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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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
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.
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.
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.
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.
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.
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.
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.
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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citing papers explorer
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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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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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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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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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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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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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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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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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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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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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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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Beyond the Training Distribution: Mapping Generalization Boundaries in Neural Program Synthesis
In a controlled arithmetic-grammar program synthesis environment, diverse sampling across semantic and syntactic spaces yields robust density generalization while support generalization for novel syntax remains poor, with performance falling over 30 percent and compute scaling following a strictly 1
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PAC-MCTS: Bias-Aware Pruning for Robust LLM-Guided Search and Planning
PAC-MCTS supplies bias-aware confidence bounds for pruning in LLM-guided MCTS, with O((Δ-4L)^{-2}) upper and Ω((Δ-2L)^{-2}) lower sample-complexity guarantees and up to 78% fewer API calls on Blocksworld and ALFWorld.
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Sampling for Quality: Training-Free Reward-Guided LLM Decoding via Sequential Monte Carlo
Sequential Monte Carlo sampling from a reward-augmented sequence distribution improves LLM performance on HumanEval by up to 54.9% and MATH500 by up to 8.8%, outperforming standard sampling and GRPO.
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On the Overscaling Curse of Parallel Thinking: System Efficacy Contradicts Sample Efficiency
Parallel thinking in LLMs suffers from overscaling where fixed global budgets waste samples; LanBo predicts per-sample budgets from latent states to raise utilization without hurting accuracy.
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Efficient Test-Time Inference via Deterministic Exploration of Truncated Decoding Trees
Distinct Leaf Enumeration (DLE) replaces stochastic self-consistency sampling with deterministic traversal of a truncated decoding tree to enumerate distinct leaves, increasing coverage and reducing redundant computation while improving performance on math, coding, and reasoning benchmarks.
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Does RL Expand the Capability Boundary of LLM Agents? A PASS@(k,T) Analysis
RL expands the capability boundary of LLM agents on compositional tool-use tasks, shown by non-converging pass curves at large k with increasing T, while SFT regresses it and the effect is absent on simpler tasks.
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Bridging the Gap Between Latent and Explicit Reasoning with Looped Transformers
LOTUS uses a looped padded Transformer with parallel cross-entropy supervision on gold CoT tokens to match explicit CoT performance at 3B parameters while reducing thought-phase latency 2.5x-6.9x.
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Addressing Over-Refusal in LLMs with Competing Rewards
SEAR trains one LLM via adversarial process rewards to explore harmful reasoning paths but flip to safe outputs, reducing over-refusal while preserving safety.
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When More Sampling Hurts: The Modal Ceiling and Correlation Ceiling of Test-Time Scaling
Test-time sampling improves coverage but stalls at modal and correlation ceilings for answer selection, with the effective number of samples as the practical limit.
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PerturbCellRL: Verifier-Guided Reinforcement Learning for Single-Cell Perturbation Prediction
PerturbCellRL is a reinforcement learning framework that post-trains single-cell transcriptomic generators using verifier rewards for improved biological consistency in perturbation predictions.
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Finding the Time to Think: Learning Planning Budgets in Real-Time RL
Trains a gating policy to select state-dependent planning budgets in variable-delay real-time RL, outperforming fixed-budget and heuristic baselines across Pac-Man, Tetris, Snake, Speed Hex, and Speed Go.
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APPO: Agentic Procedural Policy Optimization
APPO refines branching and credit assignment in agentic RL via a Branching Score and procedure-level scaling, improving baselines by nearly 4 points on 13 benchmarks.
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Breaking the Solver Bottleneck: Training Task Generators at the Learnable Frontier
PROPEL amortizes solver evaluation with a trained activation probe to optimize task generators toward a target solve rate, raising the share of learnable tasks from ~10% to ~20% in coding and SWE experiments.
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TRACE: A Unified Rollout Budget Allocation Framework for Efficient Agentic Reinforcement Learning
TRACE is a rollout budget allocation framework that models ReAct turns as tree nodes and uses a predictor to allocate samples to informative prefixes, yielding a 2.8-point accuracy gain on Multi-Hop QA at equal cost.
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Test-Time Compute Scaling for ASR with Depth-Conditioned Looped Transformers
LARM enables test-time compute scaling in non-autoregressive ASR via depth-conditioned looping with CTC checkpoints, supervision embeddings, FiLM conditioning, and posterior feedback, yielding lower WER on LibriSpeech with more loops.
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Contribution Weights: A Geometrical Analysis of Self-Attention Transformers
Contribution Weights combine attention, value magnitude, and directional alignment to measure token influence more faithfully than attention alone, and show attention sinks actively suppress information via a convex sink-rate to output-norm relationship.
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Self-Supervised On-Policy Distillation for Reasoning Language Models
SSOPD converts intra-group correct-wrong contrast into process supervision by distilling a teacher distribution from the shortest correct completion into prefixes of the longest wrong completion, improving GRPO on AIME and HMMT benchmarks.
