CoT transformers simulate any Word RAM algorithm with poly-logarithmic overhead in three architectures, improving on quadratic TM overhead.
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Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters
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abstract
Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to most effectively allocate test-time compute adaptively per prompt. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.
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- abstract Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one
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representative citing papers
EGLR adds a deterministic layer-recursion axis gated by entropy that is complementary to temperature sampling, raising joint oracle accuracy on MATH-500 from 83.4% to 91.6% for a 3B model.
UniQL is a human-verified benchmark providing aligned natural language questions and dialect-specific SQL queries for 16 SQL systems to evaluate cross-dialect generalization.
AutoTTS discovers width-depth test-time scaling controllers through agentic search in a pre-collected trajectory environment, yielding better accuracy-cost tradeoffs than hand-designed baselines on math reasoning tasks at low cost.
Test-time training with KV binding reduces to learned linear attention.
Physics-IQ benchmark reveals that generative video models exhibit limited physical understanding unrelated to their visual quality.
MedPRMBench is the first fine-grained benchmark for process reward models in medical reasoning, featuring 6500 questions, 13000 chains, 113910 step labels, and a baseline that improves downstream QA accuracy by 3.2-6.7 points.
Multi-agent LLMs generate and verify 14,073 deterministic reaction rules from 665,901 patents, enabling 97.7% classification of unseen reactions with finer resolution than fixed proprietary systems.
Preregistered placebo-controlled decomposition shows external executable counterexamples drive self-repair gains in small code models more than re-exposure or self-critique.
Empirical power-law frontier between predictive loss and structural forward work in LOB models extrapolates to held-out high-compute architectures with R²=0.941, motivating FastBiNLOB which exceeds SOTA macro-F1 at lower latency.
LBR performs token-level test-time scaling via local branch routing on hidden states, enabling end-to-end RL training and improving Pass@1 and Pass@32 on math benchmarks over CoT and RLVR baselines.
SPIRAL is a reinforcement learning framework that jointly optimizes sequential reasoning, parallel trace generation, and aggregation in language models for improved test-time performance.
SPOT-E uses entropy shaping on answer predictions with low-entropy anchors to optimize visual spotlights at test time via GRPO for better VLM performance on evidence-intensive tasks.
SWITCH uses explicit <swi> and </swi> boundary tokens to make latent chain-of-thought compatible with on-policy RL (GRPO) and open to causal mechanistic probing, outperforming prior hidden-state recurrence methods.
MARS is a margin-adversarial stopping rule for parallel LLM test-time scaling that saves 25-47% tokens while matching full-budget majority-vote accuracy by learning trace switch probabilities and applying adversarial bounds.
QGF performs test-time policy optimization for flow models in RL by guiding a behavior-cloned reference policy with value-function gradients, achieving strong results on high-dimensional offline RL benchmarks without additional policy training.
KCSAT-ML benchmark supplies human error rates for math problems and DRG metric exposes that model accuracy collapses on high-human-error items while test-time scaling shows non-monotonic gains and alignment failures.
PRISM is a contrastive, policy-aware training framework for process reward models that reduces false positives by 22% on PRMBench and boosts downstream accuracy up to 33% in Best-of-N selection by learning reliable relative comparisons instead of pointwise labels.
Three problem-level trajectory features derived from the distributional signature of failed LLM rollouts enable failure clustering at 84.3% accuracy and a training-free routing rule that improves rescue by 12.2% on hard cases.
TTT-RTL performs per-design test-time RL on an LLM policy with EDA-derived PPA rewards and an adaptive KL controller, reducing geometric-mean PPA product by 65.1% on RTLLM v2.0 and ADP by 59.4% on an industrial FPU unit.
LLMs achieve up to 78.8% accuracy and r=0.590 correlation mimicking individual SOEP respondents using cumulative microdata, with gains from more information but diminishing returns past the 75% entropy point.
Consequence-aware scheduler using an issue-text predictor routes more compute to high-cost failures and cuts cost-weighted loss by 22-33% versus difficulty-based allocation on SWE-bench tasks.
Rotate2Think estimates an orthogonal rotation from input to thinking embeddings via Procrustes analysis on a few examples and injects the resulting vector to prime reasoning traces, raising accuracy in 30 of 32 model-benchmark settings.
VLMs formulate differentiable rewards from task-specific rules to enable test-time online LoRA optimization of VGMs, delivering 16.7-point gains on symbolic and general video reasoning benchmarks over VLM-as-solver and Best-of-N baselines.
citing papers explorer
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Efficiently Representing Algorithms With Chain-of-Thought Transformers
CoT transformers simulate any Word RAM algorithm with poly-logarithmic overhead in three architectures, improving on quadratic TM overhead.
