. We evaluate on LoCoMo, HotpotQA, and ToolBench, covering conversational, long-context, and procedural memory. Under matched supervision and fixed budgets, SHARDMEMO improves over a learned router baseline by roughly +3 F1 on LoCoMo; in end-to-end LoCoMo evaluation it improves over the strongest evaluated memory baseline by up to +6.8 F1, with gains on HotpotQA and ToolBench.

The performance of large language models (LLMs) on verifiable tasks is usually measured by pass@k, the probability of answering a question correctly at least once in k trials. At a fixed budget, a more suitable metric is coverage@cost, the average number of unique questions answered as a function of the total number of attempts. We connect the two metrics and show that the empirically-observed power-law behavior in pass@k leads to a sublinear growth of the coverage@cost (diminishing returns). To solve this problem, we propose Reset-and-Discard (ReD), a query method of LLMs that increases coverage@cost for a given budget, regardless of the pass@k form. Moreover, given a pass@k, we can quantitatively predict the savings in the total number of attempts using ReD. If pass@k is not available for the model, ReD can infer its power-law exponent. Experiments on three LLMs across coding (HumanEval), math (GSM8K), and reasoning (MMLU-Pro) benchmarks demonstrate that ReD substantially reduces the required attempts, tokens, and USD cost to reach a desired coverage, while also offering an efficient way to measure inference power-laws. ReD's advantage is maintained for imperfect verifiers and outperforms the tested allocation baselines.

Across fields such as machine learning, social science, and geology, considerable attention has been given to models that factorize a nonnegative matrix into the product of two or three matrices, subject to nonnegative or row-sum-to-1 constraints. Although these models are to a large extent similar or even equivalent, they are presented under different names, and their similarity is not well known. This paper highlights similarities among five models, latent budget analysis (LBA) and latent class analysis (LCA) from social science, end-member analysis (EMA) from geology, probabilistic latent semantic analysis (PLSA) and nonnegative matrix factorization (NMF) from machine learning. We focus on the identifiability of these models. We prove that the solution of LBA, EMA, LCA, PLSA is unique if and only if the solution of NMF is unique. Consequently, existing uniqueness theorems for NMF directly apply to LBA, EMA, LCA, PLSA, and vice versa. We also provide a brief review of algorithms for the estimation of these models. We illustrate NMF on a sedimentary grain-size distribution dataset from sedimentary geology, and end the paper with a discussion of closely related model: archetypal analysis.

Operational knowledge-graph (KG) pipelines in networking and cybersecurity increasingly need to refresh embeddings under strict time, memory, and audit budgets, especially as curated feeds and LLM-assisted extraction accelerate KG updates. A recurring per-step cost in mini-batch KG learning is neighborhood-context estimation: uniform neighbor sampling without replacement followed by mean aggregation. Common frameworks implement this estimator through sampled-subgraph materialization and intermediate feature gathers, adding kernel launches, allocator pressure, and transient memory spikes. We present One-Pass Neighborhood Estimation, a fused PyTorch CUDA operator that samples neighbors and directly emits the sampled-neighborhood mean, avoiding explicit block construction while preserving GraphSAGE-mean semantics for the same sampled neighbor IDs. It supports seed-controlled sampling and optional saved-index replay for reproducible validation and regression testing. Across large-graph mini-batch workloads, it improves FP32 end-to-end step latency by 2.24x-3.48x over tuned DGL baselines and reduces transient GPU memory by up to 160x in our measurements. On OGB KG completion benchmarks such as WikiKG2 and BioKG, it reduces step time and peak VRAM while matching ranking quality within seed variability, improving time-to-quality for budgeted KG refresh.

