Token Budgets

Tensor Product Representations provide the structural fidelity required for symbolic reasoning in models but suffer from exponential dimensionality growth when encoding deep recursive structures. Conversely, Vector Symbolic Architectures maintain constant dimensionality but sacrifice capacity and fidelity due to noisy compression via superposition. In this work, we propose Orthogonal Subspace Carving (OSC), a memory architecture that binds fillers to roles by projecting onto the null space of the role basis before aggregating into a fixed order-p tensor. OSC uses projections to enforce geometric orthogonality between bound structures within a static memory trace. We show that this mechanism decouples the tensor order from the structural depth, enabling deep recursive binding within a constant memory footprint. By performing retrieval via recognition, this construction allows for component vectors that are orders of magnitude smaller than the memory tensor, giving superior memory efficiency in settings involving high superposition. We also show that TPR is a special case of binding in Clifford algebra, and give a Clifford formulation of OSC.

We propose annealed entropic allocation, an adaptive sampling policy based on an annealed, weighted soft-min formulation of static budget allocation. We replace the maximin large-deviation rate objective with a weighted log-sum-exp surrogate that blends challenger-specific pairwise scores through soft-min weights, avoiding hard switching when several challengers are nearly active. To capture tail behavior beyond the leading exponent, the surrogate incorporates saddlepoint prefactors from refined pairwise tail asymptotics. Because these corrections are subexponential, decreasing the annealing temperature with the budget preserves the same first-order target allocation. For the static problem, we prove uniform convergence to the hard minimum, concentration of soft-min weights on active challengers, and continuity of the induced target-allocation map under fixed weights. Experiments show that the proposed methods are consistently competitive: the no-saddlepoint ablation performs best in symmetric Gaussian and exponential slippage settings, while saddlepoint weighting can help in heterogeneous or asymmetric cases.

Long chain-of-thought (CoT) trajectories in large language model (LLM) reasoning cause severe inference bottlenecks due to rapid key-value (KV) cache growth. Current decoding-time compression methods mitigate this issue via token eviction, but typically assume a uniform budget distribution across all layers and heads. In contrast, existing non-uniform budget allocation methods are predominantly designed for the static prompt prefill phase, and they do not capture the stepwise context demands of autoregressive reasoning. To bridge this gap, we propose ReasonAlloc, a training-free framework that recasts decoding-time KV compression as a hierarchical budget allocation problem. ReasonAlloc operates at two complementary levels: an offline layer-wise preallocation strategy captures an architecture-driven demand pattern which we call ``\textit{Reasoning Wave}'', while an online head-wise strategy reallocates resources during decoding to information-rich heads based on real-time utility. Evaluations on mathematical reasoning benchmarks (MATH-500, AIME~2024) using DeepSeek-R1-Distill-Llama-8B, DeepSeek-R1-Distill-Qwen-14B, and AceReason-14B show that ReasonAlloc outperforms uniform-budget R-KV, SnapKV, and Pyramid-RKV (a baseline enforcing a static, monotonically decreasing layer budget), with the largest gains at small budgets (128-512 tokens). ReasonAlloc is plug-and-play with existing token-eviction policies and introduces negligible inference-time overhead.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for enhancing reasoning and agentic behavior in large language models. However, rollout-intensive policy optimization is often limited by insufficient reward contrast, arising when overly simple or complex prompts generate low-variance feedback and when outcome-only rewards assign the same terminal assessment to every decision in a multi-turn rollout. Past efforts have focused on allocating available rollout resources to promising prompts, yet they only leverage sample informativeness at the prompt level and neglect variation in prefix-level informativeness across turns within the same rollout. This work targets multi-turn agentic RL by modeling each ReAct-style thought-action-observation turn as a semantically distinct node, allowing budget allocation to extend from prompt roots to turn-level prefixes with further continuations, which naturally forms tree-structured rollouts. We introduce Tree Rollout Allocation for Contrastive Exploration (TRACE), a unified rollout allocation framework that enhances reward contrast within a fixed sampling budget. Technically, TRACE allocates rollout budget to both prompt roots and intermediate prefixes that are most likely to yield mixed terminal rewards. A shared generalizable predictor estimates conditional success probability at these anchors from prefix histories to guide this allocation. The resulting adaptive tree structure enriches outcome-only feedback and amplifies the policy-update signal. Empirically, TRACE achieves competitive performance and efficiency gains on typical agentic benchmarks, e.g., improving Qwen3-14B Multi-Hop QA average accuracy by 2.8 points over competitive baselines at equal sampling cost.

Counterfactual recourse aims to provide actionable feature changes that would alter an unfavorable decision made by a predictive model. In practice, affected individuals often benefit from multiple feasible alternatives rather than a single optimal explanation. A natural way to produce such alternatives is to prompt large language models (LLMs). However, prompting incurs a practical constraint: the number of LLM calls is often the dominant computational and economic cost. Together, the need for multiple alternatives and this cost constraint shift the problem from finding a single high-quality counterfactual to efficiently generating a set of oracle-validated counterfactuals under a fixed LLM-call budget. In this work, we study counterfactual recourse generation in the LLM-agentic setting as a fixed-budget search problem and propose Comp-MCTS, an agentic tree-search framework that maximizes the yield of unique, oracle-validated counterfactuals under this budget while maintaining favorable quantity--quality trade-offs. Comp-MCTS allocates the budget toward novel intervention directions via LLM-based proposal generation, oracle validation, and compression-guided pruning, in a training-free, oracle-only setting. Experiments on four real-world tabular datasets show that Comp-MCTS substantially outperforms single-candidate LATS-style baselines in the yield of unique, oracle-validated counterfactuals, and offers favorable quantity--quality--efficiency trade-offs against stronger multi-candidate variants: comparable or higher yield at similar or lower oracle-evaluation cost on three of four datasets, plus competitive proximity, sparsity, and novelty.

Sharing the financial impact of rare adverse events across a group can soften extreme individual burdens, but any participant made worse off by the arrangement has reason to leave. A credible mechanism must therefore provide each agent with a trustworthy cap on their future obligation and should be deployed only if the aggregate harm across participants is bounded. We formalise this as the Certified Allocation Problem: from finite data and without distributional assumptions, find a redistribution rule, produce obligation caps for every participant, and verify that no participant is made materially worse off. We propose Conformal Risk Sharing, which solves this problem by pairing an interpretable sharing policy with split conformal calibration. The sharing intensity is tuned on training data, while held-out calibration data produces distribution-free per-agent guarantees (valid under exchangeability). Experiments on synthetic and real-world data, including precipitation and energy-cooperative data, confirm that the framework can substantially reduce extreme obligations for high-risk agents while controlling harm to others.

Multi-turn LLM serving accumulates dialogue history whose Key-Value (KV) cache grows with every turn and every user, quickly exceeding the model weights themselves and making memory -- not compute -- the binding constraint on throughput. Non-uniform KV compression, which allocates heterogeneous budgets across attention heads, preserves accuracy far better than uniform schemes, yet remains impractical: modern serving stacks assume identical KV lengths across heads, so heterogeneity traps freed memory as page fragmentation, spends up to 25% of prefill time reclaiming scattered pages, and skews GPU workloads that inflate decode latency by up to $1.7\times$ or burn 15--20% of each decode step on re-planning. We observe that this heterogeneity need not be discovered at runtime: head-wise retention follows a two-level structural regularity -- an input-invariant head ranking with narrowly bounded per-head ratios -- that can be calibrated offline from as few as 50 samples. Building on this insight, we present Tangram, a serving framework that statically resolves what prior systems handle dynamically: Budget Reservation fixes each head's post-compression footprint at scheduling time, eliminating page reclamation; Ragged Paging clusters similar-budget heads into independent page tables, turning fragmentation into reclaimable memory; and Ahead-of-Time Load Balancing precomputes balanced GPU partitions with zero runtime planning. Implemented on vLLM, Tangram serves as a drop-in substrate for existing non-uniform compression methods, matching their accuracy while improving end-to-end throughput by up to $2.6\times$ over the full-KV baseline. Our implementation is publicly available at https://github.com/aiha-lab/TANGRAM.

