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Applications · Time Series

Beomjun Bark, Yun Kwan Kim

Accurate detection of clinically meaningful events in healthcare time-series data is crucial for reliable downstream analysis and decision support. However, most existing methods struggle to jointly localize event boundaries and classify event types; even detection transformer (DETR)-based approaches show limited performance when confronted with extremely sparse events typical of clinical recordings. To address these challenges, we propose a coarse-to-fine detection framework combining a global context explorer, a local detail inspector, and an adaptive gating module (AGM) that fuses multiple label perspectives. The AGM uses transformed labels—encoding event presence and temporal position—to improve learning on sparse events. This design acts as a switch that selectively activates detailed feature extraction only when an event is likely, thereby reducing noise and improving efficiency in sparse settings. We evaluate our framework on diverse healthcare datasets—including arrhythmia detection, emotion recognition, and human-activity monitoring—and demonstrate substantial performance gains over existing DETR-based models, with particularly strong improvements in sparse event detection. With precise and robust event detection, our framework enables interpretation and actionable insights in real-world clinical applications.

Deep Learning · Algorithms

Rachit Bansal, Aston Zhang, Rishabh Tiwari, Lovish Madaan, Venkata Sai Surya Subramanyam Duvvuri, Devvrit Khatri, David Brandfonbrener, David Alvarez-Melis, Prajjwal Bhargava, Mihir Kale 等

Progress on training and architecture strategies has enabled LLMs with millions of tokens in context length. However, empirical evidence suggests that such long-context LLMs can consume far more text than they can reliably use. On the other hand, it has been shown that inference-time compute can be used to scale performance of LLMs, often by generating thinking tokens, on challenging tasks involving multi-step reasoning. Through controlled experiments on sandbox long-context tasks, we find that such inference-time strategies show rapidly diminishing returns and fail at long context. We attribute these failures to score dilution, a phenomenon inherent to static self-attention. Further, we show that current inference-time strategies cannot retrieve relevant long-context signals under certain conditions. We propose a simple method that, through targeted gradient updates on the given context, provably overcomes limitations of static self-attention. We find that this shift in how inference-time compute is spent leads to consistently large performance improvements across models and long-context benchmarks. Our method leads to large 12.6 and 14.1 percentage point improvements for Qwen3-4B on average across subsets of LongBench-v2 and ZeroScrolls benchmarks. The takeaway is practical: for long context, a small amount of context-specific training is a better use of inference compute than current inference-time scaling strategies like producing more thinking tokens.

Deep Learning · Generative Models and Autoencoders

Shaobin Zhuang, Zhipeng Huang, Ying Zhang, Fangyikang Wang, Canmiao Fu, Binxin Yang, Chong Sun, Chen Li, Yali Wang

GPT has shown its remarkable success in natural language processing. However, the language sequence is not sufficient to describe spatial-temporal details in the visual world. Alternatively, the video sequence is good at capturing such details. Motivated by this fact, we propose a concise Video-GPT in this paper by treating video as new language for visual world modeling. By analogy to next token prediction in GPT, we introduce a novel next clip diffusion paradigm for pretraining Video-GPT. Different from the previous works, this distinct paradigm allows Video-GPT to tackle both short-term generation and long-term prediction, by autoregressively denoising the noisy clip according to the clean clips in the history. Extensive experiments show our Video-GPT achieves the state-of-the-art performance on video prediction, which is the key factor towards world modeling (Physics-IQ Benchmark: Video-GPT 34.97 vs. Kling 23.64 vs. Wan 20.89). Moreover, it can be well adapted on 6 mainstream video tasks in both video generation and understanding, showing its great generalization capacity in downstream.

Applications · Language, Speech and Dialog

Shenzhi Yang, Guangcheng Zhu, Haobo Wang, Xing Zheng, Yingfan MA, Zhongqi Chen, Bowen Song, Weiqiang Wang, Junbo Zhao, Gang Chen

