论文检索

Reinforcement Learning · Everything Else

Wei Shen, Guanlin Liu, Yu Yue, Ruofei Zhu, Qingping Yang, Chao Xin, Lin Yan

Reinforcement Learning from Human Feedback (RLHF) is essential for aligning large language models (LLMs) with human preferences and values. While recent research has primarily focused on algorithmic advancements—such as reducing computational overhead or strengthening reward models to mitigate reward hacking—the critical role of prompt-data construction and its scalability has received comparatively less attention. In this paper, we address this gap by systematically exploring data-driven bottlenecks that currently hinder RLHF performance scaling, focusing specifically on the challenges posed by reward hacking and decreasing response diversity. To mitigate reward hacking, we introduce a hybrid reward system combining reasoning task verifiers (RTV) and a generative reward model (GenRM). This approach not only exhibits enhanced resistance to reward hacking, but also enables accurate assessment of responses against clearly defined ground-truth solutions. Additionally, in order to ensure response diversity and enhance learning effectiveness, we propose a novel prompt-selection method named \textbf{Pre-PPO}, explicitly identifying training prompts that are inherently challenging and thus less prone to reward hacking. Furthermore, we find that \textbf{prioritizing mathematical and coding tasks during the early phases of RLHF training} significantly boosts performance, given that these tasks naturally encode fine-grained response distinctions and possess clearly defined ground truths. Through comprehensive experiments conducted across two model sizes, we validate the effectiveness and scalability of our proposed methods. Results show that RTV exhibits the strongest resistance to reward hacking, followed by GenRM with ground truth, and finally GenRM relying on SFT Best-of-N responses. Moreover, our proposed strategies enable the model to rapidly capture subtle task-specific distinctions, leading to substantial improvements in overall RLHF performance. This work underscores the importance of careful data construction and provides practical methodologies to overcome critical performance barriers in RLHF.

Applications · Everything Else

Yinfang Chen, Jiaqi Pan, Jackson Clark, Yiming Su, Noah Zheutlin, Bhavya Bhavya, Rohan R. Arora, Yu Deng, Saurabh Jha, Tianyin Xu

In cloud-scale systems, failures are the norm. A distributed computing cluster exhibits hundreds of machine failures and thousands of disk failures; software bugs and misconfigurations are reported to be more frequent. The demand for autonomous, AI-driven reliability engineering continues to grow, as existing human-in-the-loop practices can hardly keep up with the scale of modern clouds. This paper presents STRATUS, an LLM-based multi-agent system for realizing autonomous Site Reliability Engineering (SRE) of cloud services. STRATUS consists of multiple specialized agents (e.g., for failure detection, diagnosis, mitigation), organized in a state machine to assist system-level safety reasoning and enforcement. We formalize a key safety specification of agentic SRE systems like STRATUS, termed Transactional No-Regression (TNR), which enables safe exploration and iteration. We show that TNR can effectively improve autonomous failure mitigation. STRATUS significantly outperforms state-of-the-art SRE agents in terms of success rate of failure mitigation problems in AIOpsLab and ITBench (two SRE benchmark suites), by at least 1.5 times across various models. STRATUS shows a promising path toward practical deployment of agentic systems for cloud reliability.

Deep Learning · Everything Else

Xiaoyu Kong, Junguang Jiang, Bin Liu, Ziru Xu, Han Zhu, Jian Xu, Bo Zheng, Jiancan Wu, Xiang Wang