Long-horizon agents can archive large histories, but future answers still incur retrieval, rereading, and context costs. When retained memory misses answer-relevant evidence, the system must return to larger portions of the raw history. We study budgeted evidence survival: before the query is known, which source evidence should be retained so that it remains recoverable and usable under a fixed retained source-evidence token budget? We instantiate this setting as Budgeted Pre-Query Retention, where memory is written during ingestion and later read without access to the full raw stream. We introduce EMBER, a learned retention policy that constructs a compact, source-backed evidence state. EMBER stores evidence capsules: verbatim source excerpts paired with retrieval keys and update metadata, preserving both grounding and read-time access. Post-query outcome feedback trains the writer to preserve evidence across the ingestion-retrieval-answer chain. On LongMemEval-RR, our LongMemEval-derived retained-evidence protocol, EMBER-14B reaches 0.3017 F1 at the 8192-token retained-evidence comparison point, compared with 0.1765 for the strongest non-EMBER budgeted baseline. Across retained source-evidence budgets, EMBER improves F1, Retain-Recall, and Read-Recall, indicating that long-horizon memory depends on retaining evidence within the budget rather than rereading larger histories.

Low-cost 2D LiDARs lack the intensity channel that higher-end sensors use to diagnose measurement failures, yet they are widely used on educational and budget robotics platforms. We present SENTINEL, a training - free, label - free reliability estimation framework that gives range - only LiDAR an effective diagnostic signal. SENTINEL combines geometry-based scan statistics with cross - modal depth consistency between LiDAR and an RGB - D camera to compute a per - scan reliability score between 0 and 1. When the score falls below a threshold, corrupted scans are rejected and the robot falls back to calibrated wheel odometry, preventing silent SLAM corruption. We evaluate SENTINEL on a GEFIER R1 four - wheel skid-steer robot equipped with an RPLidar A2M12 and an Intel RealSense D435i in a 185 cm by 245 cm arena containing controlled transparent and reflective failure elements on a central obstacle. Spatial reliability maps across five surface conditions, including glass, mirror, shiny paper, and a mixed mirror and shiny-paper condition, show clear separation between clean and failure cases, allowing affected regions to be identified as reject or noise. Because these failure modes are absent in simulation, validation is performed entirely on real hardware.

Large Language Models can reason over long contexts, yet prefilling millions of tokens is wasteful as much of the content remains static across queries. Cartridges address this by distilling document collections into reusable key-value (KV) caches that eliminate prefilling while preserving accuracy. A critical limitation of this approach is that cartridges are monolithic and non-compositional: encoding an entire collection into a single KV block does not scale, and naively mixing cartridges trained in isolation collapses performance to near chance. We introduce Cartridges at Scale (CAS), a training framework for scalable multi-cartridge learning with dynamic distractor mixing and a memory-efficient budget manager that rotates hundreds of per-document cartridges between GPU and persistent storage. Our approach scales to collections exceeding a million tokens, improving over a monolithic cartridge by 10-31 points at comparable token budgets. Oracle cartridge accuracy falls within 2-6 points of full in-context learning even at high compression. When paired with retrieval for cartridge selection, CAS matches or exceeds conventional RAG accuracy while consuming 3-4x fewer prompt tokens.

LLM-agent budget overruns are a documented production failure class: a single retry loop can spend thousands of dollars before an operator notices, and the in-process integrity properties that would prevent it (no aliasing, no double-spend, no use-after-delegation of a cost-bearing value) are enforced, if at all, by ad-hoc wrappers rather than by the type system. Our central contribution is empirical: a catalog of 63 confirmed production incidents from 21 orchestration frameworks (2023-2026), each backed by a quoted GitHub issue and, where reported, a dollar loss, organized into an eight-cluster failure taxonomy (inter-rater Cohen's kappa = 0.837, N = 113), plus 47 supplementary structural entries. As one mitigation evaluated against this taxonomy, we build token-budgets, an 1,180-line Rust crate (no unsafe) that operationalizes affine ownership so that cloning, double-spending, or using a budget after delegating it are compile errors rather than runtime hazards an operator must remember to avoid. The dollar cap is runtime arithmetic under an estimator assumption; the affine layer makes that arithmetic non-bypassable. On single-agent workloads a 4-line Python counter matches the crate at 0/30 overshoot, so the distinguishing value is non-bypassability under operator error in multi-agent delegation: the delegation-fanout race documented in 11 incidents is rejected by the borrow checker at compile time, while the same pattern under asyncio overshoots 30/30 and three disciplined alternatives overshoot 0/30. Across five runtimes, three providers, and a temperature-stratified live-API test (N = 160), the approach reports zero cap violations and zero false refusals, at operational parity with concurrent work. Static over-reservation is 4-6x (2.11x adaptive). Binary-level cap-soundness on the running binary is left open.

Inference-time scaling has emerged as a critical avenue for enhancing Large Language Models' performance, yet real-world deployment is constrained by strict computational budgets. In this work, we formulate inference budget allocation as a global constrained optimization problem governed by economic principles. By modeling per-query reasoning utility with a shifted-surge function, we derive an optimal allocation policy based on a global shadow price that equilibrates marginal utility under resource scarcity. Based on this theory, we propose Constrained Latent-utility Equilibrium Allocation for Reasoning (CLEAR). It performs rational abandonment and reallocates resources from insolvent queries to solvable queries near their emergence thresholds. Extensive experiments on several reasoning tasks with different traffic streams demonstrate that CLEAR significantly improves the Pareto frontier of total token cost versus mean accuracy. In resource-scarce regimes, CLEAR achieves up to a 3x improvement in global accuracy compared to uniform allocation.

The rapid growth of large language model (LLM) inference services has increased the demand for efficient multi-tenant GPU scheduling. While modern inference runtimes such as vLLM improve throughput through continuous batching and optimized memory management, accurately estimating the runtime cost of heterogeneous inference requests remains challenging. In practice, admission-time workload estimates may deviate from observed execution behavior, leading to workload misclassification, queue imbalance, increased tail latency, and degraded Quality-of-Service (QoS). This paper presents DriftSched, a QoS-aware scheduling framework for multi-tenant LLM inference serving on NVIDIA L4 GPUs. DriftSched combines workload classification, token-budget estimation, tenant-aware queue management, and an online feedback mechanism to refine workload estimates using runtime observations. The framework evaluates FIFO, Priority, Weighted, Shortest-Job-First (SJF), and Aging Priority scheduling policies under heterogeneous multi-tenant workloads. Experimental results show that adaptive calibration reduces workload estimation error by an average of 38.8% (MAE) and 40.5% (RMSE), improving workload classification stability. Among all evaluated schedulers, SJF achieves the best overall performance, reducing median end-to-end latency by approximately 42% and P99 latency by approximately 16% relative to FIFO under sustained GPU contention. The results further indicate that scheduler selection has a greater impact on latency behavior than runtime calibration alone, while accurate workload characterization largely eliminates systematic estimation drift. This work contributes a reproducible framework for studying workload-estimation fidelity and QoS-aware scheduling in multi-tenant GPU inference systems.

Ultra-high-resolution image sensors offer the potential to capture fine spatial details critical for many visual perception tasks, but acquiring and processing all pixels at full resolution is often infeasible under realistic bandwidth, latency, and power constraints. Existing approaches address this challenge through acquisition strategies such as spatial or temporal downsampling, which irrevocably discard information before task relevance can be assessed. In this work, we introduce a real-time, predictive, and task-aware foveated imaging system that operates directly at image acquisition time. Leveraging emerging dual-stream sensor architectures, our method dynamically allocates limited pixel bandwidth to task-relevant regions of interest while maintaining a low-resolution global context. We formulate foveated acquisition as a sensor attention policy-learning problem, in which past observations guide actions that determine future measurements, closing the perception-acquisition loop. Through extensive simulation across multiple perception tasks, we demonstrate that our approach achieves high task performance under strict pixel budgets and significantly outperforms relevant baselines operating at the same bandwidth. We further validate our system on a 200-megapixel dual-stream sensor, capturing real-world videos under realistic bandwidth and latency constraints, demonstrating the practical feasibility of task-driven, acquisition-time foveated imaging.

