论文检索

Optimization · Sampling and Optimization

Daniel Severo, Brian Karrer, Niklas Nolte

Learning distributions over permutations is a fundamental problem in machine learning, with applications in ranking, combinatorial optimization, structured prediction, and data association. Existing methods rely on mixtures of parametric families or neural networks with expensive variational inference procedures. In this work, we propose a novel approach that leverages alternative representations for permutations, including Lehmer codes, Fisher-Yates draws, and Insertion-Vectors. These representations form a bijection with the symmetric group, allowing for unconstrained learning using conventional deep learning techniques, and can represent any probability distribution over permutations. Our approach enables a trade-off between expressivity of the model family and computational requirements. In the least expressive and most computationally efficient case our method subsumes previous families of well established probabilistic models over permutations, including Mallow's and the Repeated Insertion Model. Experiments indicate our method significantly outperforms current approaches on the jigsaw puzzle benchmark, a common task for permutation learning. However, we argue this benchmark is limited in its ability to assess learning probability distributions, as the target is a delta distribution (i.e., a single correct solution exists). We therefore propose two additional benchmarks: learning cyclic permutations and re-ranking movies based on user preference. We show that our method learns non-trivial distributions even in the least expressive mode, while traditional models fail to even generate valid permutations in this setting.

Social Aspects · Trustworthy Machine Learning

Keivan Rezaei, Mehrdad Saberi, Abhilasha Ravichander, Soheil Feizi

Large language models are trained on massive corpora of web data, which may include private data, copyrighted material, factually inaccurate data, or data that degrades model performance. Eliminating the influence of such problematic datapoints on a model through complete retraining---by repeatedly pretraining the model on datasets that exclude these specific instances---is computationally prohibitive. To address this, unlearning algorithms have been proposed, that aim to eliminate the influence of particular datapoints at a low computational cost, while leaving the rest of the model intact. However, precisely unlearning the influence of data on a large language model has proven to be a major challenge. In this work, we propose a new algorithm, MSA (**M**odel **S**tate **A**rithmetic), for unlearning datapoints in large language models. MSA utilizes prior model checkpoints--- artifacts that record model states at different stages of pretraining--- to estimate and counteract the effect of targeted datapoints. Our experimental results show that MSA achieves competitive performance and often outperforms existing machine unlearning algorithms across multiple benchmarks, models, and evaluation metrics, suggesting that MSA could be an effective approach towards more flexible large language models that are capable of data erasure.

Applications · Language, Speech and Dialog

Xiaosong Yuan, Chen Shen, Shaotian Yan, kaiyuan liu, Xiaofeng Zhang, Sinan Fan, Liang Xie, Wenxiao Wang, Renchu Guan, Ying Wang 等

Reasoning abilities of large language models (LLMs) require explicit derivations compared to general question-answering, supervised fine-tuning (SFT) can empower multiple reasoning abilities in LLMs via learning from various datasets. However, neither training the datasets jointly (mix-up) nor continually can maintain the performance of single-dataset SFT, sometimes better while sometimes even worse, illustrating vanilla SFT can not only facilitate reasoning abilities but also introduce conflicts. In this paper, we propose a novel framework to mitigate the conflicts and preserve benefits among different reasoning tasks, and even surpass each task's single dataset SFT performance. We start by exploring the differences between reasoning fine-tuned and base LLMs by analyzing their parameter variations during model inference, and we discover that each reasoning capability has exclusive parameters that benefit it more evidently than others. In contrast, the overlapped parameters of tasks can bring benefits or conflicts. Inspired by the findings, we propose to update the exclusive and overlapped parameters according to specific reasoning task combinations differentially, thereby avoiding unnecessary conflicts while maintaining benefits. Consistent improvements in mix-up and continual SFT experiments demonstrate that the proposed SFT strategy can achieve better performance on various LLMs (Llama3-8B, Mistral-7B, and Qwen2.5-14B) and diverse reasoning tasks with fewer conflicts, showing the superiority and generality of our analysis findings and the proposed approach.