The core task of recommender systems is to learn user preferences from historical user-item interactions. With the rapid development of large language models (LLMs), recent research has explored leveraging the reasoning capabilities of LLMs to enhance rating prediction tasks. However, existing distillation-based methods suffer from limitations such as the teacher model's insufficient recommendation capability, costly and static supervision, and superficial transfer of reasoning ability. To address these issues, this paper proposes RecZero, a reinforcement learning (RL)-based recommendation paradigm that abandons the traditional multi-model and multi-stage distillation approach. Instead, RecZero trains a single LLM through pure RL to autonomously develop reasoning capabilities for rating prediction. RecZero consists of two key components: (1) "Think-before-Recommendation" prompt construction, which employs a structured reasoning template to guide the model in step-wise analysis of user interests, item features, and user-item compatibility; and (2) rule-based reward modeling, which adopts group relative policy optimization (GRPO) to compute rewards for reasoning trajectories and optimize the LLM. Additionally, the paper explores a hybrid paradigm, RecOne, which combines supervised fine-tuning with RL, initializing the model with cold-start reasoning samples and further optimizing it with RL. Experimental results demonstrate that RecZero and RecOne significantly outperform existing baseline methods on multiple benchmark datasets, validating the superiority of the RL paradigm in achieving autonomous reasoning-enhanced recommender systems.

Applications · Everything Else

Wenlong Li, Yifei Xu, Yuan Rao, Zhenhua Wang, Shuiguang Deng

Video anomaly detection (VAD) focuses on identifying anomalies in videos. Su- pervised methods demand substantial in-domain training data and fail to deliver clear explanations for anomalies. In contrast, training-free methods leverage the knowledge reserves and language interactivity of large pre-trained models to detect anomalies. However, the current fixed-length temporal window sam- pling approaches struggle to accurately capture anomalies with varying temporal spans. Therefore, we propose VADTree that utilizes a Hierarchical Granularity- aware Tree (HGTree) structure for flexible sampling in VAD. VADTree leverages the knowledge embedded in a pre-trained Generic Event Boundary Detection (GEBD) model to characterize potential anomaly event boundaries. Specifically, VADTree decomposes the video into generic event nodes based on boundary confidence, and performs adaptive coarse-fine hierarchical structuring and re- dundancy removal to construct the HGTree. Then, the multi-dimensional priors are injected into the visual language models (VLMs) to enhance the node-wise anomaly perception, and anomaly reasoning for generic event nodes is achieved via large language models (LLMs). Finally, an inter-cluster node correlation method is used to integrate the multi-granularity anomaly scores. Extensive experiments on three challenging datasets demonstrate that VADTree achieves state-of-the-art performance in training-free settings while drastically reducing the number of sampled video segments. The code will be available at https: //github.com/wenlongli10/VADTree.

Computer Vision · Everything Else

Yujia Zhang, Xiaoyang Wu, Yixing Lao, Chengyao Wang, Zhuotao Tian, Naiyan Wang, Hengshuang Zhao

Humans learn abstract concepts through multisensory synergy, and once formed, such representations can often be recalled from a single modality. Inspired by this principle, we introduce Concerto, a minimalist simulation of human concept learning for spatial cognition, combining 3D intra-modal self-distillation with 2D-3D cross-modal joint embedding. Despite its simplicity, Concerto learns more coherent and informative spatial features, as demonstrated by zero-shot visualizations. It outperforms both standalone SOTA 2D and 3D self-supervised models by 14.2\% and 4.8\%, respectively, as well as their feature concatenation, in linear probing for 3D scene perception. With full fine-tuning, Concerto sets new SOTA results across multiple scene understanding benchmarks (e.g., 80.7\% mIoU on ScanNet). We further present a variant of Concerto tailored for video-lifted point cloud spatial understanding, and a translator that linearly projects Concerto representations into CLIP’s language space, enabling open-world perception. These results highlight that Concerto emerges spatial representations with superior fine-grained geometric and semantic consistency.