Speculative decoding accelerates inference by having a lightweight drafter propose tokens verified in parallel by the target language model. Block diffusion drafters such as DFlash generate an entire draft block in one pass, yielding per-position marginals; DDTree uses these to build a candidate tree that maximizes expected acceptance length under a fixed node budget. We observe, however, that acceptance length is non-decreasing in budget: it always favors larger trees regardless of verification cost, offering no principled basis for budget selection. We introduce \textbf{CaDDTree} (Cost-aware Diffusion Draft Tree), a method that directly optimizes token throughput (expected tokens generated per unit time) by jointly selecting the tree structure and node budget. We model draft and verification latencies explicitly, show that the throughput objective decomposes into a per-round one-dimensional search over the budget, and prove that under a convex verification cost the throughput function is \emph{unimodal}, enabling an efficient greedy stopping rule. CaDDTree requires no offline budget search, adapting the budget each round from the current per-position distributions and verification cost. Experiments on Qwen3-4B and Qwen3-8B across eight benchmarks spanning reasoning, coding, and instruction-following tasks show that \caDDTree{} matches or surpasses DDTree with oracle budget selection on nearly all tasks.

Chain-of-Thought (CoT) has significantly enhanced LLM reasoning, yet often incurs substantial computational overhead due to "overthinking": generating excessively long rationales without commensurate accuracy gains. Existing efficiency methods typically apply uniform compression, which overlooks a critical observation that reasoning complexity is heterogeneous at two distinct granularity: across different problems and within individual reasoning steps. This motivates our principle of Thinking Economically: intelligently allocating computational resources based on intrinsic task and step demands rather than pursuing uniform brevity. We propose Hierarchical Adaptive Budgeter (HAB), a training framework that operationalizes this principle through coarse-to-fine budgeting. At the inter-step level, HAB predicts the optimal reasoning depth for each problem. At the intra-step level, HAB learns step-specific token budgeting signals from PPL-derived step comparisons and an adaptive Pareto optimization objective that captures the local quality-efficiency trade-off, while a Fisher Information-based pruner further provides fine-grained training-time guidance, thereby encouraging the generator to internalize more economical reasoning patterns. Experiments on GSM8K and MATH500 show that HAB not only surpasses standard CoT in accuracy but also reduces token usage, achieving a stronger performance-efficiency trade-off than the compared baselines.

We study when LLM judge panels should be calibrated with low-dimensional stackers versus joint output tables under finite human-label budgets. Low-dimensional stackers have small estimation cost but miss interactions, whereas joint-table calibrators can represent interactions but pay for cell counts and unseen patterns. We cast this tradeoff as a finite-calibration regime map and instantiate it as Finite-Calibration Panel Selection, a deployable validation selector over judge path, prefix size, and aggregator family with table and parametric estimation diagnostics. On RewardBench, LLMBar, SummEval, and Arena100K with a seven-judge pool including DeepSeek V4 Flash, scalar/reliability aggregation wins 16 of 20 real dataset--budget cells, indicating that current judge outputs are often additive or redundant. Controlled calibration-growth data show the complementary regime: additive labels remain scalar-favored, whereas a six-way interaction selects a larger joint table and its test MSE drops from 0.224 to 0.061 once unseen mass vanishes. Thus the practical question is not ``how many judges?'' but whether the next judge's information is estimable under the available human labels.

While agents are increasingly spending more resources, today agent cost is mostly measured only after execution. A Budget-Aware Agent (BAGEN) should treat budget as an active control signal, rather than a passive cost metric. We first systematically define budget estimation as internal budgets (from agent computation) and external budgets (from agent actions). We then formalize budget-awareness as progressive interval estimation: at each step of a plan, an agent should predict an upper and lower bound on remaining budget, and alert when completion is unlikely. Scoring with a rollout-replay protocol, we find consistent failure patterns on four environments and five frontier agents: (1) strong agents do not necessarily have strong budget-awareness, with correlation r=0.35. (2) frontier models are consistently over-optimistic, continue spending on tasks that are unlikely to succeed, instead of alerting the user early. (3) budget-aware signal is actionable and trainable. Early stop saves 28-64% tokens on failed trajectories, and SFT+RL strengthens early stop and alert behavior. (4) precise interval calibration remains challenging, with interval coverage capping at 47% after SFT+RL. Project page: https://ragen-ai.github.io/bagen/

Speculative decoding speeds up autoregressive decoding by using a drafter to propose multiple tokens that a verifier validates in parallel. In resource-constrained deployments, the drafter uses a sparse KV cache to limit peak GPU memory and end-to-end latency under a fixed KV budget, while the verifier keeps a full KV cache. Mid-to-long context inference (4K--16K context length) is common in real applications. However, naive sparse/full speculative decoding suffers from the sparse/full mismatch as context length grows, causing the acceptance rate to drop quickly. We propose BudgetDraft, a multi-view sparse training method for sparse drafting in mid-to-long inference. The drafter is exposed to multiple sampled KV budgets during training and learns to align each sparse view with one shared full-cache teacher target. BudgetDraft combines an acceptance-aware loss on a full-cache branch with a multi-view loss on a sparse-cache branch, producing a single budget-robust drafter that recovers acceptance across sparsity levels without extra inference-time components. Experimental results on PG-19, LongBench, and LWM show that BudgetDraft achieves up to 6.55x, 4.46x, and 2.10x end-to-end speedup vs AR at 4K, 8K, and 16K context lengths, while keeping the inference pipeline memory-friendly.

Block-diffusion drafters have recently emerged as a powerful alternative for speculative decoding by predicting multiple future-token distributions in a single parallel step. However, since these parallel predictions are sampled from position-wise marginals rather than fully conditioned sequences, committing to a single greedy path often fails to capture the target model's preferred trajectory. To address this, we propose BASTION, a budget-aware speculative decoding framework with tree-based diffusion drafting. Unlike existing methods that rely on static tree topologies, BASTION dynamically constructs query-dependent trees by balancing draft quality against hardware constraints. Our framework integrates three synergistic components: (1) an acceptance surrogate that estimates expected accepted length via path confidence, (2) an online latency estimator that calibrates a hardware-aware roofline model, and (3) an adaptive best-first expansion that grows the tree until marginal gains no longer justify incremental verification costs. BASTION is training-free, preserves the target model's distribution, and requires no per-setting tuning. Across diverse benchmarks and GPU architectures, BASTION achieves up to a 6.61x speedup over standard autoregressive decoding, outperforming state-of-the-art block-diffusion baselines by 39%.

Weight-space model merging is usually formulated as an algebraic operation on checkpoints, yet at LLM scale the limiting resource is often the set of expert weights that must be read. We introduce MergePipe, a budget-aware execution layer that casts LLM merging as an \emph{expert access-set} problem: given a merge operator and a checkpoint family in a shared weight coordinate system, choose which expert delta blocks to access under an explicit I/O budget. MergePipe indexes parameter blocks, builds deterministic access plans, and executes the induced budgeted merge with replayable manifests. The plan is budget-sound by construction and recovers the full-read merge at full budget; for fixed-coefficient additive operators, the omitted-update error is bounded by the norm of omitted deltas. Across Qwen and Llama merging workloads, MergePipe reduces expert-read I/O by up to an order of magnitude and achieves up to $11\times$ speedups. Representative budget sweeps show $O(10^{-3})$ parameter deviation from full-read merges and no monotonic degradation on downstream benchmarks.

Diffusion-based neural solvers for combinatorial optimization repeatedly re-evaluate dense edge/factor interactions, making inference expensive in wall-clock time and often memory-bound at scale. Inspired by the computational methodologies of many-body physics, we introduce LoRe, a training-free, inference-time drop-in wrapper that enforces per-step interaction-evaluation budgeting: at each iteration, it evaluates only a fixed fraction of interactions by dynamically routing computation to high-conflict or high-uncertainty interactions, instead of using a fixed sparsification (e.g., static kNN graphs or static masks). Under fully inclusive end-to-end wall-clock accounting, LoRe substantially improves scalability on the Maximum Independent Set (MIS) problem, extending feasible inference more than $3\times$ beyond the baseline's out-of-memory limit, delivering a $\sim 8\times$ speedup and a $\sim 12\times$ peak-memory reduction, with solution quality preserved in this regime. Demonstrating cross-task generality on the large-scale Traveling Salesperson Problem (TSP) and zero-shot robustness to topology shifts, LoRe achieves a $\sim 15\times$ speedup at $n=1000$ with a $44\times$ memory reduction and competitive tour quality.