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Entropy-Gated Latent Recursion
EGLR adds a deterministic layer-recursion axis gated by entropy that is complementary to temperature sampling, raising joint oracle accuracy on MATH-500 from 83.4% to 91.6% for a 3B model.
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UniQL: Towards Dialect-Universal Benchmarking for Text-to-SQL
UniQL is a human-verified benchmark providing aligned natural language questions and dialect-specific SQL queries for 16 SQL systems to evaluate cross-dialect generalization.
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LLMs Improving LLMs: Agentic Discovery for Test-Time Scaling
AutoTTS discovers width-depth test-time scaling controllers through agentic search in a pre-collected trajectory environment, yielding better accuracy-cost tradeoffs than hand-designed baselines on math reasoning tasks at low cost.
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Test-Time Training with KV Binding Is Secretly Linear Attention
Test-time training with KV binding reduces to learned linear attention.
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Do generative video models understand physical principles?
Physics-IQ benchmark reveals that generative video models exhibit limited physical understanding unrelated to their visual quality.
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MedPRMBench: A Fine-grained Benchmark for Process Reward Models in Medical Reasoning
MedPRMBench is the first fine-grained benchmark for process reward models in medical reasoning, featuring 6500 questions, 13000 chains, 113910 step labels, and a baseline that improves downstream QA accuracy by 3.2-6.7 points.
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Agentic generation of verifiable rules for deterministic, self-expanding reaction classification
Multi-agent LLMs generate and verify 14,073 deterministic reaction rules from 665,901 patents, enabling 97.7% classification of unseen reactions with finer resolution than fixed proprietary systems.
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Falsification, Not Exposure: An Internally Preregistered Placebo-Controlled Decomposition of Self-Repair Feedback in Frozen Small Code Models
Preregistered placebo-controlled decomposition shows external executable counterexamples drive self-repair gains in small code models more than re-exposure or self-critique.
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The Inference-Compute Frontier and a Latency-Efficient Architecture for Limit Order Book Prediction
Empirical power-law frontier between predictive loss and structural forward work in LOB models extrapolates to held-out high-compute architectures with R²=0.941, motivating FastBiNLOB which exceeds SOTA macro-F1 at lower latency.
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Efficient and Trainable Language Model Test-Time Scaling via Local Branch Routing
LBR performs token-level test-time scaling via local branch routing on hidden states, enabling end-to-end RL training and improving Pass@1 and Pass@32 on math benchmarks over CoT and RLVR baselines.
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SPIRAL: Learning to Search and Aggregate
SPIRAL is a reinforcement learning framework that jointly optimizes sequential reasoning, parallel trace generation, and aggregation in language models for improved test-time performance.
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SPOT-E: Test-Time Entropy Shaping with Visual Spotlights for Frozen VLMs
SPOT-E uses entropy shaping on answer predictions with low-entropy anchors to optimize visual spotlights at test time via GRPO for better VLM performance on evidence-intensive tasks.
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Demystifying Hidden-State Recurrence: Switchable Latent Reasoning with On-Policy Reinforcement Learning
SWITCH uses explicit <swi> and </swi> boundary tokens to make latent chain-of-thought compatible with on-policy RL (GRPO) and open to causal mechanistic probing, outperforming prior hidden-state recurrence methods.
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MARS: Margin-Adversarial Risk-controlled Stopping for Parallel LLM Test-time Scaling
MARS is a margin-adversarial stopping rule for parallel LLM test-time scaling that saves 25-47% tokens while matching full-budget majority-vote accuracy by learning trace switch probabilities and applying adversarial bounds.
-
Test-Time Gradient Guidance of Flow Policies in Reinforcement Learning
QGF performs test-time policy optimization for flow models in RL by guiding a behavior-cloned reference policy with value-function gradients, achieving strong results on high-dimensional offline RL benchmarks without additional policy training.
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KCSAT-ML: Probing Reasoning Models with Nationwide-Cohort Human Difficulty
KCSAT-ML benchmark supplies human error rates for math problems and DRG metric exposes that model accuracy collapses on high-human-error items while test-time scaling shows non-monotonic gains and alignment failures.
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The Hidden Bias of Process Reward Models:PRISM for Rewarding the Right Reasoning
PRISM is a contrastive, policy-aware training framework for process reward models that reduces false positives by 22% on PRMBench and boosts downstream accuracy up to 33% in Best-of-N selection by learning reliable relative comparisons instead of pointwise labels.