Thomas MItchel, Hyunwoo Ryu, Vincent Sitzmann

In this paper, we identify that the key criterion for determining whether a model is truly capable of novel view synthesis (NVS) is transferability: Whether any pose representation extracted from one video sequence can be used to re-render the same camera trajectory in another. We analyze prior work on self-supervised NVS and find that their predicted poses do not transfer: The same set of poses lead to different camera trajectories in different 3D scenes. Here, we present XFactor, the first geometry-free self-supervised model capable of true NVS. XFactor combines pair-wise pose estimation with a simple augmentation scheme of the inputs and outputs that jointly enables disentangling camera pose from scene content and facilitates geometric reasoning. Remarkably, we show that XFactor achieves transferability with unconstrained latent pose variables, without any 3D inductive biases or concepts from multi-view geometry — such as an explicit parameterization of poses as elements of SE(3). We introduce a new metric to quantify transferability, and through large-scale experiments, we demonstrate that XFactor significantly outperforms prior pose-free NVS transformers, and show that latent poses are highly correlated with real-world poses through probing experiments.

Reinforcement Learning · Deep RL

Seohong Park, Deepinder Mann, Sergey Levine

In this work, we introduce dual goal representations for goal-conditioned reinforcement learning (GCRL). A dual goal representation characterizes a state by "the set of temporal distances from all other states"; in other words, it encodes a state through its relations to every other state, measured by temporal distance. This representation provides several appealing theoretical properties. First, it depends only on the intrinsic dynamics of the environment and is invariant to the original state representation. Second, it contains provably sufficient information to recover an optimal goal-reaching policy, while being able to filter out exogenous noise. Based on this concept, we develop a practical goal representation learning method that can be combined with any existing GCRL algorithm. Through diverse experiments on the OGBench task suite, we empirically show that dual goal representations consistently improve offline goal-reaching performance across 20 state- and pixel-based tasks.

Applications · Robotics

Zhao Huang, Bowen Zhang, Zhongzhu Li, Di Lin

Trajectory planning for autonomous driving is challenging due to agents' behavioral uncertainty and intricate multi-agent interaction modeling. Most existing studies generate trajectories without explicitly exploiting possible scene evolution, while world models predict consequences from ego behavior, enabling more informed planning decisions. Inspired by the world model, we propose OccDriver, a novel rasterized-to-vectorized dual-branch framework for trajectory planning. This pipeline performs a coarse-to-fine trajectory decoding process: The vectorized branch first generate multimodal coarse trajectories; Then the rasterized branch predicts future scene evolutions conditioned on each coarse trajectory via occupancy flow prediction; Lastly, the vectorized branch leverages intuitive future interaction evolution of each modality from the rasterized branch and produces refined trajectories. Several cross-modality (occupancy and trajectory) losses are further introduced to improve the consistency between trajectory and occupancy prediction. Additionally, we apply a contingency objective in both occupancy space, considering marginal and joint occupancy distributions in different planning scopes. Our model is assessed on the large-scale real-world nuPlan dataset and its associated planning benchmark. Experiments show that OccDriver achieves state-of-the-art in both Non-Reactive and Reactive closed-loop performance.

Deep Learning · Algorithms

Divyat Mahajan, Sachin Goyal, Badr Youbi Idrissi, Mohammad Pezeshki, Ioannis Mitliagkas, David Lopez-Paz, Kartik Ahuja

Next-token prediction (NTP) has driven the success of large language models (LLMs), but it struggles with long-horizon reasoning, planning, and creative writing, with these limitations largely attributed to teacher-forced training. Multi-token prediction (MTP) partially mitigates these issues by predicting several future tokens at once, but it mostly captures short-range dependencies and offers limited improvement. We propose future summary prediction (FSP), which trains an auxiliary head to predict a compact representation of the long-term future, preserving information relevant for long-form generations. We explore two variants of FSP: handcrafted summaries, for example, a bag of words summary of the future of the sequence, and learned summaries, which use embeddings produced by a reverse language model trained from right to left. Large-scale pretraining experiments (3B and 8B-parameter models) demonstrate that FSP provides improvements over both NTP and MTP across math, reasoning, and coding benchmarks.