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.

Search agents powered by large language models can autonomously decompose queries, retrieve information, and synthesize answers through multi-step reasoning. However, the rapid growth of training methods has outpaced controlled comparison: existing works differ in retrieval corpora, reward designs, and training protocols, making it unclear what actually drives improvements. We present a controlled empirical study that isolates three under-explored dimensions of search agent training. First, we identify a critical data-coverage issue in the widely used Wikipedia 2018 corpus and show that correcting it alone yields larger gains than the differences between training algorithms. Second, we systematically compare outcome-based and process-based reward methods across three base models, finding that the simplest outcome-based approach achieves competitive or superior performance in most settings, and that process-level credit assignment can over-correct agent behavior. Third, we analyze training data diversity, off-policy data utilization, and search budget scaling, distilling practical guidelines for training effective search agents. Our code is available at https://github.com/YiboZhao624/SearchAgentReview.

Sampling multiple responses improves language model reasoning, but uniform compute allocation is inefficient: easy questions are over-sampled while hard questions remain under-explored. We propose Uncertainty-Aware Budget Allocation (UAB), a concave integer optimization framework that reallocates a fixed sampling budget based on per-question uncertainty estimated at no additional inference cost. In Phase 1, every question receives one generation; its average negative log-likelihood (ANLL), extracted directly from output log-probabilities, serves as a difficulty signal while the generation contributes to the final vote. In Phase 2, the remaining budget is allocated by a marginal-greedy algorithm that solves a concave coverage-maximization surrogate exactly: uncertain questions receive more sampling budget while confident questions receive fewer additional samples. Evaluated on six open-weight and black-box models spanning 1.5B to 27B parameters and five reasoning benchmarks covering math, logic, and preference tasks, UAB outperforms baselines by up to +3% in average accuracy and up to +5% on individual benchmarks, with the largest gains in low-resource settings, requiring no auxiliary model or additional LLM call. Code is publicly available at https://github.com/manhitv/UAB.

Protein sequence optimization under tight oracle budgets requires methods that explore vast combinatorial spaces while making each evaluation informative. Existing reinforcement learning and off-policy generative approaches often degrade under surrogate noise, and position-agnostic mutation proposals risk disrupting functionally critical residues. We introduce SILO, a trajectory-level self-improvement imitation framework for oracle-budgeted protein design. SILO uses a hierarchical edit policy that decomposes each mutation into a position choice followed by a residue choice. In each active-learning round, the policy samples candidate trajectories via incremental stochastic beam search without replacement (SBS), and a UCB-based proxy ensemble, combined with an alanine-scan fitness score (AFS), selects candidates with functionally relevant edits for in silico oracle evaluation. The policy is then updated by next-action cross-entropy imitation on the round's best oracle-labeled trajectories, avoiding value-function estimation. Across eight reproduced protein fitness landscapes and five strong baselines from prior work, SILO achieves the highest maximum and top-100 mean fitness on 8 of 8 landscapes within our evaluations, often exhibiting faster early-stage improvement. In low-data and noisy-proxy stress tests on two landscapes per setting, SILO remains competitive or best when several baselines degrade. Ablations show that SBS with AFS account for much of the gains, with iterative imitation providing additional improvement. Code is available at: https://github.com/grimmlab/SILO.git

Reinforcement learning (RL) is the dominant paradigm for post-training large language models. However, in the online, on-policy setting, rollout generation dominates the computational cost of training. Group-based policy optimization methods compute advantages from multiple rollouts per prompt, yet they indiscriminately allocate budget to prompts with collapsed reward distributions, wasting expensive rollouts on negligible learning signals. We demonstrate that group-based updates are most effective in regimes of high reward variance. Since the policy evolves throughout training, prompt informativeness must be estimated online rather than precomputed, but exhaustively evaluating every prompt is computationally prohibitive. We introduce Pilot-Commit, a budget-aware rollout allocation framework for group-based RL post-training. Pilot-Commit decouples prompt evaluation from exploitation: a pilot stage estimates per-prompt informativeness using a fraction of the budget, and the remaining rollouts are allocated to high-leverage prompts while low-signal prompts are skipped. Across multiple math reasoning benchmarks and model scales from 1.5B to 14B parameters, Pilot-Commit matches baseline accuracy with significantly lower sampling costs, reaching target accuracy up to $1.9\times$ faster than GRPO and $4.0\times$ faster than DAPO in cumulative rollouts.

Tool-using agents increasingly operate in open-ended deployment environments, where they compose file systems, web APIs, code interpreters, and enterprise services at runtime. This creates a safety gap in tool composition: an agent can satisfy every per-tool permission check and still produce an unsafe end-to-end effect, such as reading a confidential document, summarizing it, and sending the summary to an external endpoint. We call this failure mode permission laundering. ChainCaps addresses it with a runtime rule: every value carries a sink-specific capability budget, and tool composition propagates budgets by intersection. A value can preserve or lose authority as it moves through a tool chain, but it cannot gain new authority through composition. We implement ChainCaps as a transparent MCP proxy that requires no changes to the agent or tool servers. On 82 tasks across five frontier models from three providers, ChainCaps reduces attack success rate from 25-68% to 0-4.8% while preserving 96-100% benign completion. In replay experiments, it also outperforms scalar-IFC and per-function-isolation baselines. Manifest quality is the dominant deployment bottleneck: expert manifests reach 100% attack blocking, while naive manifests fall to 27.3%. Our claims are limited to explicit-flow composition safety under trusted manifests and proxy-visible data movement, a practical gap in deployed tool-using agents today.

This is a planning-method note with an unpaired pilot audit. We adapt the classical paired-binary sample-size calculation (Miettinen, 1968) to quantization benchmarks, giving a conservative minimum detectable effect (MDE) bound $δ^{*} \le (z_{1-α/2}+z_{1-β})\sqrt{ρ_d/m}$ in the paired item count $m$ and the FP16-NF4 disagreement rate $ρ_d$. The bound turns "how reliable is my quantization claim?" into a one-line budget a benchmark designer can commit to before running. We illustrate the bound on four models and four benchmarks ($k=5$ splits of $n=100$), and add a parallel MMLU prompt-template study to put the bound's quantization-noise scale alongside the prompt-noise scale. Assuming $ρ_d=0.10$ (an unmeasured planning value), all observed NF4-FP16 deltas fall below the implied MDE, and most cross-split SDs lie within $\pm 1.5$ pp of the binomial reference $\sqrt{p(1-p)/n}$, so much of the variance reported as "benchmark unreliability" on $n=100$ subsamples is binomial sampling noise. The single borderline cell (OPT-WinoGrande, $|Δ|=3.2$ pp) is below the implied MDE at $ρ_d=0.10$ but above it at $ρ_d=0.05$, illustrating the planning trade-off the bound makes explicit. On MMLU, prompt-template ranges of 2-10 pp meet or exceed the largest observed quantization delta (3.2 pp), so a quantization audit that does not first fix the prompt template absorbs template variance into its noise floor. We complement the bound with a five-line pre-registration template.

Existing LLM routing frameworks treat queries as independent events, neglecting the sequential nature of real-world user sessions constrained by global computational budgets. This mismatch inevitably leads to budget bankruptcy: myopic routing policies exhaust resources on early interactions, forcing subsequent and often more complex queries onto inadequate models. We introduce SeqRoute, a framework that formulates multi-turn routing as a finite-horizon Markov Decision Process and solves it via offline reinforcement learning. By incorporating the remaining budget into the state space and training with Conservative Q-Learning (CQL), SeqRoute learns delayed gratification to strategically preserve resources for high-stakes turns later in the session. To overcome data starvation, we propose Hindsight Budget Relabeling (HBR). This technique retrospectively simulates historical trajectories under diverse hypothetical budgets, expanding 10,000 raw sessions into 2.38 million transitions enriched with critical bankruptcy signals. At deployment, a dynamic $λ$-sweep mechanism enables zero-shot navigation of the cost-quality Pareto frontier without retraining. Extensive evaluations demonstrate that SeqRoute reduces operational costs by 6.0-73.5% while maintaining or improving quality, and suppresses bankruptcy rates to under 1%, strictly dominating behavior cloning, budget-aware heuristics, and static baselines across the entire Pareto frontier.