Deep Learning · Everything Else

Maximilian Forstenhäusler, Daniel Külzer, Christos Anagnostopoulos, Shameem Puthiya Parambath, Natascha Weber

Understanding user intent is essential for situational and context-aware decision-making. Motivated by a real-world scenario, this work addresses intent predictions of smart device users in the vicinity of vehicles by modeling sequential spatiotemporal data. However, in real-world scenarios, environmental factors and sensor limitations can result in non-stationary and irregularly sampled data, posing significant challenges. To address these issues, we propose STaRFormer, a Transformer-based approach that can serve as a universal framework for sequential modeling. STaRFormer utilizes a new dynamic attention-based regional masking scheme combined with a novel semi-supervised contrastive learning paradigm to enhance task-specific latent representations. Comprehensive experiments on 56 datasets varying in types (including non-stationary and irregularly sampled), tasks, domains, sequence lengths, training samples, and applications demonstrate the efficacy of STaRFormer, achieving notable improvements over state-of-the-art approaches.

Computer Vision · Everything Else

Shuang Zeng, Xinyuan Chang, Mengwei Xie, Xinran Liu, Yifan Bai, Zheng Pan, Mu Xu, Xing Wei

Vision–Language–Action (VLA) models are increasingly used for end-to-end driving due to their world knowledge and reasoning ability. Most prior work, however, inserts textual chains-of-thought (CoT) as intermediate steps tailored to the current scene. Such symbolic compressions can blur spatio-temporal relations and discard fine visual cues, creating a cross-modal gap between perception and planning. We propose FSDrive, a visual spatio-temporal CoT framework that enables VLAs to think in images. The model first acts as a world model to generate a unified future frame that overlays coarse but physically-plausible priors—future lane dividers and 3D boxes—on the predicted future image. This unified frame serves as the visual CoT, capturing both spatial structure and temporal evolution. The same VLA then functions as an inverse-dynamics model, planning trajectories from current observations and the visual CoT. To equip VLAs with image generation while preserving understanding, we introduce a unified pre-training paradigm that expands the vocabulary to include visual tokens and jointly optimizes VQA (for semantics) and future-frame prediction (for dynamics). A progressive easy-to-hard scheme first predicts lane/box priors to enforce physical constraints, then completes full future frames for fine details. On nuScenes and NAVSIM, FSDrive improves trajectory accuracy and reduces collisions under both ST-P3 and UniAD metrics, and attains competitive FID for future-frame generation despite using lightweight autoregression. It also advances scene understanding on DriveLM. Together, these results indicate that visual CoT narrows the cross-modal gap and yields safer, more anticipatory planning. Code is available at https://github.com/MIV-XJTU/FSDrive.

Computer Vision · Everything Else

Junyi Wang, Yuze Wang, Wantong Duan, Meng Wang, Yue Qi

Visual localization is a critical component across various domains. The recent emergence of novel scene representations, such as 3D Gaussian Splatting (3D GS), introduces new opportunities for advancing localization pipelines. In this paper, we propose a novel 3D GS-based framework for RGB based, scene-independent camera relocalization, with three main contributions. First, we design a two-stage pipeline with fully exploiting 3D GS. The pipeline consists of an initial stage, which utilizes 2D-3D correspondences between image pixels and 3D Gaussians, followed by pose refinement using the rendered image by 3D GS. Second, we introduce a 3D GS based Relocalization Network, termed GS-RelocNet, to establish correspondences for initial camera pose estimation. Additionally, we present a refinement network that further optimizes the camera pose. Third, we propose a unidirectional 2D-3D feature fusion module and a bidirectional image feature fusion module, integrated into GS-RelocNet and the refinement network, respectively, to enhance feature sharing across the two stages. Experimental results on public 7 Scenes, Cambridge Landmarks, TUM RGB-D and Bonn demonstrate state-of-the-art performance. Furthermore, the beneficial effects of the two feature fusion modules and pose refinement are also highlighted. In summary, we believe that the proposed framework can be a novel universal localization pipeline for further research.