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Failed Reasoning Traces Tell You What Is Fixable (But Not by Reading Them)
Three problem-level trajectory features derived from the distributional signature of failed LLM rollouts enable failure clustering at 84.3% accuracy and a training-free routing rule that improves rescue by 12.2% on hard cases.
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Alpha-RTL: Test-Time Training for RTL Hardware Optimization
TTT-RTL performs per-design test-time RL on an LLM policy with EDA-derived PPA rewards and an adaptive KL controller, reducing geometric-mean PPA product by 65.1% on RTLLM v2.0 and ADP by 59.4% on an industrial FPU unit.
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Synthetic Personalities: How Well Can LLMs Mimic Individual Respondents Using Socio-Economic Microdata?
LLMs achieve up to 78.8% accuracy and r=0.590 correlation mimicking individual SOEP respondents using cumulative microdata, with gains from more information but diminishing returns past the 75% entropy point.
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Not All Errors Are Equal: Consequence-Aware Reasoning Compute Allocation
Consequence-aware scheduler using an issue-text predictor routes more compute to high-cost failures and cuts cost-weighted loss by 22-33% versus difficulty-based allocation on SWE-bench tasks.
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Rotate2Think: Geometric Priming via Orthogonal Rotation to Improve Language Model Reasoning
Rotate2Think estimates an orthogonal rotation from input to thinking embeddings via Procrustes analysis on a few examples and injects the resulting vector to prime reasoning traces, raising accuracy in 30 of 32 model-benchmark settings.
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VLMs are Good Teachers for Video Reasoning via Adaptive Test-Time Optimization
VLMs formulate differentiable rewards from task-specific rules to enable test-time online LoRA optimization of VGMs, delivering 16.7-point gains on symbolic and general video reasoning benchmarks over VLM-as-solver and Best-of-N baselines.
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ATLAS: Agentic Test-time Learning-to-Allocate Scaling
ATLAS introduces an LLM-orchestrated agentic framework for dynamic test-time scaling via extensible 'explore' actions, achieving higher accuracy with fewer API calls than fixed-workflow baselines on four benchmarks.
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Unlocking the Working Memory of Large Language Models for Latent Reasoning
RiM trains LLMs to perform latent reasoning via fixed memory blocks processed in one forward pass using a two-stage curriculum, matching or exceeding prior latent methods on benchmarks.
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The Chain Holds, the Answer Folds: Trace-Answer Dissociation in Reasoning Models Under Adversarial Pressure
The paper identifies unfaithful capitulation, a failure mode where chain-of-thought remains correct but the emitted answer flips wrong under sustained adversarial pressure in multi-turn dialogue.
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LaneRoPE: Positional Encoding for Collaborative Parallel Reasoning and Generation
LaneRoPE adds an inter-sequence attention mask and extended RoPE to enable collaborative parallel sequence generation in LLMs, yielding accuracy gains on math reasoning under length limits.
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Co-ReAct: Rubrics as Step-Level Collaborators for ReAct Agents
Co-ReAct adds step-level rubric guidance to ReAct agents via a GRPO-trained generator using list-wise ranking rewards, yielding consistent gains on DeepResearchBench and SQA-CS-V2.
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HIDBench: Benchmarking Large Language Models for Host-Based Intrusion Detection
HIDBench unifies DARPA-E3, DARPA-E5, and NodLink datasets with a data pipeline to benchmark LLMs for host-based intrusion detection, showing high precision on simple logs but sharp drops in MCC and rises in false positives on complex noisy data.
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Goodbye Drift: Anchored Tree Sampling for Long-Horizon Video-to-Video Generation
Anchored Tree Sampling converts horizon-compounding drift into anchor-bounded drift by organizing video generation as a sparse-to-dense tree of imputations instead of left-to-right autoregressive rollout.
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Learning How to Cube
A neuro-symbolic post-training pipeline lets a 4B transformer learn cubing heuristics that reach pass@5 of 53 on 100 SAT competition instances, matching the strongest symbolic baseline.
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CAPS: Cascaded Adaptive Pairwise Selection for Efficient Parallel Reasoning
CAPS is a four-stage inference-only cascade that adapts how much of each solution the verifier sees and how comparisons are distributed, halving per-candidate verifier tokens while outperforming uniform pairwise verification on most benchmarks.
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Minerva-Ego: Spatiotemporal Hints for Egocentric Video Understanding
Minerva-Ego is a new benchmark for egocentric visual reasoning with dense human-annotated traces and masks, showing that spatiotemporal hints substantially improve frontier model performance.