Agentic RAG systems that equip language models with dozens to hundreds of tool definitions face a critical resource conflict: tool schemas consume the same context window needed for retrieval-augmented generation. We present the first systematic study of this tool-context trade-off, evaluating 14 models spanning 1.5B-32B local models plus one frontier API model across 6,566 controlled API calls at three context budgets (8K, 16K, 32K) with 28 tool definitions. Applying TSCG conservative-profile compression (44-50% schema token savings), we observe a binary enablement effect: at 8K tokens, JSON-schema tool definitions overflow the context window entirely, yielding near-zero EM (2.6% average), while compressed schemas restore RAG functionality with +20.5 pp average exact-match lift across all eight models (+24.7 pp among the six exhibiting full enablement). At 32K -- where both formats fit -- four of five tested models show delta <= 1 pp, confirming the effect is purely budget-driven. External validation on HotpotQA (50 multi-hop questions) shows +48 pp EM under the same overflow scenario. Frontier scaling tests demonstrate that JSON schemas overflow at ~494 tools while compressed schemas remain operational beyond 800 tools. Our results establish tool-schema compression as a necessary infrastructure layer for agentic RAG in constrained-context deployments. All code, data, and checkpoints are publicly available.

Long-horizon LLM inference turns the key--value (KV) cache into the dominant GPU memory consumer and makes per-token attention increasingly expensive. Many common eviction policies use static recency windows or historical attention, leaving unused a signal computed on every decoding step: the model's current uncertainty. We introduce CONF-KV, a KV-cache manager that converts the next-token distribution into a scalar confidence score and uses it to choose the per-step cache budget, retaining more context when the model is uncertain and pruning aggressively when it is confident. Within each budget, tokens are ranked by a composite of accumulated attention mass and recency, while a protected recent window preserves local coherence. We combine the policy with blockwise online-softmax attention, mixed FP16/INT8 storage, and a pyramidal per-layer budget variant. Across four model families and generated lengths up to 4K, CONF-KV stays near the footprint of a fixed 512-token sliding window while remaining within 1.5--2.1 perplexity points of full KV. On Needle-in-a-Haystack up to 32K tokens, CONF-KV reaches 91.4% retrieval accuracy versus 53.8% for sliding windows and 80.6% for H2O; on 75 VisualWebArena tasks it retains 95.3% of full-KV success at 2.8 times lower peak memory.

Evaluating large language models increasingly relies on LLM-as-a-judge protocols, but such evaluations remain costly: different judges have different prices and reliabilities, and the difficulty of each prompt-response pair can vary substantially. This raises a basic allocation question: under a fixed budget, how should one distribute evaluation queries across heterogeneous judges and instances to obtain the most accurate score estimates? We formalize this question as budgeted heteroskedastic multi-judge estimation. Given $K$ prompt-response pairs, $J$ judges with known costs, and unknown query-judge variances, the goal is to estimate a bounded score vector while minimizing an $\ell_p$-error. Our first contribution is to analyze the inverse-variance weighted estimator (IVWE) and to derive the oracle allocation that minimizes its error rate. Since this allocation depends on the unknown variances, we then address the practical unknown-variance setting by proposing EST-IVWE, an adaptive algorithm that constructs and leverages optimistically biased variance estimates to stabilize the empirical allocation. We prove that EST-IVWE matches the oracle IVWE rate up to lower-order terms in the budget. Our second and central theoretical contribution is a matching local minimax lower bound, which establishes the instance-optimality of the proposed algorithms. A key technical insight is that Fano-type high-probability arguments are too coarse for this problem: their packing construction loses the local variance structure that governs the optimal allocation. We instead use an Assouad-type in-expectation argument, based on local perturbations, which preserves this structure and yields the sharp allocation-dependent lower bound. Finally, we numerically validate the superiority of our approach over naïve uniform allocation on synthetic and HelpSteer2 datasets.

Extracting structured information from visual documents (Visual Information Extraction, VIE) is a cornerstone of business automation. While recent Multimodal Large Language Models (MLLMs) have shown promising capabilities, existing benchmarks suffer from critical limitations in scale and realism, lack semantic granularity, and fail to cover diverse document types. To bridge this gap, we introduce ReceiptBench, a large-scale, human-annotated benchmark consisting of 10k diverse receipts, organizing information extraction into four hierarchical sub-tasks: (1) Basic Perception for raw text spotting, (2) Format Normalization for strictly following standardization instructions, (3) Semantic Reasoning for inferring implicit attributes from context, and (4) Structure Parsing for handling nested line items. Furthermore, we propose a two-stage training framework incorporating Metric-Aware Group Relative Policy Optimization (GRPO), which translates rigorous evaluation constraints into reinforcement learning signals to enhance structural consistency. Extensive experiments demonstrate that our method yields state-of-the-art performance, surpassing leading proprietary models on complex reasoning tasks. We release our datasets and code at https://github.com/wwwT0ri/ReceiptBench.

As autonomous agents increasingly execute end-to-end tasks under fixed monetary budgets, the pressing open question shifts from whether the budget is respected, to how to spend it effectively. Existing budget-aware methods typically control reasoning step-by-step within a single agent, or learn resource allocation policies via RL. None address how to split a budget across the composing phases of a multi-agent pipeline at inference time. We propose ZEBRA, a zero-shot framework that reduces multi-phase budget allocation to a continuous nonlinear knapsack problem: an LLM controller estimates per-phase utility curves, and a water-filling search on the Lagrange multiplier returns the per-phase split. Additive and multiplicative aggregations are unified under the same solver. On a $150$-task APPS coding benchmark, both ZEBRA variants outperform LLM-direct (budget allocation directly by an LLM) on every aggregate metric. At a budget of $α= 0.5$ of the unconstrained spend, ZEBRA recovers $94.4\%$ of unconstrained quality, versus $88.1\%$ for LLM-direct. The advantage is statistically significant and transfers beyond coding: on a $3$-phase HotpotQA pipeline, ZEBRA beats LLM-direct by $14.3$pp, with allocations empirically robust to curve-estimation noise. On HotpotQA, ZEBRA arrives at a different budget split (near-balanced) compared to the APPS one (skewed towards a refinement phase), showing adaptation to the pipeline structure. More broadly, we show that lightweight algorithmic guidance at inference time can improve the economic behavior of autonomous multi-agent systems.

Recent advances in Video Large Language Models (Video-LLMs) have greatly expanded multimodal reasoning capabilities. However, the massive number of visual tokens extracted from long video sequences incurs prohibitive computational costs, limiting their deployment in real-world scenarios. Existing training-free token compression methods select tokens based on attention magnitude as a proxy for semantic importance, but often overlook positional bias and rely only on short-term temporal locality, leading to redundant spatio-temporal coverage and inefficient token usage. We present DynaTok, a training-free, temporally adaptive and bias-aware token compression framework that allocates token budgets across both temporal and spatial dimensions. Through a lightweight exponential moving average (EMA) memory, the Temporal Budget Allocation (TBA) module dynamically assigns fewer tokens to redundant frames and more to novel frames, capturing long-term temporal variation. The Spatial Budget Allocation (SBA) module complements this by selecting spatially diverse and semantically important features using activation-based attention maps, while leveraging a spatial memory to reduce redundancy from previously selected regions and mitigate positional bias. DynaTok integrates seamlessly with existing Video-LLMs such as LLaVA-OneVision and LLaVA-Video without retraining, and effectively preserves semantic coverage under aggressive compression. Experiments on four representative VideoQA benchmarks-MVBench, LongVideoBench, MLVU, and VideoMME-show that DynaTok retains over 95% of baseline accuracy even with a 90% token reduction, surpassing recent training-free approaches. These results demonstrate that DynaTok provides a principled foundation for efficient and robust video reasoning, paving the way toward real-time streaming video understanding with future Video-LLMs.

In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks to select $k$ vertices whose labels enable accurate prediction of the labels on the remaining vertices. This problem formalizes distilling a small representative set from the whole graph. We present the first $\tilde{O}(\log^{1.5} n)$-approximation algorithm for graph label selection under the standard budget constraint. Prior work either relies on resource augmentation, allowing substantially more than $k$ labeled vertices, or consists primarily of heuristics without provable guarantees. Finally, we demonstrate that practical heuristic variants of our algorithm scale to significantly larger graphs than previous methods, while essentially retaining their quality.