Activation-aware low-rank factorization techniques yield strong compression results but are generally confined to linear layers, while existing whitening-based theory typically makes an implicit full-rank assumption on activations. We introduce a layer representation framework that extends activation-aware factorization beyond linear layers, including standard and grouped convolutions. Within this framework, our whitening-based formulation is more general than prior ones, naturally covering rank-deficient activations, and yields an optimal low-rank projection that attains the reconstruction error of the best low-rank approximation to layer activations. The resulting singular spectrum provides a closed-form per-layer distortion proxy, which we use to allocate per-layer ranks under explicit FLOP or parameter-count budgets via a Lagrangian relaxation with negligible overhead. Together, these components form BALF, an end-to-end pipeline for efficient vision model compression. Across CNNs and vision transformers on CIFAR-10 and ImageNet-1K, BALF generally achieves higher accuracy than SVD-based factorization baselines at matched FLOP or parameter count targets and remains competitive with other fine-tuning-free compression techniques.

In this work, we present the \texttt{LLM ORDER BY} semantic operator as a logical abstraction and conduct a systematic study of its physical implementations. First, we propose several improvements to existing semantic sorting algorithms and introduce a semantic-aware external merge sort algorithm. Our extensive evaluation reveals that no single implementation offers universal optimality on all datasets. From our evaluations, we observe a general scaling relationship between sorting cost and the ordering quality for comparison-based algorithms. Building on these insights, we design a budget-aware optimizer that utilizes heuristic rules, LLM-as-Judge evaluation, and consensus aggregation to dynamically select the near-optimal access path for LLM ORDER BY. In our extensive evaluations, our optimizer consistently achieves ranking accuracy on par with or superior to the best static methods across all benchmarks. We believe that this work provides foundational insights into the principled optimization of semantic operators essential for building robust, large-scale LLM-powered analytic systems.

This paper presents a fully probabilistic approach for solving optimal experimental design problems under budget constraints. The experimental design is viewed as a random variable and is associated with a parametric conditional distribution that inherently models the budget constraints. The original optimization problem is replaced with an optimization over the expected value of the original objective, which is then optimized over the distribution parameters. The resulting optimal parameter (policy) is used to sample the feasible region of binary space to produce estimates of the optimal solution(s) of the original optimization problem. In this work we extend the family of conditional Bernoulli models to model the random variable conditioned by the total number of nonzero entries, that is, the budget constraint. This approach (a) is generally applicable to binary optimization problems with nonstochastic black-box objective functions and budget constraints; (b) employs conditional probabilities to model and sample only the feasible region and thus considerably reduces the computational cost compared with employing soft constraints; and (c) does not employ soft constraints and thus does not require tuning of a regularization parameter, for example to promote sparsity, which is generally challenging. The proposed approach is verified numerically using an optimal sensor placement experiment based on an advection-diffusion forward model in a parameter identification setup.

To solve the fractional knapsack problem, Dantzig's greedy rule orders items according to their value-to-cost ratio. This ordering introduces priority issues. An arbitrarily small perturbation to the input can change the allocation if the budget is exhausted between two items with very similar ratios. To mitigate that problem, we introduce a two-stage rule. We group items sharing attributes within a radius $\delta$. These groups are then evaluated in descending order of ratio, and divide their group's budget share without further ranking. Consider a group featuring an aggregate capacity $U_G$, unit costs contained in $[w^-,w^+]$, and a representative value $\widehat{v}$. The group's loss compared to the exact optimum is bounded by $\widehat{v}\, U_G\frac{w^+-w^-}{w^++w^-}+\varepsilon_v U_G$, in which $\varepsilon_v$ limits the group's internal value variation. Moreover, for any group size, this harmonic factor remains tight. The overall loss becomes restricted to the single budget-binding group whenever the grouping remains order-compatible; thus, groups containing at most $K$ items suffer a per-item loss of $\mathcal{O}(\frac{K}{n})$. Should group ratio intervals exhibit an overlap of at most $\omega$, an additive term $\omega C$ degrades this bound. Within the separation margin between adjacent groups, the grouped allocation remains Lipschitz continuous with respect to cost data, exhibiting a modulus of $\frac{K}{w_{\min}}$. Computing this allocation takes $\mathcal{O}(n+m\log m+|\Gamma|\log|\Gamma|)$ time given $m$ groups and a boundary group $\Gamma$. Alternatively, the time complexity drops to $\mathcal{O}(n+m\log m)$ if a linear-time selection method identifies the boundary group's allocation.