Deep Learning · Everything Else

Ruihan Yang, yikai zhang, Aili Chen, Xintao Wang, Jiangjie Chen, Siyu Yuan, Deqing Yang, Yanghua Xiao

Large language models (LLMs) have enabled agents to perform complex reasoning and decision-making through free-form language interactions. However, in open-ended language action environments (e.g., negotiation or question-asking games), the action space can be formulated as a joint distribution over tokens, resulting in an extremely large and combinatorial action space. Sampling actions in such a space can lead to extreme reward sparsity, which brings large reward variance, hindering effective reinforcement learning (RL). To address this, we propose **ARIA**, a method that **A**ggregates **R**ewards in **I**ntention space to enable efficient and effective language **A**gents training. ARIA aims to project natural language actions from the high-dimensional joint token distribution space into a low-dimensional intention space, where semantically similar actions are clustered and assigned shared rewards. This intention-aware reward aggregation reduces reward variance by densifying reward signals, fostering efficient and effective policy optimization. Extensive experiments demonstrate that ARIA not only significantly reduces gradient variance, but also delivers substantial performance gains of average 9.95% across four downstream tasks (e.g., negotiation and text-based games), consistently outperforming strong offline and online RL baselines.

Deep Learning · Everything Else

Lei Wang, Jieming Bian, Letian Zhang, Jie Xu

Large Language Models (LLMs) have demonstrated impressive capabilities across various tasks, but fine-tuning them for domain-specific applications often requires substantial domain-specific data that may be distributed across multiple organizations. Federated Learning (FL) offers a privacy-preserving solution, but faces challenges with computational constraints when applied to LLMs. Low-Rank Adaptation (LoRA) has emerged as a parameter-efficient fine-tuning approach, though a single LoRA module often struggles with heterogeneous data across diverse domains. This paper addresses two critical challenges in federated LoRA fine-tuning: 1. determining the optimal number and allocation of LoRA experts across heterogeneous clients, and 2. enabling clients to selectively utilize these experts based on their specific data characteristics. We propose FedLEASE (Federated adaptive LoRA Expert Allocation and SElection), a novel framework that adaptively clusters clients based on representation similarity to allocate and train domain-specific LoRA experts. It also introduces an adaptive top-$M$ Mixture-of-Experts mechanism that allows each client to select the optimal number of utilized experts. Our extensive experiments on diverse benchmark datasets demonstrate that FedLEASE significantly outperforms existing federated fine-tuning approaches in heterogeneous client settings while maintaining communication efficiency.

Reinforcement Learning · Everything Else

Josiah Hanna, Nicholas Corrado

Recent work on large language models has demonstrated the use of model-free reinforcement learning (RL) to train reasoning-like capabilities. The emergence of "thinking" through model-free RL is interesting as thinking actions neither produce reward nor change the external world state to one where the agent is more likely to get reward. This paper seeks to build a domain-independent understanding of when model-free RL will lead to such "thinking" as a strategy for reward maximization. To build this understanding, we first introduce a theoretical model which we call a thought Markov decision process (MDP). Thought MDPs minimally extend the classical MDP model to include an abstract notion of thought state and thought action. Using the thought MDP model, we prove the importance of policy initialization in determining whether or not thinking emerges and show formally that thought actions are equivalent to the agent choosing to perform a step of policy improvement before continuing to act. We then show that open-source LLMs satisfy the conditions that our theory predicts are necessary for model-free RL to produce thinking-like behavior. Finally, we hypothesize sufficient conditions that would enable thinking to be learned outside of language generation and introduce a toy domain where a combination of multi-task pre-training and designated thought actions enable more data-efficient RL compared to non-thinking agents.

General Machine Learning · Everything Else

Guanghao Li, Wenhao Jiang, Mingfeng Chen, Yan Li, Hao Yu, Shuting Dong, Tao Ren, Ming Tang, Chun Yuan