Reinforcement learning with verifiable rewards (RLVR) has proven effective in training large reasoning models (LRMs) by leveraging answer-verifiable signals to guide policy optimization, which, however, suffers from high annotation costs. To alleviate this problem, recent work has explored unsupervised RLVR methods that derive rewards solely from the model’s internal consistency, such as through entropy and majority voting. While seemingly promising, these methods often suffer from model collapse in the later stages of training, which may arise from the reinforcement of incorrect reasoning patterns in the absence of external supervision. In this work, we investigate a novel semi-supervised RLVR paradigm that utilizes a small labeled set to **guide** RLVR training on unlabeled samples. Our key insight is that supervised rewards are essential for stabilizing consistency-based training on unlabeled samples, ensuring that only reasoning patterns verified on labeled instances are incorporated into RL training. Technically, we propose an effective policy optimization algorithm TraPO that filters out reliable unlabeled samples by matching their learning trajectory similarity to labeled ones. Building on this, TraPO achieves remarkable data efficiency and strong generalization on nine advanced benchmarks. With only 1K labeled and 3K unlabeled samples, TraPO reaches 42.6% average accuracy, surpassing the best unsupervised method trained on 45K unlabeled samples (38.3%). Notably, when using 4K labeled and 12K unlabeled samples, TraPO even **outperforms the fully supervised model** trained on the full 45K labeled samples on all benchmarks, while using only **10%** of the labeled data. The code is available via https://github.com/ShenzhiYang2000/TRAPO.

Applications · Language, Speech and Dialog

Danqing Wang, Zhuorui Ye, Xinran Zhao, Fei Fang, Lei Li

Winning competitive debates requires sophisticated reasoning and argument skills. There are unique challenges in the competitive debate: (1) The time constraints force debaters to make strategic choices about which points to pursue rather than covering all possible arguments; (2) The persuasiveness of the debate relies on the back-and-forth interaction between arguments, which a single final game status cannot evaluate. To address these challenges, we propose TreeDebater, a novel debate framework that excels in competitive debate. We introduce two tree structures: the Rehearsal Tree and Debate Flow Tree. The Rehearsal Tree anticipates the attack and defenses to evaluate the strength of the claim, while the Debate Flow Tree tracks the debate status to identify the active actions. TreeDebater allocates its time budget among candidate actions and uses the speech time controller and feedback from the simulated audience to revise its statement. The human evaluation on both the stage-level and the debate-level comparison shows that our TreeDebater outperforms the state-of-the-art multi-agent debate system, with a +15.6% improvement in stage-level persuasiveness with DeepSeek and +10% debate-level opinion shift win. Further investigation shows that TreeDebater shows better strategies in limiting time to important debate actions, aligning with the strategies of human debate experts.

Social Aspects · Accountability, Transparency and Interpretability

Ruimeng Ye, Zihan Wang, Zinan Ling, Yang Xiao, Manling Li, Xiaolong Ma, Bo Hui

Humans shift between different personas depending on social context. Large Language Models (LLMs) demonstrate a similar flexibility in adopting different personas and behaviors. Existing approaches, however, typically adapt such behavior through external knowledge such as prompting, retrieval-augmented generation (RAG), or fine-tuning. We ask: do LLMs really need external context or parameters to adapt to different behaviors, or do they already have such knowledge embedded in their parameters? In this work, we show that LLMs already contain persona-specialized subnetworks in their parameter space. Using small calibration datasets, we identify distinct activation signatures associated with different personas. Guided by these statistics, we develop a masking strategy that isolates lightweight persona subnetworks. Building on the findings, we further discuss: how can we discover opposing subnetworks from the model that lead to binary-opposing personas, such as introvert-extrovert? To further enhance separation in binary opposition scenarios, we introduce a contrastive pruning strategy that identifies parameters responsible for the statistical divergence between opposing personas. Our method is entirely training-free and relies solely on the language model's existing parameter space. Across diverse evaluation settings, the resulting subnetworks exhibit significantly stronger persona alignment than baselines that require external knowledge while being more efficient. Our findings suggest that diverse human-like behaviors are not merely induced in LLMs, but are already embedded in their parameter space—pointing toward a new perspective on controllable and interpretable personalization in large language models. Our code is available at https://github.com/Ruimeng-Ye/Persona.git.

