论文检索

Theory · Learning Theory

Yuka Hashimoto, Sho Sonoda, Isao Ishikawa, Masahiro Ikeda

We derive a new Rademacher complexity bound for deep neural networks using Koopman operators, group representations, and reproducing kernel Hilbert spaces (RKHSs). The proposed bound describes why the models with high-rank weight matrices generalize well. Although there are existing bounds that attempt to describe this phenomenon, these existing bounds can be applied to limited types of models. We introduce an algebraic representation of neural networks and a kernel function to construct an RKHS to derive a bound for a wider range of realistic models. This work paves the way for the Koopman-based theory for Rademacher complexity bounds to be valid for more practical situations.

Social Aspects · Trustworthy Machine Learning

Dawood Wasif, Terrence Moore, Jin-Hee Cho

Federated Learning (FL) has gained prominence in machine learning applications across critical domains, offering collaborative model training without centralized data aggregation. However, FL frameworks that protect privacy often sacrifice fairness and reliability; differential privacy reduces data leakage but hides sensitive attributes needed for bias correction, worsening performance gaps across demographic groups. This work explores the trade-off between privacy and fairness in FL-based object detection and introduces RESFL, an integrated solution optimizing both. RESFL incorporates adversarial privacy disentanglement and uncertainty-guided fairness-aware aggregation. The adversarial component uses a gradient reversal layer to remove sensitive attributes, reducing privacy risks while maintaining fairness. The uncertainty-aware aggregation employs an evidential neural network to weight client updates adaptively, prioritizing contributions with lower fairness disparities and higher confidence. This ensures robust and equitable FL model updates. We demonstrate the effectiveness of RESFL in high-stakes autonomous vehicle scenarios, where it achieves high mAP on FACET and CARLA, reduces membership-inference attack success by 37%, reduces equality-of-opportunity gap by 17% relative to the FedAvg baseline, and maintains superior adversarial robustness. However, RESFL is inherently domain-agnostic and thus applicable to a broad range of application domains beyond autonomous driving.

Social Aspects · Fairness, Equity, Justice and Safety

Raghu Arghal, Kevin He, Shirin Saeedi Bidokhti, Saswati Sarkar

Algorithms increasingly serve as information mediators -- from social media feeds and targeted advertising to the increasing ubiquity of LLMs. This engenders a joint process where agents combine private, algorithmically-mediated signals with observational learning from peers to arrive at decisions. To study such settings, we introduce a model of controlled sequential social learning in which an information-mediating planner (e.g., an LLM) controls the information precision of agents while they also learn from the decisions of earlier agents. The planner may seek to improve social welfare (an altruistic planner) or to induce a specific action the planner prefers (a biased planner). Our framework presents a new optimization problem for social learning that combines dynamic programming with decentralized action choices and Bayesian belief updates. In this setting, we prove the convexity of the value function and characterize the optimal policies of altruistic and biased planners, which attain desired tradeoffs between the costs they incur and the payoffs they earn from induced agent choices. The characterization reveals that the optimal planner operates in different modes depending on the range of belief values. The modes include investing the maximum allowed resource, not investing any resource, or the investment increasing or decreasing with increase in the belief. Notably, for some ranges of belief the biased planner even intentionally obfuscates the agents' signals. Even under stringent transparency constraints—information parity with individuals, no lying or cherry‑picking, and full observability—we show that information mediation can substantially shift social welfare in either direction. We complement our theory with simulations in which LLMs act as both planner and agents. Notably, the LLM-based planner in our simulations exhibits emergent strategic behavior in steering public opinion that broadly mirrors the trends predicted, though key deviations suggest the influence of non-Bayesian reasoning—consistent with the cognitive patterns of both human users and LLMs trained on human-like data. Together, we establish our framework as a tractable basis for studying the impact and regulation of LLM information mediators that corresponds to real behavior.