Computer Vision · Everything Else

Bohao Xing, Xin Liu, Guoying Zhao, Chengyu Liu, Xiaolan Fu, Heikki Kälviäinen

Emotion understanding is a critical yet challenging task. Recent advances in Multimodal Large Language Models (MLLMs) have significantly enhanced their capabilities in this area. However, MLLMs often suffer from ``hallucinations'', generating irrelevant or nonsensical content. To the best of our knowledge, and despite the importance of this issue, there has been no dedicated effort to evaluate emotion-related hallucinations in MLLMs. In this work, we introduce \textbf{EmotionHallucer}, the first benchmark for detecting and analyzing emotion hallucinations in MLLMs. Unlike humans, whose emotion understanding stems from the interplay of biology and social learning, MLLMs rely solely on data-driven learning and lack innate emotional instincts. Fortunately, emotion psychology provides a solid foundation of knowledge about human emotions. Building on this knowledge, we assess emotion hallucinations from two perspectives: emotion psychology knowledge and realworld multimodal perception. To support robust evaluation, we utilize an adversarial binary question–answer (QA) framework, which employs carefully crafted basic and hallucinated pairs to assess the emotion hallucination tendencies of MLLMs. By evaluating 41 LLMs and MLLMs on EmotionHallucer, we find that: (1) most current models exhibit substantial issues with emotion hallucinations; (2) closed-source models outperform open-source models in detecting emotion hallucinations, and reasoning capability provides additional advantages; and (3) existing models perform better in emotion psychology knowledge than in multimodal emotion perception. As a byproduct, these findings inspire us to propose the \textbf{PEP-MEK} framework, which yields an average improvement of 9.90\% in emotion hallucination detection across selected models. Resources will be available on GitHub.

Yifeng Wu, Huimin Huang, Shangjie Zhou, Yawen Huang, Hao Zheng, Yun Chen, Xian Wu, Ruize Han, Guanhua Chen

High-resolution visual representation learning remains challenging due to the quadratic complexity of Vision Transformers and the limitations of existing efficient approaches, where fixed scanning patterns in recent Mamba-based models hinder content-adaptive perception. To address these limitations, a novel Information-aware Scanning mechanism (InfoScan) tailored for state-space visual backbones is proposed, which dynamically allocates computational resources to the most salient regions of an image. Specifically, InfoScan rigorously assesses the informativeness of image patches by integrating entropy with local structural analyses, formulates a joint optimization objective balancing fine-grained detail preservation and broader contextual coherence, and learns an adaptive scanning policy via reinforcement learning. Built upon the innovative Visual Information State Space (VISS) block, InfoScan establishes a new family of models that achieve superior efficiency-accuracy trade-offs across diverse tasks. Extensive empirical evaluation in different downstream vision tasks demonstrates that our information-driven dynamic scanning paradigm offers a robust and principled alternative to fixed or global-first traversal methods. Collectively, our work positions adaptive, content-aware processing as a promising and effective new paradigm for efficient high-resolution visual representation.

Deep Learning · Algorithms

Filipe Laitenberger, Dawid Kopiczko, Cees G Snoek, Yuki Asano

We introduce GateSkip, a simple residual-stream gating mechanism that enables token-wise layer skipping in decoder-only LMs. Each Attention/MLP branch is equipped with a sigmoid-linear gate that compresses the branch’s output before it re-enters the residual stream. During inference we rank tokens by the gate and skip low-importance ones using a per-layer budget. While early-exit or router-based Mixture-of-Depths models are known to be unstable and need extensive retraining, our smooth, differentiable gates fine-tune stably on top of pretrained models. On long-form reasoning, we save up to 15% compute while retaining >90% of baseline accuracy. On instruction-tuned models we see accuracy gains at full compute and match baseline quality near 50% savings. The learned gates give insight into transformer information flow (e.g., BOS tokens act as anchors), and the method combines easily with quantization, pruning, and self-speculative decoding.

Applications · Chemistry and Drug Discovery

Yanru Qu, Yijie Zhang, Wenjuan Tan, Xiangzhe Kong, Xiangxin Zhou, Chaoran Cheng, Mathieu Blanchette, Jiaxuan You, Ge Liu

Accurate molecular representations are critical for drug discovery, and a central challenge lies in capturing the chemical environment of molecular fragments, as key interactions, such as H-bond and π stacking, which occur only under specific local conditions. Most existing approaches represent molecules as atom-level graphs; however, individual atoms cannot express stereochemistry, lone pairs, conjugation, and other complex features. Fragment-based methods (e.g., principal subgraph or functional group libraries) fail to preserve essential information such as chirality, aromatic bond integrity, and ionic states. This work addresses these limitations from two aspects. (i) OverlapBPE tokenization. We propose a novel data-driven molecule tokenization method. Unlike existing approaches, our method allows overlapping fragments, reflecting the inherently fuzzy boundaries of small-molecule substructures and, together with enriched chemical information at the token level, thereby preserving a more complete chemical context. (ii) h- MINT model. We develop a hierarchical molecular interaction network capable of jointly modeling drug–target interactions at both atom and fragment levels. By supporting fragment overlaps, the model naturally accommodates the many-to- many atom–fragment mappings introduced by the OverlapBPE scheme. Extensive evaluation against state-of-the-art methods shows our method improves binding affinity prediction by 2-4% Pearson/Spearman correlation on PDBBind and LBA, enhances virtual screening by 1-3% in key metrics on DUD-E and LIT-PCBA, and achieves the best overall HTS performance on PubChem assays. Further analysis demonstrates that our method effectively captures interactive information while maintaining good generalization.