Reinforcement Learning · Deep RL

Devvrit Khatri, Lovish Madaan, Rishabh Tiwari, Rachit Bansal, Venkata Sai Surya Subramanyam Duvvuri, Manzil Zaheer, Inderjit Dhillon, David Brandfonbrener, Rishabh Agarwal

Reinforcement learning (RL) has become central to training large language models (LLMs), yet the field lacks predictive scaling methodologies comparable to those established for pre-training. Despite rapidly rising compute budgets, there is no principled understanding of how to evaluate algorithmic improvements for scaling RL compute. We present the first large-scale systematic study, amounting to more than 400,000 GPU-hours, that defines a principled framework for analyzing and predicting RL scaling in LLMs. We fit sigmoidal compute-performance curves for RL training and ablate a wide range of common design choices to analyze their effects on asymptotic performance and compute efficiency. We observe: (1) Not all recipes yield similar asymptotic performance, Details such as loss aggregation, normalization, curriculum, and off-policy algorithm primarily modulate compute efficiency without materially shifting the asymptote, and (3) Stable, scalable recipes follow predictable scaling trajectories, enabling extrapolation from smaller-scale runs. Combining these insights, we propose a _best-practice_ recipe, ScaleRL, and demonstrate its effectiveness by successfully scaling and predicting validation performance on a single RL run scaled up to 100,000 GPU-hours. Our work provides both a _scientific framework_ for analyzing scaling in RL and a practical recipe that brings RL training closer to the predictability long achieved in pre-training.

General Machine Learning · Everything Else

Ellie Cheng, Logan Weber, Tian Jin, Michael Carbin

The rise of large language models (LLMs) has introduced a new type of programming: natural language programming. Users write prompts, which are instructions in natural language, to direct LLMs to perform tasks such as natural language processing, code generation, reasoning, etc. An emerging area of research enables interoperability between prompts and programs. We present a novel programming abstraction, shared program state, that removes the manual work required to enable interoperability between prompts and program states. With shared program state, programmers can write prompts that directly access program variables, compute with program objects, and implement control flow in the program. We present a schema for specifying natural function interfaces that extend programming systems to support programs with prompts and leverage this schema to specify shared program state as a natural function interface. We implement shared program state in the Nightjar programming system. Nightjar enables programmers to write Python programs containing prompts that share the Python program state. We show that Nightjar programs achieve comparable or higher task accuracy than manually written implementations (+4-19\%), while decreasing the lines of code by 39.6\% on average. The tradeoff is that Nightjar may incur runtime overhead (0.4-4.3x manual implementations).

Deep Learning · Generative Models and Autoencoders

Mehrsa Pourya, Bassam El Rawas, Michael Unser

We introduce Flower, a solver for linear inverse problems. It leverages a pre-trained flow model to produce reconstructions that are consistent with the observed measurements. Flower operates through an iterative procedure over three steps: (i) a flow-consistent destination estimation, where the velocity network predicts a denoised target; (ii) a refinement step that projects the estimated destination onto a feasible set defined by the forward operator; and (iii) a time-progression step that re-projects the refined destination along the flow trajectory. We provide a theoretical analysis that demonstrates how Flower approximates Bayesian posterior sampling, thereby unifying perspectives from plug-and-play methods and generative inverse solvers. On the practical side, Flower achieves state-of-the-art reconstruction quality while using nearly identical hyperparameters across various linear inverse problems. Our code is available at https://github.com/mehrsapo/Flower.

General Machine Learning · Representation Learning

Geunhyeok Yu, Sunjae Jeong, Yoonyoung Choi, Jaeseung Kim, Hyoseok Hwang

Vision Transformers are widely adopted as the backbone of vision foundation models, but they are known to produce high-norm artifacts that degrade representation quality. When knowledge distillation transfers these features to students, high-norm artifacts dominate the objective, so students overfit to artifacts and underweight informative signals, diminishing the gains from larger models. Prior work attempted to remove artifacts but encountered an inherent trade-off between artifact suppression and preserving informative signals from teachers. To address this, we introduce Singular Nullspace-Guided Energy Reallocation (SiNGER), a novel distillation framework that suppresses artifacts while preserving informative signals. The key idea is principled teacher feature refinement: during refinement, we leverage the nullspace-guided perturbation to preserve information while suppressing artifacts. Then, the refined teacher's features are distilled to a student. We implement this perturbation efficiently with a LoRA-based adapter that requires minimal structural modification. Extensive experiments show that SiNGER consistently improves student models, achieving state-of-the-art performance in multiple downstream tasks and producing clearer and more interpretable representations.