Deep Learning · Graph Neural Networks

Jeongwhan Choi, Jongwoo Kim, Woosung Kang, Noseong Park

One of the most challenging problems in graph machine learning is generalizing across graphs with diverse properties. Graph neural networks (GNNs) face a fundamental limitation: they require separate training for each new graph, preventing universal generalization across diverse graph datasets. A critical challenge facing GNNs lies in their reliance on labeled training data for each individual graph, a requirement that hinders the capacity for universal node classification due to the heterogeneity inherent in graphs --- differences in homophily levels, community structures, and feature distributions across datasets. Inspired by the success of large language models (LLMs) that achieve in-context learning through massive-scale pre-training on diverse datasets, we introduce NodePFN. This universal node classification method generalizes to arbitrary graphs without graph-specific training. NodePFN learns posterior predictive distributions (PPDs) by training only on thousands of synthetic graphs generated from carefully designed priors. Our synthetic graph generation covers real-world graphs through the use of random networks with controllable homophily levels and structural causal models for complex feature-label relationships. We develop a dual-branch architecture combining context-query attention mechanisms with local message passing to enable graph-aware in-context learning. Extensive evaluation on 23 benchmarks demonstrates that a single pre-trained NodePFN achieves 71.27\% average accuracy. These results validate that universal graph learning patterns can be effectively learned from synthetic priors, establishing a new paradigm for generalization in node classification.

Applications · Everything Else

Keane Ong, Wei Dai, Carol Li, Dewei Feng, Hengzhi Li, Jingyao Wu, Jiaee Cheong, Rui Mao, Gianmarco Mengaldo, Erik Cambria 等

Using intelligent systems to perceive psychological and social behaviors, that is, the underlying affective, cognitive, and pathological states that are manifested through observable behaviors and social interactions, remains a challenge due to their complex, multifaceted, and personalized nature. Existing work tackling these dimensions through specialized datasets and single-task systems often miss opportunities for scalability, cross-task transfer, and broader generalization. To address this gap, we curate Human Behavior Atlas, a unified benchmark of diverse behavioral tasks designed to support the development of foundation models for understanding psychological and social behaviors. Human Behavior Atlas comprises over 100,000 samples spanning text, audio, and visual modalities, covering tasks on *affective states*, *cognitive states*, *pathologies*, and *social processes*. Our unification efforts can reduce redundancy and cost, enable training to scale efficiently across tasks, and enhance generalization of behavioral features across domains. On Human Behavior Atlas, we train three models: Omnisapiens-7B SFT, Omnisapiens-7B BAM, and Omnisapiens-7B RL. We show that training on Human Behavior Atlas enables models to consistently outperform existing multimodal LLMs across diverse behavioral tasks. Pretraining on Human Behavior Atlas also improves transfer to novel behavioral datasets; with the targeted use of behavioral descriptors yielding meaningful performance gains. The benchmark, models, and codes can be found at: https://github.com/MIT-MI/human_behavior_atlas.

Applications · Time Series

Dewei Feng, Wei Dai, Carol Li, Alistair Pernigo, Paul Liang

The ability of AI to sense and identify various substances based on their smell alone can have profound impacts on allergen detection (e.g. detecting peanut contamination or allergens in food), monitoring the manufacturing process, and sensing hormones that indicate emotional states, stress levels, and diseases. Despite these broad impacts, there are few standardized datasets, and therefore little progress, for training and evaluating AI systems' ability to "smell" in the real-world. In this paper, we use small gas and chemical sensors to create SmellNet, a comparatively large dataset for sensor-based machine olfaction that digitizes a diverse range of smells in the natural world. SmellNet contains about 828,000 time-series data points across 50 substances, spanning nuts, spices, herbs, fruits, and vegetables, and 43 mixtures among them with fixed ingredient volumetric ratios, with 68 hours of data collected. Using SmellNet, we developed ScentFormer, a Transformer-based architecture combining temporal differencing and sliding-window augmentation for smell data. For the SmellNet-Base classification tasks, ScentFormer achieves 63.3% Top-1 accuracy with GC-MS supervision, and for the SmellNet-Mixture distribution prediction tasks, ScentFormer achieves 50.2% Top-1@0.1 on the test-seen split. ScentFormer's ability to generalize across conditions and capture transient chemical dynamics demonstrates the promise of temporal modeling in sensor-based olfactory AI. SmellNet and ScentFormer lay the groundwork for sensor-based olfactory applications across healthcare, food and beverage, environmental monitoring, manufacturing, and entertainment.