Applications · Time Series

Hwijin Kim, Jaeho Kim, Changhee Lee

Explaining predictions of black-box time-series models remains a challenging problem due to the dynamically evolving patterns within individual sequences and their complex temporal dependencies. Unfortunately, existing explanation methods largely focus on point-wise explanations, which fail to capture broader temporal context, while methods that attempt to highlight interpretable temporal patterns (e.g., achieved by incorporating a regularizer or fixed-length patches) often lack principled definitions of meaningful segments. This limitation frequently leads to fragmented and confusing explanations for end users. As such, the notion of segment-wise explanations has remained underexplored, with little consensus on what constitutes an *interpretable* segment or how such segments should be identified. To bridge this gap, we define segment-wise explanation for black-box time-series models as the task of selecting contiguous subsequences that maximize their joint mutual information with the target prediction. Building on this formulation, we propose TimeSeg, a novel information-theoretic framework that employs reinforcement learning to sequentially identify predictive temporal segments at a per-instance level. By doing so, TimeSeg produces segment-wise explanations that capture holistic temporal patterns rather than fragmented points, providing class-predictive patterns in a human-interpretable manner. Extensive experiments on both synthetic and real‑world datasets demonstrate that TimeSeg produces more coherent and human-understandable explanations, while achieving performance that matches or surpasses existing methods on downstream tasks using the identified segments.

Computer Vision · Image and Video Generation

Ouxiang Li, Yuan Wang, Xinting Hu, Houcheng Jiang, Jack tao, Yanbin Hao, James Ma, Fuli Feng

Erasing concepts from large-scale text-to-image (T2I) diffusion models has become increasingly crucial due to the growing concerns over copyright infringement, privacy violations, and offensive content. In scalable erasure applications, fine-tuning-based methods are time-consuming to precisely erase multiple target concepts, while real-time editing-based methods often degrade the generation quality of non-target concepts due to conflicting optimization objectives. To address this dilemma, we introduce SPEED, a ***scalable, precise, and efficient*** concept erasure approach that directly edits model parameters. SPEED searches for a null space, a model editing space where parameter updates do not affect non-target concepts, to achieve scalable and precise erasure. To facilitate accurate null space optimization, we incorporate three complementary strategies: Influence-based Prior Filtering (IPF) to selectively retain the most affected non-target concepts, Directed Prior Augmentation (DPA) to enrich the filtered retain set with semantically consistent variations, and Invariant Equality Constraints (IEC) to preserve key invariants during the T2I generation process. Extensive evaluations across multiple concept erasure tasks demonstrate that SPEED consistently outperforms existing methods in non-target preservation while achieving efficient and high-fidelity concept erasure, successfully erasing 100 concepts within only 5 seconds. Our code and models are available at: https://github.com/Ouxiang-Li/SPEED.

Reinforcement Learning · Batch/Offline

Qiyang Li, Seohong Park, Sergey Levine

Bootstrapping bias problem is a long-standing challenge in temporal-difference (TD) methods in off-policy reinforcement learning (RL). Multi-step return backups can alleviate this issue but require delicate importance sampling to correct their off-policy bias. Recent work has proposed to use chunked critics, which estimate the value of short action sequences ("chunks") rather than individual actions, enabling unbiased multi-step backup. However, extracting policies from chunked critics is challenging: policies must output the entire action chunk open-loop, which can be sub-optimal in environments that require policy reactivity and also challenging to model especially when the chunk length grows. Our key insight is to decouple the chunk length of the critic from that of the policy, allowing the policy to operate over shorter action chunks. We propose a novel algorithm that achieves this by optimizing the policy against a distilled critic for partial action chunks, constructed by optimistically backing up from the original chunked critic to approximate the maximum value achievable when a partial action chunk is extended to a complete one. This design retains the benefits of multi-step value propagation while sidestepping both the open-loop sub-optimality and the difficulty of learning policies over long action chunks. We evaluate our method on challenging, long-horizon offline goal-conditioned benchmarks and show that it reliably outperforms prior methods.