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Multi-Rollout On-Policy Distillation via Peer Successes and Failures
MOPD improves on-policy distillation by using peer successes and failures from multiple rollouts to construct more informative teacher signals, yielding consistent gains over baselines on reasoning benchmarks.
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fg-expo: Frontier-guided exploration-prioritized policy optimization via adaptive kl and gaussian curriculum
FG-ExPO improves GRPO by adaptively scaling the KL penalty with batch accuracy and sampling questions via a Gaussian centered at 0.5 accuracy, delivering up to 13.34 point gains on AIME 2025 pass@32.
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Test-Time Compute for Frozen Embedding Models through Agentic Program Search
Agentic program search over a frozen encoder API yields retrieval programs that improve nDCG@10 on held-out tasks and unseen encoder families with no per-domain training.
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What should post-training optimize? A test-time scaling law perspective
Tail-extrapolated estimators approximate best-of-N policy gradients from limited training rollouts by leveraging upper-tail reward statistics under structural assumptions.
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Breaking the Reward Barrier: Accelerating Tree-of-Thought Reasoning via Speculative Exploration
SPEX delivers 1.2-3x speedup on ToT algorithms via speculative path selection, dynamic budget allocation, and adaptive early termination, reaching up to 4.1x when combined with token-level speculative decoding.
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Revisiting Transformer Layer Parameterization Through Causal Energy Minimization
CEM recasts Transformer layers as energy minimization steps, enabling constrained parameterizations like weight sharing and low-rank interactions that match standard baselines in 100M-scale language modeling.
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Distributional Process Reward Models: Calibrated Prediction of Future Rewards via Conditional Optimal Transport
Conditional optimal transport is used to turn raw PRM outputs into monotonic quantile functions that improve calibration and downstream Best-of-N performance on MATH-500 and AIME.
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Power Distribution Bridges Sampling, Self-Reward RL, and Self-Distillation
The power distribution is the target of power sampling, the closed-form solution to self-reward KL-regularized RL, and the basis for power self-distillation that matches sampling performance at lower cost.
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When Less is Enough: Efficient Inference via Collaborative Reasoning
A large model generates a compact reasoning signal that a small model uses to solve tasks, reducing the large model's output tokens by up to 60% on benchmarks like AIME and GPQA.
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State Stream Transformer (SST) V2: Parallel Training of Nonlinear Recurrence for Latent Space Reasoning
SST V2 introduces parallel-trainable nonlinear recurrence in latent space to let transformers reason continuously across positions, delivering +15 points on GPQA-Diamond and halving remaining GSM8K errors over matched baselines.
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DORA: A Scalable Asynchronous Reinforcement Learning System for Language Model Training
DORA's multi-version streaming rollout enables 2-3x higher throughput in asynchronous RL for LLMs while preserving convergence by maintaining policy consistency, data integrity, and bounded staleness.
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TTVS: Boosting Self-Exploring Reinforcement Learning via Test-time Variational Synthesis
TTVS lets large reasoning models self-evolve during testing using only unlabeled queries by synthesizing semantic variations and hybrid exploration, outperforming both other test-time methods and supervised RL trained on large labeled datasets.
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ARCS: Autoregressive Circuit Synthesis with Topology-Aware Graph Attention and Spec Conditioning
ARCS generates valid SPICE-simulatable analog circuits in milliseconds via graph VAE, flow-matching, and GRPO reinforcement learning, reaching 99.9% validity with 8 evaluations across 32 topologies.
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CRISP: Compressed Reasoning via Iterative Self-Policy Distillation
CRISP achieves 57-59% token reduction on MATH-500 with 9-16 point accuracy gains on Qwen3 models via iterative self-distillation of concise reasoning behavior.
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What Does Flow Matching Bring To TD Learning?
Flow matching critics outperform monolithic ones in RL by 2x performance and 5x sample efficiency via test-time error recovery through integration and multi-point velocity supervision that preserves feature plasticity.
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Towards Generalizable Reasoning: Group Causal Counterfactual Policy Optimization for LLM Reasoning
Group Causal Counterfactual Policy Optimization trains LLMs on generalizable reasoning by defining episodic rewards for counterfactual robustness and transferability then optimizing the policy with token-level advantages.
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OGPO: Sample Efficient Full-Finetuning of Generative Control Policies
OGPO enables sample-efficient full-finetuning of generative control policies via off-policy critics and modified PPO, achieving SOTA on robot manipulation tasks while rescuing poorly initialized behavior cloning policies without expert data.
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FASTER: Value-Guided Sampling for Fast RL
FASTER models multi-candidate denoising as an MDP and trains a value function to filter actions early, delivering the performance of full sampling at lower cost in diffusion RL policies.
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One Step Forward and K Steps Back: Better Reasoning with Denoising Recursion Models
Denoising Recursion Models train multi-step noise reversal in looped transformers and outperform the prior Tiny Recursion Model on ARC-AGI.