Applications · Neuroscience, Cognitive Science

Gaspard Oliviers, Mufeng Tang, Rafal Bogacz

Predictive coding (PC) is an influential computational model of visual learning and inference in the brain. Classical PC was proposed as a top-down generative model, where the brain actively predicts upcoming visual inputs, and inference minimises the prediction errors. Recent studies have also shown that PC can be formulated as a discriminative model, where sensory inputs predict neural activities in a feedforward manner. However, experimental evidence suggests that the brain employs both generative and discriminative inference, while unidirectional PC models show degraded performance in tasks requiring bidirectional processing. In this work, we propose bidirectional PC (bPC), a PC model that incorporates both generative and discriminative inference while maintaining a biologically plausible circuit implementation. We show that bPC matches or outperforms unidirectional models in their specialised generative or discriminative tasks, by developing an energy landscape that simultaneously suits both tasks. We also demonstrate bPC's superior performance in two biologically relevant tasks including multimodal learning and inference with missing information, suggesting that bPC resembles biological visual inference more closely.

Applications · Everything Else

Yuhang He, He Liang, Yash Jain, Andrew Markham, Vibhav Vineet

We present Aurelius, a new framework that enables relation aware text-to-audio (TTA) generation research at scale. Given the lack of essential audio event and relation corpora, Aurelius contributes a large-scale audio event corpus AudioEventSet and another large-scale relation corpus AudioRelSet. Comprising 110 event categories, AudioEventSet maximally covers all commonly heard audio events and each event is unique, realistic and of high-quality. AudioRelSet consists of 100 relations, comprehensively covering the relations that present in the physical world or can be neatly described by text. As the two corpora provide audio event and relation independently, they can be combined to create massive pairs with our pair generation strategy to support relation aware TTA investigation at scale. We comprehensively benchmark all existing TTA models from both general and relation aware evaluation perspective. We further provide an in-depth investigation into scaling existing TTA models' relation aware generation by either training from scratch or leveraging cross-domain general TTA knowledge. The introduced corpora and the findings from investigation potentially facilitate future research on relation aware TTA generation.

Deep Learning · Graph Neural Networks

Vijay Prakash Dwivedi, Sri Jaladi, Yangyi Shen, Federico Lopez, Charilaos Kanatsoulis, Rishi Puri, Matthias Fey, Jure Leskovec

Relational Deep Learning (RDL) is a promising approach for building state-of-the-art predictive models on multi-table relational data by representing it as a heterogeneous temporal graph. However, commonly used Graph Neural Network models suffer from fundamental limitations in capturing complex structural patterns and long-range dependencies that are inherent in relational data. While Graph Transformers have emerged as powerful alternatives to GNNs on general graphs, applying them to relational entity graphs presents unique challenges: (i) Traditional positional encodings fail to generalize to massive, heterogeneous graphs; (ii) existing architectures cannot model the temporal dynamics and schema constraints of relational data; (iii) existing tokenization schemes lose critical structural information. Here we introduce the Relational Graph Transformer (RelGT), the first graph transformer architecture designed specifically for relational tables. RelGT employs a novel multi-element tokenization strategy that decomposes each node into five components (features, type, hop distance, time, and local structure), enabling efficient encoding of heterogeneity, temporality, and topology without expensive precomputation. Our architecture combines local attention over sampled subgraphs with global attention to learnable centroids, incorporating both local and database-wide representations. Across 21 tasks from the RelBench benchmark, RelGT consistently matches or outperforms GNN baselines by up to 18%, establishing Graph Transformers as a powerful architecture for Relational Deep Learning.

Applications · Robotics

Guopeng Li, Matthijs T. J. Spaan, Julian Kooij

When safety is formulated as a limit of cumulative cost, safe reinforcement learning (RL) aims to learn policies that maximize return subject to the cost constraint in data collection and deployment. Off-policy safe RL methods, although offering high sample efficiency, suffer from constraint violations due to cost-agnostic exploration and estimation bias in cumulative cost. To address this issue, we propose Constrained Optimistic eXploration Q-learning (COX-Q), an off-policy safe RL algorithm that integrates cost-bounded online exploration and conservative offline distributional value learning. First, we introduce a novel cost-constrained optimistic exploration strategy that resolves gradient conflicts between reward and cost in the action space and adaptively adjusts the trust region to control the training cost. Second, we adopt truncated quantile critics to stabilize the cost value learning. Quantile critics also quantify epistemic uncertainty to guide exploration. Experiments on safe velocity, safe navigation, and autonomous driving tasks demonstrate that COX-Q achieves high sample efficiency, competitive test safety performance, and controlled data collection cost. The results highlight COX-Q as a promising RL method for safety-critical applications.