Mixed-precision quantization improves the budget--accuracy trade-off for large language models (LLMs) by allocating more bits to sensitive modules. However, automating this allocation at LLM scale faces a unique combination of constraints: learnable approaches require quantization-aware training, which is infeasible for billion-parameter models; training-free alternatives rely on static proxy metrics that miss cross-module interactions and must be recomputed per target budget; and search-based methods are expensive without guaranteeing exact budget compliance. We propose GAMMA, a quantizer-agnostic framework that learns module-wise precision preferences entirely within a post-training pipeline. GAMMA optimizes a teacher-forced hidden-state reconstruction objective under an augmented Lagrangian constraint, and projects the learned preferences into exact budget-feasible discrete assignments via integer programming. A key property is score reuse: because the learned preferences encode a stable sensitivity ranking rather than budget-specific weights, a single training run serves arbitrary deployment targets by re-solving only the integer program, reducing per-budget adaptation from hours to a few minutes. Across Llama and Qwen models (8B--32B), GAMMA outperforms both fixed-precision baselines (up to +12.99 Avg.) and search-based mixed-precision methods (up to +7.00 Avg.), and can match fixed 3-bit quality at 2.5-bit average precision, enabling deployment at substantially smaller memory footprints.

Predicting model performance at larger scales enables the design of training strategies and architectures tailored to specific performance targets. Empirical scaling law research identifies functional forms to aid this prediction task. These describe the relationship between loss and compute using a loss-compute frontier defined by learning curves. Due to the empirical nature of this approach, the computational burden is substantial, making strategic resource allocation essential - yet it remains surprisingly underexplored. In this work, we address this shortcoming by exploring the suitability of Successive Halving (SH) and SH combined with parametric and non-parametric surrogate models. In addition to enabling a more systematic allocation of a given compute budget, our findings show that SH paired with surrogate models yields a set of learning curves that includes one with a lower loss-compute value than what naive uniform allocation or an SH-only approach can obtain. Our experiments demonstrate mean relative improvements of up to 2.84% and 5.47% on real-world and synthetic learning curve datasets. This strategic resource allocation enables us to obtain accurate scaling laws at significantly reduced computational costs, saving up to 98.7% over the traditional exhaustive approach.

Quantization can preserve predictive accuracy under low-bit deployment while silently breaking algorithmic recourse: an actionable change that flips a decision before quantization may fail after quantization, or become substantially more costly. We formalize counterfactual sensitivity under quantization through validity, cost, and direction stability, and introduce two metrics: Validity Drop (VD) and Counterfactual Recourse Gap (CRG) that reveal recourse failures invisible to accuracy. We propose Counterfactual-Faithful Quantization (CFQ), which trains quantizer parameters and mixed-precision bit allocation to preserve counterfactual behavior by enforcing the target outcome at teacher recourse points under a global bit budget. A margin-based analysis gives a sufficient condition for recourse transfer under bounded quantization perturbations. Experiments on Adult, German Credit, and COMPAS show that accuracy-matched baselines can significantly degrade recourse stability, while CFQ maintains accuracy and substantially improves VD and CRG across bit budgets.

Large Reasoning Models (LRMs) generate chain-of-thought traces whose length tracks human reaction times across cognitive tasks, but recent debate questions whether this alignment reflects genuine computational structure or surface verbosity. We test whether the alignment varies with inference-time reasoning effort. Across GPT-OSS-20B and GPT-OSS-120B, three effort levels, and six reasoning tasks, within-task and cross-task alignment remain invariant: Bayes Factors lean toward the null, and mean alignment is numerically near-identical across conditions. A manipulation check reveals that the effort parameter sets an upper budget on generation rather than driving real-time allocation, suggesting that the allocation policy is crystallized at training time. Arithmetic complexity contrasts further show that token allocation tracks fine-grained, format-dependent human difficulty patterns, with model scale improving the match. Cognitive cost alignment between LRMs and humans appears to be a training-time achievement, robust to inference-time perturbations, supporting a compiled rather than online account of LRM problem-solving.

Scaling LLMs requires tremendous computational resources, and recent advances in AI have gone hand in hand with massive amounts of capital expenditure. While it is established that scaling up LLMs reliably increases model quality (quantified in terms of loss or downstream evaluations), it is unclear how these quality improvements translate to potential revenue, and whether revenue increases would offset costs of larger-scale training and inference. In this work, we develop an economic model for characterizing the rational behavior of an LLM training firm by combining scaling laws with microeconomic theory. Under our model of firm behavior, LLM quality can be increased with more parameters and training tokens, leading to more potential adoption by consumers, who each have a quality threshold for using the LLM. On the other hand, additional parameters and training tokens both incur additional costs. We analyze the profit maximization problem for this model under compute-bound and data-bound regimes. In the compute-bound regime, optimal model size and token budget track hardware efficiency $E$ (FLOPs/$) at a near-linear rate; total training cost then scales sub-quadratically in $E$. Data efficiency improvements incentivize larger models and training expenditure. When we are limited to $D$ data, profit-optimal training expenditure scales as $D^2/E$, i.e, increase with data and decreases with hardware efficiency (as well as data efficiency). Finally, we analyze practical trends in training expenditure: current trends are consistent with our most permissive model variants in the compute-bound regime, but are not profit-optimal in the data-bound regime or assuming hardware advances will stall. Overall, our results provide a theory of profit-optimal LLM training, providing a foundation for engaging critically with industry statements and supporting long-term economic decision making.

Large Language Models (LLMs) have demonstrated remarkable abilities in reasoning. However, maximizing their potential through inference-time scaling faces challenges in trade-off between sampling budget and reasoning quality. Current strategies remain inefficient as they typically treat sampling width and depth as orthogonal objectives, where width consensus methods risk reinforcing hallucinations, while depth pruning mechanisms prematurely truncate complex yet valid reasoning chains. Therefore, we propose Dual-Dimensional Consistency (DDC), a unified framework that bridges path quality with adaptive termination. By coupling Confidence-Weighted Bayesian protocol with a Trend-Aware Stratified Pruning, our method ensures that computational resources are concentrated on high quality reasoning paths, filtering hallucinations while accelerating consensus. Evaluations across five benchmarks demonstrate that this approach reduces token consumption by over 10 times while maintaining or exceeding the accuracy of strong baselines across various LLMs.

Estimating an $N \times N$ quantum kernel from circuit fidelities requires $Θ(N^2 S)$ measurement shots, the dominant bottleneck for deployment on near-term hardware. Existing budget-saving methods (Nyström-QKE, ShoFaR, kernel-target alignment) sub-sample \emph{which} entries to measure but allocate shots \emph{uniformly} within their chosen subset, ignoring how much each entry drives the downstream classifier. We close this gap with two contributions. \textbf{First, a complete regime decomposition} for shot-budgeted quantum kernel learning: a principled menu of when each allocator wins. Our method, \emph{AQKA}, dominates the budget-limited regime ($B \lesssim 16 n_{\mathrm{pairs}}$) on sparse-sensitivity KRR, with the gap \emph{growing} from $+8$ to $+25$ pts over uniform as $N$ scales $225{\to}1000$ and reaching $+26$--$32$ pts on an \texttt{ibm_pittsburgh} (156-qubit Heron) hardware kernel; Nyström-QKE wins at saturating budgets on planted-sparse via low-rank reconstruction; ShoFaR is competitive only at extreme low budgets. \textbf{Second, a closed-form pair-level acquisition theory}: $s_{ij}^{\star} \propto |g_{ij}|\sqrt{K_{ij}(1-K_{ij})}$ with explicit gradient $g_{ij}$ for KRR (Lemma1, $|β_iα_j+β_jα_i|\sqrt{K_{ij}(1-K_{ij})}$) and SVM via the envelope theorem ($|η_i^*η_j^*|\sqrt{K_{ij}(1-K_{ij})}$); a \emph{corrected} sparsity-aware Cauchy--Schwarz rate $ρ\le 2m/N$ matching empirics (vs.\ the naive $m^2/N^2$); an explicit-constant plug-in regret bound (Theorem2); and a tighter SVM ceiling $ρ^{\mathrm{SVM}} \le m_{\mathrm{sv}}^2/N^2$. We close with the first multi-seed live online adaptive shot allocation on quantum hardware: $+17.0 \pm 4.8$ pts at $N{=}20$ on \texttt{ibm_aachen} ($3.5σ$, 5 seeds), with the advantage holding at $N{=}30$ at higher budget on \texttt{ibm_berlin} ($+14.0 \pm 8.5$ pts, 5 seeds).