Chain-of-Thought (CoT) prompting improves the reasoning performance of large language models (LLMs) by encouraging step-by-step thinking. However, CoT-based methods depend on intermediate reasoning steps, which limits scalability and generalization. Recent work explores recursive reasoning, where LLMs reuse internal layers across iterations to refine latent representations without explicit CoT supervision. While promising, these approaches often require costly pretraining and lack a principled framework for how reasoning should evolve across iterations. We address this gap by introducing **Flow Chain-of-Thought (Flow CoT)**, a reasoning paradigm that models recursive inference as a progressive trajectory of latent cognitive states. Flow CoT frames each iteration as a distinct cognitive stage—deepening reasoning across iterations without relying on manual supervision. To realize this, we propose **SCOUT** (*Stepwise Cognitive Optimization Using Teachers*), a lightweight fine-tuning framework that enables Flow CoT-style reasoning without the need for pretraining. SCOUT uses progressive distillation to align each iteration with a teacher of appropriate capacity, and a cross-attention-based retrospective module that integrates outputs from previous iterations while preserving the model’s original computation flow. Experiments across eight reasoning benchmarks show that SCOUT consistently improves both accuracy and explanation quality, achieving up to 1.8\% gains under fine-tuning. Qualitative analyses further reveal that SCOUT enables progressively deeper reasoning across iterations—refining both belief formation and explanation granularity. These results not only validate the effectiveness of SCOUT, but also demonstrate the practical viability of Flow CoT as a scalable framework for enhancing reasoning in LLMs.

Reinforcement Learning · Everything Else

Cheng Qian, Emre Can Acikgoz, Qi He, Hongru WANG, Xiusi Chen, Dilek Hakkani-Tur, Gokhan Tur, Heng Ji

Current Large Language Models (LLMs) often undergo supervised fine-tuning (SFT) to acquire tool use capabilities. However, SFT struggles to generalize to unfamiliar or complex tool use scenarios. Recent advancements in reinforcement learning (RL), particularly with R1-like models, have demonstrated promising reasoning and generalization abilities. Yet, reward design for tool use presents unique challenges: multiple tools may be invoked with diverse parameters, and coarse-grained reward signals, such as answer matching, fail to offer the finegrained feedback required for effective learning. In this work, we present the first comprehensive study on reward design for tool selection and application tasks within the RL paradigm. We systematically explore a wide range of reward strategies, analyzing their types, scales, granularity, and temporal dynamics. Building on these insights, we propose a principled reward design tailored for tool use tasks and apply it to train LLMs using RL methods. Empirical evaluations across diverse benchmarks demonstrate that our approach yields robust, scalable, and stable training, achieving a 17\% improvement over base models and a 15\% gain over SFT models. These results highlight the critical role of thoughtful reward design in enhancing the tool use capabilities and generalization performance of LLMs. All the codes are released to facilitate future research.

Computer Vision · Everything Else

Shaohong Wang, Lu Bin, Xinyu Xiao, Hanzhi Zhong, Bowen Pang, Tong Wang, Zhiyu Xiang, Hangguan Shan, Eryun Liu

Collaborative visual perception methods have gained widespread attention in the autonomous driving community in recent years due to their ability to address sensor limitation problems. However, the absence of explicit depth information often makes it difficult for camera-based perception systems, e.g., 3D object detection, to generate accurate predictions. To alleviate the ambiguity in depth estimation, we propose RayFusion, a ray-based fusion method for collaborative visual perception. Using ray occupancy information from collaborators, RayFusion reduces redundancy and false positive predictions along camera rays, enhancing the detection performance of purely camera-based collaborative perception systems. Comprehensive experiments show that our method consistently outperforms existing state-of-the-art models, substantially advancing the performance of collaborative visual perception. Our code will be made publicly available.

General Machine Learning · Everything Else

Antonios Valkanas, Soumyasundar Pal, Pavel Rumiantsev, Yingxue Zhang, Mark Coates