Deep Learning · Graph Neural Networks

Filip Rydin, Attila Lischka, Jiaming Wu, Morteza Haghir Chehreghani, Balazs Kulcsar

Learning-based methods for routing have gained significant attention in recent years, both in single-objective and multi-objective contexts. Yet, existing methods are unsuitable for routing on multigraphs, which feature multiple edges with distinct attributes between node pairs, despite their strong relevance in real-world scenarios. In this paper, we propose two graph neural network-based methods to address multi-objective routing on multigraphs. Our first approach operates directly on the multigraph by autoregressively selecting edges until a tour is completed. The second model, which is more scalable, first simplifies the multigraph via a learned pruning strategy and then performs autoregressive routing on the resulting simple graph. We evaluate both models empirically, across a wide range of problems and graph distributions, and demonstrate their competitive performance compared to strong heuristics and neural baselines.

Deep Learning · Generative Models and Autoencoders

Gautham Anil, Shaan Ul Haque, Nithish Kannen, Dheeraj Nagaraj, Sanjay Shakkottai, Karthikeyan Shanmugam

Diffusion models are widely used for generative tasks across domains. Given a pre-trained diffusion model, it is often desirable to fine-tune it further either to correct for errors in learning or to align with downstream applications. Towards this, we examine the effect of shaping the distribution at intermediate noise levels induced by diffusion models. First, we show that existing variants of Rejection sAmpling based Fine-Tuning (RAFT), which we unify as GRAFT, can implicitly perform KL regularized reward maximization with reshaped rewards. Motivated by this observation, we introduce P-GRAFT to shape distributions at intermediate noise levels and demonstrate empirically that this can lead to more effective fine-tuning. We mathematically explain this via a bias-variance tradeoff. Next, we look at correcting learning errors in pre-trained flow models based on the developed mathematical framework. In particular, we propose inverse noise correction, a novel algorithm to improve the quality of pre-trained flow models without explicit rewards. We empirically evaluate our methods on text-to-image(T2I) generation, layout generation, molecule generation and unconditional image generation. Notably, our framework, applied to Stable Diffusion v2, improves over policy gradient methods on popular T2I benchmarks in terms of VQAScore and shows an 8.81% relative improvement over the base model. For unconditional image generation, inverse noise correction improves FID of generated images at lower FLOPs/image.

Social Aspects · Accountability, Transparency and Interpretability

Ekdeep Singh Lubana, Can Rager, Sai Sumedh R. Hindupur, Valérie Costa, Oam Patel, Sonia Murthy, Thomas Fel, Greta Tuckute, Daniel Wurgaft, Eric Bigelow 等

A central aim of interpretability tools applied to language models is to recover meaningful concepts from model activations. Existing feature extraction methods focus on single activations regardless of the context, implicitly assuming independence (and therefore stationarity). This leaves open whether they can capture the rich temporal and context-sensitive structure in the activations of language models (LMs). Adopting a Bayesian view, we demonstrate that standard Sparse Autoencoders (SAEs) impose priors that assume independence of concepts across time. We then show that LM representations exhibit rich temporal dynamics, including systematic growth in conceptual dimensionality, context-dependent correlations, and pronounced non-stationarity, in direct conflict with the priors of SAEs. This mismatch casts doubt on existing SAEs' ability to reflect temporal structures of interest in the data. We introduce a novel SAE architecture---Temporal SAE---with a temporal inductive bias that decomposes representations at a given time into two parts: a predictable component, which can be inferred from the context, and a residual component, which captures novel information that cannot be captured by the context. Experiments on LLM activations with Temporal SAE demonstrate its ability to correctly parse garden path sentences, identify event boundaries, and more broadly delineate abstract, slow-moving information from novel, fast-moving information, while existing SAEs show significant pitfalls in all the above tasks. Our results underscore the need for inductive biases that match the data in designing robust interpretability tools.