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.

A key technical difficulty in differential privacy is selecting a privacy budget that satisfies privacy requirements while maximizing utility. A natural and well-studied workaround is to use personalized privacy budgets, which may differ across agents. In this paper, we show that personalized budgets come with major limitations and that for mean estimation, the dominant factor is not full personalization, but rather choosing the right effective privacy budget. This can be achieved through a simple thresholding operator that we describe. Compared with this thresholding baseline, the gains obtained by fully personalized mechanisms are limited. In particular, we precisely quantify the constant-factor improvement in settings with mixed private and public datasets and in private datasets with two levels of privacy requirements. We also establish upper bounds and identify regimes of maximal gain for arbitrary privacy requirements.

AlphaEvolve and FunSearch have demonstrated the potential of combining large language models (LLMs) with evolutionary search for automated algorithm discovery. However, discovery success is shaped not only by model capability but also significantly by the design of the execution infrastructure, i.e., the harness. This paper investigates effective harness design through three questions: under a fixed token budget, is it better to produce many algorithms with brief thought or fewer algorithms with deeper thought? How should the harness handle evaluation hacks, where generated programs exploit the scoring function? And how can agents that require full filesystem access execute safely in parallel? Using Vesper, an algorithm discovery framework that incorporates harness improvements addressing these questions, we evaluate on Circle Packing under the same token budget. Interestingly, generating fewer algorithms while thinking more deeply about each one achieved higher scores. That is, scaling the quality of each individual is more budget-efficient than scaling the number of evolutionary generations. Surprisingly, more capable models produced evaluation hacks at higher rates, making hack detection increasingly necessary as models scale.

We study optimal policy learning under combined budget and minimum coverage constraints. We show that the problem admits a knapsack-type structure and that the optimal policy can be characterized by an affine threshold rule involving both budget and coverage shadow prices. We establish that the linear programming relaxation of the combinatorial solution has an O(1) integrality gap, implying asymptotic equivalence with the optimal discrete allocation. Building on this result, we analyze two implementable approaches: a Greedy-Lagrangian (GLC) and a rank-and-cut (RC) algorithm. We show that the GLC closely approximates the optimal solution and achieves near-optimal performance in finite samples. By contrast, RC is approximately optimal whenever the coverage constraint is slack or costs are homogeneous, while misallocation arises only when cost heterogeneity interacts with a binding coverage constraint. Monte Carlo evidence supports these findings.

Hard constraints in generative sampling are typically enforced by projection, applied either once at the end of sampling or after every update. This binary framing overlooks a fundamental issue: projection changes the distribution of states which future updates depend on. As a result, delayed projection can produce samples that are feasible but inconsistent with the intended sampling dynamics, even after final projection. We formalize constraint enforcement as a correction scheduling problem over the generative rollout. Using one-step constraint defect as a local signal of geometric mismatch, we introduce adaptive correction scheduling, a state-dependent policy that allocates projection budget to the steps that most strongly perturb the trajectory. Terminal and stepwise projection arise as limiting cases of this family. Across controlled manifold rollouts and a learned projected diffusion sampler, adaptive scheduling improves the cost-accuracy frontier at matched projection budgets, recovering 71.2% of full stepwise benefit with 75% fewer corrections. These results show that constraint timing is a first-class design variable in generative sampling, and that enforcing feasibility alone is insufficient to preserve the intended constrained sampling dynamics.

Large language models (LLMs) have emerged as powerful tools for automatic algorithm design (AAD). However, existing pipelines remain inefficient. They operate at the granularity of full algorithms, redundantly rewriting recurring substructures and discarding low-fitness candidates that may contain valuable algorithmic features. We formalize budget-efficient automatic algorithm design, wherein the search policy maximizes realized fitness subject to limited computational cost. We propose a directed acyclic graph representation of algorithms and build a search framework that fully exploits the LLM's output. Instead of querying the LLM for full algorithms, we use it to obtain corrections: compact operators that add, replace, or remove code blocks. Each correction augments the graph, yielding new algorithms that compose with prior corrections. This graph structure decomposes algorithms into sets of corrections, enabling correction-level credit assignment that informs subsequent queries. We complement this framework with theoretical insights into the ideal balance between search depth and breadth at different budget levels. We validate our method empirically on three combinatorial optimization problems, demonstrating consistent superiority of our graph-based search over full-algorithm search at equal token budget. Finally, our experiments suggest that rich contexts help only when the LLM's prior knowledge is shallow, and can hinder performance otherwise.

We address the problem of maximizing Gain from Trade (GFT) in repeated buyer-seller exchanges subject to global budget balance constraints. While this problem is well-understood in purely adversarial and stochastic settings, these environments exhibit a sharp dichotomy: adversarial environments allow for no-regret learning against the best fixed-price mechanism, whereas stochastic environments allow for no-regret learning against the best distribution over prices that is budget balanced in expectation. This gap is significant, as policies balanced in expectation can increase the GFT by a multiplicative factor of two. In this work, we bridge these extremes by studying perturbed markets, where an underlying stochastic distribution is subject to an adversarial corruption $C$. We design an algorithm that adaptively scales with the level of corruption, achieving an $\tilde{\mathcal{O}}(T^{3/4}) + \mathcal{O}(C\log(T))$ regret bound against the best budget-balanced distribution over prices. Simultaneously, our algorithm maintains the worst-case $\tilde{\mathcal{O}}(T^{3/4})$ regret bound relative to a per-round budget-balanced baseline, ensuring optimality even in fully adversarial environments.

Large reasoning models, such as OpenAI o1 and DeepSeek-R1, tend to become increasingly verbose as their reasoning capabilities improve. These inflated Chain-of-Thought (CoT) trajectories often exceed what the underlying problems require, wasting compute, latency, and context budgets. While introducing length-based efficiency rewards during reinforcement learning offers a natural remedy, existing methods struggle with two fundamental challenges: the optimal balance between correctness and efficiency is non-stationary throughout training, and intrinsic reasoning budgets vary drastically across problems. Relying on static reward weights and global length constraints inevitably forces a compromise between degraded accuracy and unrealized compression. To overcome these limitations, we propose LEAD (Length-Efficient Adaptive and Dynamic reasoning), a method that replaces static heuristics with online, self-adaptive mechanisms. LEAD dynamically calibrates the correctness-efficiency trade-off at each step using a Potential-Scaled Instability, directing optimization capacity to the most informative learning signal. Furthermore, it estimates an adaptive per-problem target length online based on the model's own correct rollouts, applying a symmetric efficiency reward that penalizes both overthinking and over-compression. Evaluated on five mathematical reasoning benchmarks, LEAD achieves the highest accuracy and Accuracy-Efficiency Score among RL-trained efficient-reasoning methods while producing substantially shorter outputs than the base model.

Agents built on large language models (LLMs) rely on a range of reliability techniques, including retry, majority voting, and self-consistency, that have been developed in parallel rather than within a common analytical framework. We observe that an LLM sampled at temperature $T$ is a discrete stochastic channel $p(y \mid x)$ in the sense of Shannon's coding theory, and use this identity as the entry point for such a framework grounded in communication theory. Each of these techniques is a special case of one of six classical reliability operators: diversity combining, hybrid retransmission, iterative generator-critic decoding, rateless sampling, structured redundant verification, and difficulty-adaptive routing. Within the framework we give two closed-form results: a noise-variance threshold above which uniform averaging beats quality-weighted averaging, and a contractivity criterion for generator-critic refinement, consistent with a contractive-to-divergent transition we observe between 3B- and 14B-parameter models. We further introduce a cost-aware semantic-nearest-neighbor router whose single Lagrangian knob traverses the quality-cost frontier without retraining. Across six channel configurations spanning local and cloud models on 69 hard tasks, no fixed model-technique-budget choice dominates, motivating per-task allocation. On a 300-item hard split of MMLU, GSM8K, and HumanEval, our router occupies the full empirical Pareto frontier: at matched quality, its normalized cost is ${\approx}56$% lower than the strongest fixed technique; at matched normalized cost, it improves quality by ${\approx}7$% ($26$% over single-shot decoding). These results argue for consolidating these reliability techniques into a single tunable layer informed by channel coding.