Hsuan Su, Ting-Yao Hu, Hema Swetha Koppula, Kundan Krishna, Hadi Pouransari, Cheng-Yu Hsieh, Cem Koc, Joseph Cheng, Oncel Tuzel, Raviteja Vemulapalli

Large language models (LLMs) often generate hallucinations---unsupported content that undermines reliability. While most prior works frame hallucination detection as a binary task, many real-world applications require identifying hallucinated spans, which is a multi-step decision making process. This naturally raises the question of whether explicit reasoning can help the complex task of detecting hallucination spans. To answer this question, we first evaluate pretrained models with and without Chain-of-Thought (CoT) reasoning, and show that CoT reasoning has the potential to generate at least one correct answer when sampled multiple times. Motivated by this, we propose RL4HS, a reinforcement learning framework that incentivizes reasoning with a span-level reward function. RL4HS builds on Group Relative Policy Optimization and introduces Class-Aware Policy Optimization to mitigate reward imbalance issue. Experiments on the RAGTruth benchmark (summarization, question answering, data-to-text) show that RL4HS surpasses pretrained reasoning models and supervised fine-tuning, demonstrating the necessity of reinforcement learning with span-level rewards for detecting hallucination spans.

Applications · Chemistry and Drug Discovery

Manasa Kaniselvan, Benjamin Miller, Meng Gao, Juno Nam, Daniel Levine

Machine-Learned Interatomic Potentials (MLIPs) require vast amounts of atomic structure data to learn forces and energies, and their performance continues to improve with training set size. Meanwhile, the even greater quantities of accompanying data in the Hamiltonian matrix $\mathbf{H}$ behind these datasets has so far gone unused for this purpose. Here, we provide a recipe for integrating the orbital interaction data within $\mathbf{H}$ towards training pipelines for atomic-level properties. We first introduce HELM ('Hamiltonian-trained Electronic-structure Learning for Molecules'), a state-of-the-art Hamiltonian prediction model which bridges the gap between Hamiltonian prediction and universal MLIPs by scaling to $\mathbf{H}$ of structures with 100+ atoms, high elemental diversity, and large basis sets including diffuse functions. To accompany HELM, we release a curated Hamiltonian matrix dataset, 'OMol\_CSH\_58k', with unprecedented elemental diversity (58 elements), molecular size (up to 150 atoms), and basis set (def2-TZVPD). Finally, we introduce 'Hamiltonian pretraining' as a method to extract meaningful descriptors of atomic environments even from a limited number atomic structures, and repurpose this shared embedding space to improve performance on energy-prediction in low-data regimes. Our results highlight the use of electronic interactions as a rich and transferable data source for representing chemical space.

Social Aspects · Trustworthy Machine Learning

Ryota Ushio, Takashi Ishida, Masashi Sugiyama

While the performance of machine learning systems has experienced significant improvement in recent years, relatively little attention has been paid to the fundamental question: to what extent can we improve our models? This paper provides a means of answering this question in the setting of binary classification, which is practical and theoretically supported. We extend a previous work that utilizes soft labels for estimating the Bayes error, the optimal error rate, in two important ways. First, we theoretically investigate the properties of the bias of the hard-label-based estimator discussed in the original work. We reveal that the decay rate of the bias is adaptive to how well the two class-conditional distributions are separated, and it can decay significantly faster than the previous result suggested as the number of hard labels per instance grows. Second, we tackle a more challenging problem setting: estimation with _corrupted_ soft labels. One might be tempted to use calibrated soft labels instead of clean ones. However, we reveal that _calibration guarantee is not enough_, that is, even perfectly calibrated soft labels can result in a substantially inaccurate estimate. Then, we show that isotonic calibration can provide a statistically consistent estimator under an assumption weaker than that of the previous work. Our method is _instance-free_, i.e., we do not assume access to any input instances. This feature allows it to be adopted in practical scenarios where the instances are not available due to privacy issues. Experiments with synthetic and real-world datasets show the validity of our methods and theory. The code is available at https://github.com/RyotaUshio/bayes-error-estimation.

Computer Vision · Image and Video Generation

Alexander Becker, Julius Erbach, Dominik Narnhofer, Konrad Schindler

We introduce a novel formulation for continuous space-time video super-resolution. Instead of decoupling the representation of a video sequence into separate spatial and temporal components and relying on brittle, explicit frame warping for motion compensation, we encode video as a continuous, spatio-temporally coherent 3D Video Fourier Field (VFF). That representation offers three key advantages: (1) it enables cheap, flexible sampling at arbitrary locations in space and time; (2) it is able to simultaneously capture fine spatial detail and smooth temporal dynamics; and (3) it offers the possibility to include an analytical, Gaussian point spread function in the sampling to ensure aliasing-free reconstruction at arbitrary scale. The coefficients of the proposed, Fourier-like sinusoidal basis are predicted with a neural encoder with a large spatio-temporal receptive field, conditioned on the low-resolution input video. Through extensive experiments, we show that our joint modeling substantially improves both spatial and temporal super-resolution and sets a new state of the art for multiple benchmarks: across a wide range of upscaling factors, it delivers sharper and temporally more consistent reconstructions than existing baselines, while being computationally more efficient. Project page: https://v3vsr.github.io.