Noah Amsel, David Persson, Christopher Musco, Robert M. Gower

Computing the polar decomposition and the related matrix sign function has been a well-studied problem in numerical analysis for decades. Recently, it has emerged as an important subroutine within the Muon algorithm for training deep neural networks. However, the requirements of this application differ sharply from classical settings: deep learning demands GPU-friendly algorithms that prioritize high throughput over high precision. We introduce *Polar Express*, a new method for computing the polar decomposition. Like Newton–Schulz and other classical polynomial methods, our approach uses only matrix-matrix multiplications, making it very efficient on GPUs. Inspired by earlier work of Chen \& Chow and Nakatsukasa \& Freund, *Polar Express* adapts the update rule at each iteration by solving a minimax optimization problem. We prove that this strategy minimizes error in a worst-case sense, allowing *Polar Express* to converge as rapidly as possible both in the early iterations and asymptotically. We also address finite-precision issues, making it practical to use in `bfloat16`. When integrated into Muon, our method yields consistent improvements in validation loss for a GPT-2 model on one to ten billion tokens from the FineWeb dataset, outperforming recent alternatives across a range of learning rates.

Optimization · Everything Else

Noah Amsel, David Persson, Christopher Musco, Robert M. Gower

Computing the polar decomposition and the related matrix sign function has been a well-studied problem in numerical analysis for decades. Recently, it has emerged as an important subroutine within the Muon algorithm for training deep neural networks. However, the requirements of this application differ sharply from classical settings: deep learning demands GPU-friendly algorithms that prioritize high throughput over high precision. We introduce *Polar Express*, a new method for computing the polar decomposition. Like Newton–Schulz and other classical polynomial methods, our approach uses only matrix-matrix multiplications, making it very efficient on GPUs. Inspired by earlier work of Chen \& Chow and Nakatsukasa \& Freund, *Polar Express* adapts the update rule at each iteration by solving a minimax optimization problem. We prove that this strategy minimizes error in a worst-case sense, allowing *Polar Express* to converge as rapidly as possible both in the early iterations and asymptotically. We also address finite-precision issues, making it practical to use in `bfloat16`. When integrated into Muon, our method yields consistent improvements in validation loss for a GPT-2 model on one to ten billion tokens from the FineWeb dataset, outperforming recent alternatives across a range of learning rates.

Computer Vision · Vision Models & Multimodal

Hanrong Ye, Chao-Han Huck Yang, Arushi Goel, Wei Huang, Zhen Wan, Jinchuan Tian, An-Chieh Cheng, Ligeng Zhu, Yuanhang Su, Yuming Lou 等

Advancing machine intelligence requires developing the ability to perceive across multiple modalities, much as humans sense the world. We introduce OmniVinci, an initiative to build a strong, open-source, omni-modal LLM. We carefully study the design choices across model architecture and data curation. For model architecture, we present three key innovations: (i) OmniAlignNet for strengthening alignment between vision and audio embeddings in a shared omni-modal latent space; (ii) Temporal Embedding Grouping for capturing relative temporal alignment between vision and audio signals; and (iii) Constrained Rotary Time Embedding for encoding absolute temporal information in omni-modal embeddings. We introduce a curation and synthesis pipeline that generates 24M single-modal and omni-modal conversations. We find that modalities reinforce one another in both perception and reasoning. Our model, OmniVinci, improves over Qwen2.5-Omni with +19.05 on DailyOmni (cross-modal understanding), +1.7 on MMAR (audio), and +3.9 on Video-MME (vision), while using just 0.2T training tokens — a 6× reduction compared to Qwen2.5-Omni’s 1.2T. We finally demonstrate omni-modal advantages in downstream applications spanning robotics, medical AI, and smart factory.

Computer Vision · Vision Models & Multimodal

An-Chieh Cheng, Yang Fu, Yukang Chen, Zhijian Liu, Xiaolong Li, Subhashree Radhakrishnan, Song Han, Yao Lu, Jan Kautz, Pavlo Molchanov 等

We present Spatial Region 3D (SR-3D) aware vision-language model that connects single-view 2D images and multi-view 3D data through a shared visual token space. SR-3D supports flexible region prompting, allowing users to annotate regions with bounding boxes, segmentation masks on any frame, or directly in 3D, without the need for exhaustive multi-frame labeling. We achieve this by enriching 2D visual features with 3D positional embeddings, which allows the 3D model to draw upon strong 2D priors for more accurate spatial reasoning across frames, even when objects of interest do not co-occur within the same view. Extensive experiments on both general 2D vision language and specialized 3D spatial benchmarks demonstrate that SR-3D achieves state-of-the-art performance, underscoring its effectiveness for unifying 2D and 3D representation space on scene understanding. Moreover, we observe applicability to in-the-wild videos without sensory 3D inputs or ground-truth 3D annotations, where SR-3D accurately infers spatial relationships and metric measurements. We show more qualitative results at https://www.anjiecheng.me/sr3d.