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Beyond Individual Intelligence: Surveying Collaboration, Failure Attribution, and Self-Evolution in LLM-based Multi-Agent Systems
A survey that unifies prior work on multi-agent LLM systems via the LIFE framework, mapping dependencies across collaboration, failure attribution, and autonomous self-evolution while identifying cross-stage challenges.
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Test-Time Learning with an Evolving Library
EvoLib enables LLMs to accumulate, reuse, and evolve knowledge abstractions from inference trajectories at test time, yielding substantial gains on math reasoning, code generation, and agentic benchmarks without parameter updates or supervision.
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Uncovering the Representation Geometry of Minimal Cores in Overcomplete Reasoning Traces
Language models produce overcomplete reasoning traces where on average 46% of steps can be removed while preserving the answer in 86% of cases, with necessity concentrated in the top three steps.
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Query-Conditioned Test-Time Self-Training for Large Language Models
QueST adapts LLMs at test time by generating query-specific problem-solution pairs for self-supervised fine-tuning, improving reasoning performance without external data.
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Think Twice, Act Once: Verifier-Guided Action Selection For Embodied Agents
VeGAS improves MLLM-based embodied agents by sampling action ensembles and using a verifier trained on LLM-synthesized failure cases, yielding up to 36% relative gains on hard multi-object long-horizon tasks in Habitat and ALFRED.
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StepCodeReasoner: Aligning Code Reasoning with Stepwise Execution Traces via Reinforcement Learning
StepCodeReasoner aligns code reasoning with verifiable stepwise execution traces via print anchors and bi-level GRPO reinforcement learning, reaching SOTA results on CRUXEval (91.1%) and LiveCodeBench (86.5%) for a 7B model.
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Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities
Presents a likelihood-based benchmark for equation-suffix prediction in technical papers with controls to detect shortcut vulnerabilities in model forecasts.
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V-ABS: Action-Observer Driven Beam Search for Dynamic Visual Reasoning
V-ABS is an action-observer beam search method with entropy-based adaptive weighting and an 80k-sample SFT dataset that delivers 19.7% average gains on visual reasoning tasks for MLLMs.
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Active Testing of Large Language Models via Approximate Neyman Allocation
Proposes surrogate semantic entropy stratification followed by approximate Neyman allocation for active testing of LLMs on generative benchmarks, reporting up to 28% MSE reduction and 22.9% average budget savings versus uniform sampling.
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RubricRefine: Improving Tool-Use Agent Reliability with Training-Free Pre-Execution Refinement
RubricRefine is a training-free pre-execution method that creates rubrics to score and fix inter-tool contract violations in agent code, reaching 0.86 average on M3ToolEval across seven models with zero executions and lower latency.
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BubbleSpec: Turning Long-Tail Bubbles into Speculative Rollout Drafts for Synchronous Reinforcement Learning
BubbleSpec exploits long-tail bubbles in synchronous RL by using faster ranks' idle time to pre-generate rollout drafts for speculative decoding, reducing steps by 50% and raising throughput up to 1.8x while preserving exact synchrony.
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CollabVR: Collaborative Video Reasoning with Vision-Language and Video Generation Models
CollabVR improves video reasoning performance by coupling vision-language models and video generation models in a closed-loop step-level collaboration that detects and repairs generation failures.
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DUET: Optimize Token-Budget Allocation for Reinforcement Learning with Verifiable Rewards
DUET improves RLVR by allocating tokens across both prompt selection and rollout length, outperforming full-budget baselines even when using only half the tokens.
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CA-SQL: Complexity-Aware Inference Time Reasoning for Text-to-SQL via Exploration and Compute Budget Allocation
CA-SQL achieves 51.72% execution accuracy on the challenging tier of the BIRD benchmark using GPT-4o-mini by scaling exploration breadth according to estimated task difficulty, evolutionary prompt seeding, and candidate voting.
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Beyond Negative Rollouts: Positive-Only Policy Optimization with Implicit Negative Gradients
POPO uses bounded importance sampling on positive rollouts and a siamese policy network to achieve implicit negative gradients and stable optimization, matching or exceeding GRPO on math benchmarks such as 36.67% on AIME 2025.
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Joint Consistency: A Unified Test-Time Aggregation Framework via Energy Minimization
Joint Consistency casts test-time aggregation as Ising-type energy minimization with pairwise LLM-judge interactions, subsuming voting methods and outperforming baselines across reasoning tasks.