Social Aspects · Fairness, Equity, Justice and Safety

Yuhui Wang, Rongyi Zhu, Ting Wang

Harmful fine-tuning attacks represent a major threat to the security of large language models (LLMs), allowing adversaries to compromise safety guardrails with minimal harmful data. While existing defenses attempt to reinforce LLM alignment, they fail to address models' inherent `trainability' on harmful data, leaving them vulnerable to stronger attacks with increased learning rates or larger harmful datasets. To overcome this limitation, we introduce SEAM, a novel alignment-enhancing defense that transforms LLMs into self-destructive models with intrinsic resilience to misalignment attempts. Specifically, these models retain their capabilities for legitimate tasks while exhibiting substantial performance degradation when fine-tuned on harmful data. The protection is achieved through a novel loss function that couples the optimization trajectories of benign and harmful data, enhanced with adversarial gradient ascent to amplify the self-destructive effect. To enable practical training, we develop an efficient Hessian-free gradient estimate with theoretical error bounds. Extensive evaluation across LLMs and datasets demonstrates that SEAM creates a no-win situation for adversaries: the self-destructive models achieve state-of-the-art robustness against low-intensity attacks and undergo catastrophic performance collapse under high-intensity attacks, rendering them effectively unusable. The code is available: https://github.com/ZJUWYH/seam (warning: this paper contains potentially harmful content generated by LLMs.)

Computer Vision · Vision Models & Multimodal

Shunki Uebayashi, Kento Masui, Kyohei Atarashi, Han Bao, Hisashi Kashima, Naoto Inoue, Mayu Otani, Koh Takeuchi

Multimodal Large Language Models (MLLMs) have recently emerged as general architectures capable of reasoning over diverse modalities. Benchmarks for MLLMs should measure their ability for cross‑modal integration. However, current benchmarks are filled with shortcut questions, which can be solved using only single modality, and thereby yielding unreliable rankings. For example, in vision-language cases, we can find the correct answer without either the image or the text. These low-quality questions unnecessarily increase the size and computational requirements of benchmarks. We introduce a multi-modal and multidimensional item response theory framework (M3IRT) that extends classical IRT by decomposing both model ability and item difficulty into image‑only, text‑only, and cross‑modal components. M3IRT estimates cross‑modal ability of MLLMs and each question’s cross‑modal difficulty, enabling compact, high‑quality subsets that better reflect multimodal reasoning. Across 24 VLMs on three benchmarks, M3IRT prioritizes genuinely cross‑modal questions over shortcuts and preserves ranking fidelity even when 50\% of items are artificially generated low‑quality questions, thereby reducing evaluation cost while improving reliability. M3IRT thus offers a practical tool for assessing cross‑modal reasoning and refining multimodal benchmarks.

Applications · Chemistry and Drug Discovery

Zhanghan Ni, Yanjing Li, Zeju Qiu, Bernhard Schölkopf, Hongyu Guo, Weiyang Liu, Shengchao Liu

Generative models have recently advanced $\textit{de novo}$ protein design by learning the statistical regularities of natural structures. However, current approaches face three key limitations: (1) Existing methods cannot jointly learn protein geometry and design tasks, where pretraining can be a solution; (2) Current pretraining methods mostly rely on local, non-rigid atomic representations for property prediction downstream tasks, limiting global geometric understanding for protein generation tasks; and (3) Existing approaches have yet to effectively model the rich dynamic and conformational information of protein structures. To overcome these issues, we introduce $\textbf{RigidSSL}$ ($\textit{Rigidity-Aware Self-Supervised Learning}$), a geometric pretraining framework that front-loads geometry learning prior to generative finetuning. Phase I (RigidSSL-Perturb) learns geometric priors from 432K structures from the AlphaFold Protein Structure Database with simulated perturbations. Phase II (RigidSSL-MD) refines these representations on 1.3K molecular dynamics trajectories to capture physically realistic transitions. Underpinning both phases is a bi-directional, rigidity-aware flow matching objective that jointly optimizes translational and rotational dynamics to maximize mutual information between conformations. Empirically, RigidSSL variants improve designability by up to 43\% while enhancing novelty and diversity in unconditional generation. Furthermore, RigidSSL-Perturb improves the success rate by 5.8\% in zero-shot motif scaffolding and RigidSSL-MD captures more biophysically realistic conformational ensembles in G protein-coupled receptor modeling. The code is available at: https://github.com/ZhanghanNi/RigidSSL.git.