Reinforcement Learning · Deep RL

Wei Huang, Yi Ge, Shuai Yang, Yicheng Xiao, Huizi Mao, Yujun Lin, Hanrong Ye, Sifei Liu, Ka Chun Cheung, Hongxu (Danny) Yin 等

We propose QeRL, a Quantization-enhanced Reinforcement Learning framework for large language models (LLMs). While RL is essential for LLMs' reasoning capabilities, it is resource-intensive, requiring substantial GPU memory and long rollout duration. QeRL addresses these issues by combining NVFP4 quantization with Low-Rank Adaptation (LoRA), accelerating rollout phase of RL while reducing memory overhead. Beyond efficiency, our findings show that quantization noise increases policy entropy, enhancing exploration in LoRA-based RL, and enabling the discovery of better strategies during RL. To further optimize exploration, QeRL introduces an Adaptive Quantization Noise (AQN) mechanism, which dynamically adjusts noise throughout training. Experiments demonstrate that QeRL delivers over 1.5× speedup in the rollout phase compared to QLoRA, and around 1.3× speedup compared to BF16 LoRA in 7B model. Moreover, this is the first framework to enable RL training of a 32B LLM on a single H100 80GB GPU, while delivering overall speedups for RL training. It also achieves faster reward growth and higher final accuracy than 16-bit LoRA and QLoRA, while matching the performance of full-parameter fine-tuning on mathematical benchmarks such as GSM8K (90.8%) and MATH 500 (77.4%) in the 7B model. These results establish QeRL as an efficient and effective framework for RL training in LLMs.

Deyu Zou, Yongqiang Chen, Jianxiang Wang, Garry YANG, Mufei Li, Qing Da, James Cheng, Pan Li, Yu Gong

Active reasoning requires large language model (LLM) agents to interact with external sources and strategically gather information to solve problems in multiple turns. Central to this process is belief tracking: maintaining an accurate representation of the underlying state and uncertainty in understanding and solving the problem. However, due to limited reasoning capabilities, LLM-based agents often suffer belief deviation: their internal beliefs drift from the true problem state, leading to loss of state awareness and uninformative or repetitive actions. Once this happens, errors compound in the trajectories used for reinforcement learning (RL), leading to misattributed credits and limited exploration. To address this issue, we propose to track belief deviation and develop $\mathbf{T^3}$, a simple yet principled method that detects excessive deviation and truncates training trajectories to suppress uninformative tail effects. Hence, $\mathbf{T^3}$ preserves credits for informative prefixes and systematically improves policy optimization. Across 5 challenging tasks, $\mathbf{T^3}$ consistently enhances training stability and yields performance gains of up to 30 points while cutting token cost by up to 34%. These results highlight belief control as a key principle for building robust LLM agents capable of active reasoning.

Peihao Wang, Ruisi Cai, Zhen Wang, Hongyuan Mei, Qiang Liu, Pan Li, Zhangyang Wang

Scaling inference-time compute for Large Language Models (LLMs) has unlocked unprecedented reasoning capabilities. However, existing inference-time scaling methods typically rely on inefficient and suboptimal discrete search algorithms or trial-and-error prompting to improve the online policy. In this paper, we propose $\nabla$-Reasoner, an iterative generation framework that integrates differentiable optimization over token logits into the decoding loop to refine the policy on the fly. Our core component, Differentiable Textual Optimization (DTO), leverages gradient signals from both the LLM’s likelihood and a reward model to refine textual representations. $\nabla$-Reasoner further incorporates rejection sampling and acceleration design to robustify and speed up decoding. Theoretically, we show that performing inference-time gradient descent in the sample space to maximize reward is dual to aligning an LLM policy via KL-regularized reinforcement learning. Empirically, $\nabla$-Reasoner achieves over 20% accuracy improvement on a challenging mathematical reasoning benchmark, while reducing number of model calls by approximately 10-40% compared to strong baselines. Overall, our work introduces a paradigm shift from zeroth-order search to first-order optimization at test time, offering a cost-effective path to amplify LLM reasoning.