Large language models (LLMs) have achieved impressive results on complex reasoning tasks, but their high inference cost remains a major barrier to real-world deployment. A promising solution is to use cascaded inference, where small, cheap models handle easy queries, and only the hardest examples are escalated to more powerful models. However, existing cascade methods typically rely on supervised training with labeled data, offer no theoretical generalization guarantees, and provide limited control over test-time computational cost. We introduce **C3PO** (*Cost Controlled Cascaded Prediction Optimization*), a self-supervised framework for optimizing LLM cascades under probabilistic cost constraints. By focusing on minimizing regret with respect to the most powerful model (MPM), C3PO avoids the need for labeled data by constructing a cascade using only unlabeled model outputs. It leverages conformal prediction to bound the probability that inference cost exceeds a user-specified budget. We provide theoretical guarantees on both cost control and generalization error, and show that our optimization procedure is effective even with small calibration sets. Empirically, C3PO achieves state-of-the-art performance across a diverse set of reasoning benchmarks including GSM8K, MATH-500, BigBench-Hard and AIME, outperforming strong LLM cascading baselines in both accuracy and cost-efficiency. Our results demonstrate that principled, label-free cascade optimization can enable scalable LLM deployment.

Applications · Everything Else

Guoqing Hu, An Zhang, Shuchang Liu, Wenyu Mao, Jiancan Wu, Xun Yang, Xiang Li, Lantao Hu, Han Li, Kun Gai 等

Recommenders aim to rank items from a discrete item corpus in line with user interests, yet suffer from extremely sparse user preference data. Recent advances in diffusion models have inspired diffusion-based recommenders, which alleviate sparsity by injecting noise during a forward process to prevent collapse of perturbed preference distributions. However, current diffusion‑based recommenders predominantly rely on continuous Gaussian noise, which is intrinsically mismatched with the discrete nature of user preference data in recommendation. In this paper, building upon recent advances in discrete diffusion, we propose \textbf{PreferGrow}, a discrete diffusion-based recommender modeling preference ratios by fading and growing user preferences over the discrete item corpus. PreferGrow differs from existing diffusion-based recommenders in three core aspects: (1) Discrete modeling of preference ratios: PreferGrow models relative preference ratios between two items, where a positive value indicates a more preferred one over another less preferred. This formulation aligns naturally with the discrete and ranking-oriented nature of recommendation tasks. (2) Perturbing via preference fading: Instead of injecting continuous noise, PreferGrow fades user preferences by replacing the preferred item with alternatives---physically akin to negative sampling---thereby eliminating the need for any prior noise assumption. (3) Preference reconstruction via growing: PreferGrow reconstructs user preferences by iteratively growing the preference signal from the estimated ratios. We further provide theoretical analysis showing that PreferGrow preserves key properties of discrete diffusion processes. PreferGrow provides a well-defined matrix‑based formulation for discrete diffusion-based recommendation and empirically outperforms existing diffusion‑based recommenders across five benchmark datasets, underscoring its superior effectiveness. Our codes are available at \url{https://anonymous.4open.science/r/PreferGrow_Commit-2259/}.

Deep Learning · Everything Else

Peiwen Yuan, Yiwei Li, Shaoxiong Feng, Xinglin Wang, Yueqi Zhang, Jiayi Shi, Chuyi Tan, Boyuan Pan, Yao Hu, Prof. Kan

LLM-as-Benchmark-Generator methods have been widely studied as a supplement to human annotators for scalable evaluation, while the potential biases within this paradigm remain underexplored. In this work, we systematically define and validate the phenomenon of inflated performance in models evaluated on their self-generated benchmarks, referred to as self-bias, and attribute it to sub-biases arising from question domain, language style, and wrong labels. On this basis, we propose Silencer, a general framework that leverages the heterogeneity between multiple generators at both the sample and benchmark levels to neutralize bias and generate high-quality, self-bias-silenced benchmark. Experimental results across various settings demonstrate that Silencer can suppress self-bias to near zero, significantly improve evaluation effectiveness of the generated benchmark (with an average improvement from 0.655 to 0.833 in Pearson correlation with high-quality human-annotated benchmark), while also exhibiting strong generalizability.