Applications · Everything Else

Siqi Lai, Yansong Ning, Zirui Yuan, Zhixi Chen, Hao Liu

Large language models (LLMs) have shown emerging potential in spatiotemporal reasoning, making them promising candidates for building urban agents that support diverse urban downstream applications. Despite these benefits, existing studies primarily focus on evaluating urban LLM agent on outcome-level metrics (e.g., prediction accuracy, traffic efficiency), offering limited insight into their underlying reasoning processes. As a result, the strengths and limitations of urban LLM agents in spatiotemporal reasoning remain poorly understood. To this end, we introduce USTBench, the first benchmark to evaluate LLMs’ spatiotemporal reasoning abilities as urban agents across four decomposed dimensions: spatiotemporal understanding, forecasting, planning, and reflection. Specifically, USTBench supports five diverse urban decision-making and four spatiotemporal prediction tasks, all running within our constructed interactive city environment UAgentEnv. The benchmark includes 62,466 structured QA pairs for process-based evaluation and standardized end-to-end task assessments, enabling fine-grained diagnostics and broad task-level comparison across diverse urban scenarios. Through extensive evaluation of fourteen leading LLMs, we reveal that although LLMs show promising potential across various urban downstream tasks, they still struggle in long-horizon planning and reflective adaptation in dynamic urban contexts. Notably, recent advanced reasoning models (e.g., DeepSeek-R1) trained on general logic or mathematical problems do not consistently outperform non-reasoning LLMs. This discrepancy highlights the need for domain-specialized adaptation methods to enhance urban spatiotemporal reasoning. Overall, USTBench provides a foundation to build more adaptive and effective LLM-based urban agents and broad smart city applications. Our project is available at https://github.com/usail-hkust/USTBench.

Applications · Chemistry and Drug Discovery

Gen Zhou, Sugitha Janarthanan, Lianghong Chen, Pingzhao Hu

To address the global health threat of antimicrobial resistance, antimicrobial peptides (AMP) are being explored for their potent and promising ability to fight resistant pathogens. While artificial intelligence (AI) is being employed to advance AMP discovery and design, most AMP design models struggle to balance key goals like activity, toxicity, and novelty, using rigid or unclear scoring methods that make results hard to interpret and optimize. As the capabilities of Large Language Models (LLM) advance and evolve swiftly, we turn to AI multi-agent collaboration based on such models (multi-agent LLMs), which show rapidly rising potential in complex scientific design scenarios. Based on this, we introduce $\textbf{MAC-AMP}$, a closed-loop multi-agent collaboration (MAC) system for multi-objective AMP design. The system implements a fully autonomous simulated peer review-adaptive reinforcement learning framework that requires only a task description and example dataset to design novel AMPs. The novelty of our work lies in introducing a closed-loop multi-agent system for AMP design, with cross-domain transferability, that supports multi-objective optimization while remaining explainable rather than a 'black box'. Experiments show that MAC-AMP outperforms other AMP generative models by effectively optimizing AMP generation for multiple key molecular properties, demonstrating exceptional results in antibacterial activity, AMP likeliness, toxicity compliance, and structural reliability.

Optimization · Non-Convex

Damien Scieur, David Martinez-Rubio, thomas Kerdreux, Alexandre d'Aspremont, Sebastian Pokutta

Strong convexity plays a key role in designing and analyzing convex optimization algorithms and is well-understood in Hilbert spaces. However, the notion of strongly convex sets beyond Hilbert spaces remains unclear. In this paper, we propose various definitions of strong convexity for uniquely geodesic sets in a Riemannian manifold, examine their relationships, introduce tools to identify geodesically strongly convex sets, and analyze the convergence of optimization algorithms over these sets. In particular, we show that the Riemannian Frank-Wolfe algorithm converges linearly when the Riemannian scaling inequalities hold.