As LLM agents evolve, tokens have emerged as the core economic primitives of Agentic AI. However, their exponential consumption introduces severe computational, collaborative, and security bottlenecks. Current surveys remain fragmented across system optimization, architecture design, and trust, lacking a unified framework to evaluate the fundamental trade-off between output quality and economic cost. To bridge this gap, this survey presents the first comprehensive survey of Token Economics. By unifying computer science and economics, we conceptualize tokens as production factors, exchange mediums, and units of account. We synthesize existing literature across a four-dimensional taxonomy: (1) Micro-level (Single Agent): Optimizing budget-constrained factor substitution via neoclassical firm theory. (2) Meso-level (Multi-Agent Systems): Minimizing collaboration friction using transaction cost and principal-agent theories. (3) Macro-level (Agent Ecosystems): Addressing congestion externalities and pricing via mechanism design. (4) Security: Internalizing adversarial threats as endogenous economic constraints. Finally, we outline frontier directions, including differentiable token budgets and dynamic markets, to lay the theoretical foundation for scalable next-generation agent systems.

While recent advancements in inference-time learning have improved LLM reasoning on Text-to-SQL tasks, current solutions still struggle to perform well on the most challenging tasks in the Bird-Bench (BIRD) benchmark. This is due to inadequate solution space exploration, which is necessary to uncover promising candidate queries that can be further refined to produce the correct output. To address this challenge, we introduce CA-SQL, a novel Text-to-SQL pipeline that utilizes the estimated difficulty of a task to dynamically scale the breadth of the exploration for generating solution candidates. In addition, we use a custom prompt seeding method, based on principles of evolutionary search, to further elicit exploratory behavior from the base LLM and a novel voting method to select the best candidate solution at the end of the search. Experiments demonstrate that our solution achieves a state-of-the-art score of 51.72% on the "challenging" tier of BIRD development set problems, using only GPT-4o-mini, out-performing other in-context learning approaches, even those that leverage larger models. Overall, our method attains a competitive 61.06% execution accuracy and 68.77% Soft F1 score on the BIRD development dataset.

Training a family of large language models (LLMs), either from scratch or via iterative compression, is prohibitively expensive and inefficient, requiring separate training runs for each model in the family. In this paper, we introduce Star Elastic, a novel LLM post-training method that adds N nested submodels to a given parent reasoning model using the compute of one run (N-fold savings) via a single post-training job. Beyond reducing training costs, Star Elastic also addresses a fundamental limitation of efficient reasoning: the rigidity of static architectures, which forces the allocation of constant resources regardless of token difficulty. By unlocking elastic budget control, Star Elastic enables a novel inference scheme that uses different submodels for each reasoning phase (thinking and answering). Star Elastic supports (1) nesting along the SSM, embedding channel, MoE, and FFN axes, (2) learning nested submodels via an end-to-end trainable router, and (3) curriculum-based knowledge distillation. Building on the Nemotron Elastic framework, we apply Star Elastic to the NVIDIA Nemotron Nano models, with a particular focus on hybrid Mixture-of-Experts (MoE) architectures: from Nemotron Nano v3 (30B/3.6A), we generate 23B (2.8A) and 12B (2.0A) variants with 160B training tokens. All nested models match or outperform independently trained baselines of comparable size and achieve a 360x reduction versus pretraining from scratch and a 7x reduction over state-of-the-art compression. Crucially, elastic budget control advances the accuracy-latency Pareto frontier, achieving up to 16% higher accuracy and 1.9x lower latency via dynamic per-phase model selection. We further extend Star Elastic to quantized regimes via Quantization-Aware Distillation (QAD), producing nested NVFP4 and FP8 elastic checkpoints that preserve zero-shot slicing while delivering smaller deployment footprints.

We study budget-constrained contextual bandits with adversarial contexts, where each action yields a random reward and incurs a random cost. We adopt the standard realizability assumption: conditioned on the observed context, rewards and costs are drawn independently from fixed distributions whose expectations belong to known function classes. We focus on the continuing setting, in which the algorithm operates over the entire horizon even after the budget for cumulative cost is exhausted. In this setting, the objective is to simultaneously control regret and the violation of the budget constraint. Building on the seminal $\mathsf{SquareCB}$ framework of Foster et al. [2018], we propose a simple and modular framework that leverages online regression oracles to reduce the constrained problem to a standard unconstrained contextual bandit problem with adaptively defined surrogate reward functions. In contrast to prior works, which focus on stochastic contexts, our reduction yields improved guarantees for more general adversarial contexts, together with an efficient algorithm with a compact and transparent analysis.

LLM search agents increasingly rely on tools at inference time, but their trajectories are often constrained by hard limits on both tool calls and generated tokens. Under such dual budgets, better answers require not only stronger models, but also explicit control over which search action should receive the next budget unit and when the accumulated evidence is sufficient to commit a final answer. We study this problem in multi-hop question answering (QA) and formulate it as two-stage inference-time budget control. At search time, our controller assigns each feasible action a task-level Value-of-Information (VOI) score, defined as an operational estimate of marginal task value per unit budget under the current search state and remaining dual budget, and uses this score to choose among retrieval, decomposition, and answer commitment. After search, a selective evidence-grounded finalizer compares the trajectory answer with a refined candidate and rewrites only when the residual error appears to be a low-risk answer-form error. Across four multi-hop QA benchmarks, three LLM backbones, and four budget levels, the method yields positive aggregate gains over four audited baselines under the same hard dual-budget protocol. Ablations show that search-time budget control, especially budget-dependent penalty, provides the main performance gain, while answer-time control helps mainly when the retrieval path is already adequate. These results suggest that inference-time budget control for LLM search agents should govern both how budget is spent during search and how the final answer is committed.

Transformers usually expose one inference cost per trained model, while deployed systems often need multiple cost-quality operating points. We study Budgeted Attention Allocation, a monotone head-gating mechanism conditioned on a requested attention budget. Dense warm-starting is important for stability: on a robust synthetic sequence task, one budgeted model reaches 99.7% accuracy at 0.303 estimated attention cost and 100.0% accuracy at 0.504 cost. On held-out AG News with a custom word-level transformer, hard-gate adaptation turns soft cost control into measured single-thread CPU speed, reaching 82.1% accuracy with 1.28x speedup at budget 0.50. In pretrained BERT-Mini AG News, budgeted structural pruning reaches 87.6% accuracy with 1.20x speedup at budget 0.50; a validation-ranked zero-shot dense post-hoc structural baseline reaches 86.1%, and one recovery epoch raises that per-budget specialist to 87.9%. On DBpedia14, BERT-Mini budgeted gates reach 97.4% at exact budget 0.50 versus 96.6% for dense full attention. Static fixed-budget gates and recovered dense specialists remain strong. The contribution is therefore not universal dominance, but a reproducible feasibility study of one controllable checkpoint across budgets that can trade attention cost for accuracy and be converted into measured structural speedups on small CPU benchmarks.

Multi-agent LLM systems for code generation face a fundamental routing problem: the optimal orchestration topology depends on the structural complexity of the code under modification, yet existing systems select topologies without consulting the codebase. We present Retrieval-Guided Adaptive Orchestration (RGAO), an architecture that closes this loop by extracting a structural complexity vector from a hierarchical code index before selecting the orchestration topology. RGAO operates within Code-Agent, a multi-agent framework whose sub-agents are governed by formal contracts with six-dimensional budget vectors. Our headline contribution is the composition of two previously separate lines of work -- complexity-conditioned LLM routing and formal resource algebras -- yielding a property neither admits alone: provable budget conservation under retrieval-conditioned dynamic topology selection. Concretely we contribute: (1) a complexity-conditioned topology router that reduces proxy-measured misrouting from 30.1% to 8.2%; (2) a budget algebra with a structural-induction conservation theorem; and (3) a hierarchical code retrieval engine. Empirical evaluation demonstrates sub-millisecond DAG construction and linear tree-index scalability.