General Machine Learning · Transfer, Multitask and Meta-learning

Shaocong Ma, Peiran Yu, Heng Huang

Fine-tuning Large Language Models (LLMs) typically involves either full fine-tuning, which updates all model parameters, or Parameter-Efficient Fine-Tuning (PEFT), which adjusts a small subset of parameters. However, both approaches have inherent limitations: full fine-tuning is computationally expensive, while PEFT often struggles to learn new knowledge and exhibits suboptimal performance. To overcome these issues, we propose a novel *hybrid fine-tuning* approach that jointly updates both LLMs and PEFT modules using a combination of zeroth-order and first-order optimization methods. To analyze our new algorithm, we develop a theoretical framework centered on the concept of *hybrid smoothness condition*, which accounts for the heterogeneous nature of the optimization landscape in joint LLM and PEFT training. We derive a rigorous convergence analysis for the convergence of reshuffling-type SGD algorithm under multiple learning rates and demonstrate its effectiveness through extensive empirical studies across various downstream tasks and model architectures. On the practical side, our results demonstrate consistent performance improvement, making the approach a viable solution for large-scale language model fine-tuning.

Applications · Everything Else

Xiaoyang Liu, Tao Zhu, Zineng Dong, Yuntian Liu, Guo qingfeng, Liu ZhaoXuan, Yu Chen, Tao Luo

Despite significant strides in statement autoformalization, a critical gap remains in the development of automated evaluation metrics capable of assessing formal translation quality. Existing metrics often fail to balance semantic and structural information: string-based methods neglect semantics, whereas proof-based approaches offer no graded similarity when proofs fail. To address these issues, we introduce ASSESS (A Semantic and Structural Evaluation Framework for Statement Similarity), which captures syntactic structure by transforming formal statements into operator trees and computes a real-valued similarity score using our novel TransTED (Transformation Tree Edit Distance) Similarity metric by incorporating semantic transformations. For rigorous validation, we present EPLA (Evaluating Provability and Likeness for Autoformalization), a benchmark comprising 1,247 expert-annotated formal statement pairs derived from miniF2F and ProofNet, distinctively labeled for both semantic provability and structural likeness. Experiments on the EPLA benchmark demonstrate that TransTED Similarity surpasses existing methods, achieving state-of-the-art accuracy and Kappa score. The benchmark dataset, code, and detailed experimental results are available at https://github.com/XiaoyangLiu-sjtu/ASSESS.

Chunyi Li, Jiahao Xiao, Jianbo Zhang, Farong Wen, Zicheng Zhang, Yuan Tian, Xiangyang Zhu, Xiaohong Liu, Zhengxue Cheng, Weisi Lin 等

Embodied AI has developed rapidly in recent years, but it is still mainly deployed in laboratories, with various distortions in the Real-world limiting its application. Traditionally, Image Quality Assessment (IQA) methods are applied to predict human preferences for distorted images; however, there is no IQA method to assess the usability of an image in embodied tasks, namely, the perceptual quality for robots. To provide accurate and reliable quality indicators for future embodied scenarios, we first propose the topic: IQA for Embodied AI. Specifically, we (1) based on the Mertonian system and meta-cognitive theory, constructed a perception-cognition-decision-execution pipeline and defined a comprehensive subjective score collection process; (2) established the Embodied-IQA database, containing over 30k reference/distorted image pairs, with more than 5m fine-grained annotations provided by Vision Language Models/Vision Language Action-models/Real-world robots; (3) trained and validated the performance of mainstream IQA methods on Embodied-IQA, demonstrating the need to develop more accurate quality indicators for Embodied AI. We sincerely hope that through evaluation, we can promote the application of Embodied AI under complex distortions in the Real-world.