Reinforcement Learning · Everything Else

Xin Liu, Haoran Li, Dongbin Zhao

Humans can efficiently extract knowledge and learn skills from the videos within only a few trials and errors. However, it poses a big challenge to replicate this learning process for autonomous agents, due to the complexity of visual input, the absence of action or reward signals, and the limitations of interaction steps. In this paper, we propose a novel, unsupervised, and sample-efficient framework to achieve imitation learning from videos (ILV), named Behavior Cloning from Videos via Latent Representations (BCV-LR). BCV-LR extracts action-related latent features from high-dimensional video inputs through self-supervised tasks, and then leverages a dynamics-based unsupervised objective to predict latent actions between consecutive frames. The pre-trained latent actions are fine-tuned and efficiently aligned to the real action space online (with collected interactions) for policy behavior cloning. The cloned policy in turn enriches the agent experience for further latent action finetuning, resulting in an iterative policy improvement that is highly sample-efficient. We conduct extensive experiments on a set of challenging visual tasks, including both discrete control and continuous control. BCV-LR enables effective (even expert-level on some tasks) policy performance with only a few interactions, surpassing state-of-the-art ILV baselines and reinforcement learning methods (provided with environmental rewards) in terms of sample efficiency across 24/28 tasks. To the best of our knowledge, this work for the first time demonstrates that videos can support extremely sample-efficient visual policy learning, without the need to access any other expert supervision.

Applications · Everything Else

Tomer Raz, Michael Shalyt, Elyasheev Leibtag, Rotem Kalisch, Shachar Weinbaum, Yaron Hadad, Ido Kaminer

The constant $\large \pi$ has fascinated scholars throughout the centuries, inspiring numerous formulas for its evaluation, such as infinite sums and continued fractions. Despite their individual significance, many of the underlying connections among formulas remain unknown, missing unifying theories that could unveil deeper understanding. The absence of a unifying theory reflects a broader challenge across math and science: knowledge is typically accumulated through isolated discoveries, while deeper connections often remain hidden. In this work, we present an automated framework for the unification of mathematical formulas. Our system combines large language models (LLMs) for systematic formula harvesting, an LLM-code feedback loop for validation, and a novel symbolic algorithm for clustering and eventual unification. We demonstrate this methodology on the hallmark case of $\large \pi$, an ideal testing ground for symbolic unification. Applying this approach to 455,050 arXiv papers, we validate 385 distinct formulas for $\large \pi$ and prove relations between 360 (94\%) of them, of which 166 (43\%) can be derived from a single mathematical object—linking canonical formulas by Euler, Gauss, Brouncker, and newer ones from algorithmic discoveries by the Ramanujan Machine. Our method generalizes to other constants, including $e$, $\zeta(3)$, and Catalan’s constant, demonstrating the potential of AI-assisted mathematics to uncover hidden structures and unify knowledge across domains.

Deep Learning · Everything Else

Ibrahim Alabdulmohsin, Xiaohua Zhai

Inspired by recent findings on the fractal geometry of language, we introduce Recursive INference Scaling (RINS) as a complementary, plug-in recipe for scaling inference time in language and multimodal systems. RINS is a particular form of recursive depth that significantly outperforms +55 other variants, including the recent "repeat-all-over" (RAO) strategy in Mobile LLM (Liu et al., 2024) and latent recurrent thinking (Geiping et al., 2025). Unlike prior works, we carry out our comparisons on a compute-matched regime, and demonstrate that for a fixed model size and training compute budget, RINS substantially improves language modeling performance. It also generalizes beyond pure language tasks, delivering gains in multimodal systems, including a +2% improvement in 0-shot ImageNet accuracy for SigLIP-B/16. Additionally, by deriving data scaling laws, we show that RINS improves both the asymptotic performance limits and the scaling exponents. More importantly, with light-weight (linear) adapters (comprising <1% of model parameters) and stochastic dropout, RINS offers a no-regret strategy, meaning that RINS-enabled pretraining improves performance in language modeling even when recursive depth is not applied at inference time. This corresponds to improving performance on a training compute-, parameter-, and inference-matched regime, suggesting its potential as a viable component of LLM pretraining!