Social Aspects · Fairness, Equity, Justice and Safety

Yi Yu, Qixin ZHANG, Shuhan YE, Xun Lin, Qianshan Wei, Kun Wang, Wenhan Yang, Dacheng Tao, Jiang Xudong

Spiking neural networks (SNNs) compute with discrete spikes and exploit temporal structure, yet most adversarial attacks change intensities or event counts instead of timing. We study a timing-only adversary that retimes existing spikes while preserving spike counts and amplitudes in event-driven SNNs, thus remaining rate-preserving. We formalize a capacity-1 spike-retiming threat model with a unified trio of budgets: per-spike jitter $B_{\infty}$, total delay $B_{1}$, and tamper count $B_{0}$. Feasible adversarial examples must satisfy timeline consistency and non-overlap, which makes the search space discrete and constrained. To optimize such retimings at scale, we use projected-in-the-loop (PIL) optimization: shift-probability logits yield a differentiable soft retiming for backpropagation, and a strict projection in the forward pass produces a feasible discrete schedule that satisfies capacity-1, non-overlap, and the chosen budget at every step. The objective maximizes task loss on the projected input and adds a capacity regularizer together with budget-aware penalties, which stabilizes gradients and aligns optimization with evaluation. Across event-driven benchmarks (CIFAR10-DVS, DVS-Gesture, N-MNIST) and diverse SNN architectures, we evaluate under binary and integer event grids and a range of retiming budgets, and also test models trained with timing-aware adversarial training designed to counter timing-only attacks. For example, on DVS-Gesture the attack attains high success (over 90\%) while touching fewer than 2\% of spikes under ${B}_{0}$. Taken together, our results show that spike retiming is a practical and stealthy attack surface that current defenses struggle to counter, providing a clear reference for temporal robustness in event-driven SNNs. Code is available at https://github.com/yuyi-sd/Spike-Retiming-Attacks.

Applications · Chemistry and Drug Discovery

Kevin Tirta Wijaya, Bing Hu, Hans-Peter Seidel, Wojciech Matusik, Vahid Babaei

Accurate regression models are essential for scientific discovery, yet high-quality numeric labels are scarce and expensive. In contrast, rankings (especially pairwise) are easier to obtain from domain experts or artificial intelligence judges. We introduce RankRefine++, a novel plug-and-play method that improves a base regressor's prediction for a query by leveraging pairwise rankings between the query and reference items with known labels. RankRefine++ performs a Bayesian update that combines a Gaussian likelihood from the regressor and the Bradley-Terry likelihood from the ranker. This yields a strictly log-concave posterior with a unique maximum likelihood solution and fast Newton updates. We show that prior state-of-the-art is a special case of our framework, and we identify a fundamental failure mode: Bradley-Terry likelihoods suffer from scale mismatch and curvature dominance when the number of reference items is large, which can degrade performance. From this analysis, we derive a calibration method to adjust the information originating from the expert rankings. RankRefine++ shows a stunning 97.65\% median improvement across 12 datasets over previous state-of-the-art method using a realistically-accurate ranker, and runs efficiently on a consumer-grade CPU.

Reinforcement Learning · Deep RL

Zhongwen Xu, Zihan Ding

We revisit policy-gradient optimization for Large Language Models (LLMs) from a single-stream perspective. Prevailing group-based methods like GRPO reduce variance with on-the-fly baselines but suffer from critical flaws: frequent degenerate groups erase learning signals, and synchronization barriers hinder scalability. We introduce Single-stream Policy Optimization (SPO), which eliminates these issues by design. SPO replaces per-group baselines with a persistent, KL-adaptive value tracker and normalizes advantages globally across the batch, providing a stable, low-variance learning signal for every sample. Being group-free, SPO enables higher throughput and scales effectively in long-horizon or tool-integrated settings where generation times vary. Furthermore, the persistent value tracker naturally enables an adaptive curriculum via prioritized sampling. Experiments using Qwen3-8B show that SPO converges more smoothly and attains higher accuracy than GRPO, while eliminating computation wasted on degenerate groups. Ablation studies confirm that SPO's gains stem from its principled approach to baseline estimation and advantage normalization, offering a more robust and efficient path for LLM reasoning. Across five hard math benchmarks with Qwen3-8B, SPO improves the average maj@32 by $+3.4\ \text{percentage points} (\mathrm{pp})$ over GRPO, driven by substantial absolute point gains on challenging datasets, including $+7.3\ \mathrm{pp}$ on BRUMO 25, $+4.4\ \mathrm{pp}$ on AIME 25, $+3.3\ \mathrm{pp}$ on HMMT 25, and achieves consistent relative gain in pass@$k$ across the evaluated $k$ values. SPO's success challenges the prevailing trend of adding incidental complexity to RL algorithms, highlighting a path where fundamental principles, not architectural workarounds, drive the next wave of progress in LLM reasoning.