Daily Papers

Critical Error Detection (CED) in machine translation aims to determine whether a translation is safe to use or contains unacceptable deviations in meaning. While the WMT21 English-German CED dataset provided the first benchmark, it is limited in scale, label balance, domain coverage, and temporal freshness. We present SynCED-EnDe, a new resource consisting of 1,000 gold-labeled and 8,000 silver-labeled sentence pairs, balanced 50/50 between error and non-error cases. SynCED-EnDe draws from diverse 2024-2025 sources (StackExchange, GOV.UK) and introduces explicit error subclasses, structured trigger flags, and fine-grained auxiliary judgments (obviousness, severity, localization complexity, contextual dependency, adequacy deviation). These enrichments enable systematic analyses of error risk and intricacy beyond binary detection. The dataset is permanently hosted on GitHub and Hugging Face, accompanied by documentation, annotation guidelines, and baseline scripts. Benchmark experiments with XLM-R and related encoders show substantial performance gains over WMT21 due to balanced labels and refined annotations. We envision SynCED-EnDe as a community resource to advance safe deployment of MT in information retrieval and conversational assistants, particularly in emerging contexts such as wearable AI devices.

Digitization of scanned receipts aims to extract text from receipt images and save it into structured documents. This is usually split into two sub-tasks: text localization and optical character recognition (OCR). Most existing OCR models only focus on the cropped text instance images, which require the bounding box information provided by a text region detection model. Introducing an additional detector to identify the text instance images in advance adds complexity, however instance-level OCR models have very low accuracy when processing the whole image for the document-level OCR, such as receipt images containing multiple text lines arranged in various layouts. To this end, we propose a localization-free document-level OCR model for transcribing all the characters in a receipt image into an ordered sequence end-to-end. Specifically, we finetune the pretrained instance-level model TrOCR with randomly cropped image chunks, and gradually increase the image chunk size to generalize the recognition ability from instance images to full-page images. In our experiments on the SROIE receipt OCR dataset, the model finetuned with our strategy achieved 64.4 F1-score and a 22.8% character error rate (CER), respectively, which outperforms the baseline results with 48.5 F1-score and 50.6% CER. The best model, which splits the full image into 15 equally sized chunks, gives 87.8 F1-score and 4.98% CER with minimal additional pre or post-processing of the output. Moreover, the characters in the generated document-level sequences are arranged in the reading order, which is practical for real-world applications.

Large language models encapsulate knowledge and have demonstrated superior performance on various natural language processing tasks. Recent studies have localized this knowledge to specific model parameters, such as the MLP weights in intermediate layers. This study investigates the differences between entity and relational knowledge through knowledge editing. Our findings reveal that entity and relational knowledge cannot be directly transferred or mapped to each other. This result is unexpected, as logically, modifying the entity or the relation within the same knowledge triplet should yield equivalent outcomes. To further elucidate the differences between entity and relational knowledge, we employ causal analysis to investigate how relational knowledge is stored in pre-trained models. Contrary to prior research suggesting that knowledge is stored in MLP weights, our experiments demonstrate that relational knowledge is also significantly encoded in attention modules. This insight highlights the multifaceted nature of knowledge storage in language models, underscoring the complexity of manipulating specific types of knowledge within these models.

Visual localization is the task of estimating a 6-DoF camera pose of a query image within a provided 3D reference map. Thanks to recent advances in various 3D sensors, 3D point clouds are becoming a more accurate and affordable option for building the reference map, but research to match the points of 3D point clouds with pixels in 2D images for visual localization remains challenging. Existing approaches that jointly learn 2D-3D feature matching suffer from low inliers due to representational differences between the two modalities, and the methods that bypass this problem into classification have an issue of poor refinement. In this work, we propose EP2P-Loc, a novel large-scale visual localization method that mitigates such appearance discrepancy and enables end-to-end training for pose estimation. To increase the number of inliers, we propose a simple algorithm to remove invisible 3D points in the image, and find all 2D-3D correspondences without keypoint detection. To reduce memory usage and search complexity, we take a coarse-to-fine approach where we extract patch-level features from 2D images, then perform 2D patch classification on each 3D point, and obtain the exact corresponding 2D pixel coordinates through positional encoding. Finally, for the first time in this task, we employ a differentiable PnP for end-to-end training. In the experiments on newly curated large-scale indoor and outdoor benchmarks based on 2D-3D-S and KITTI, we show that our method achieves the state-of-the-art performance compared to existing visual localization and image-to-point cloud registration methods.

We present a new framework for Patch Distribution Modeling, PaDiM, to concurrently detect and localize anomalies in images in a one-class learning setting. PaDiM makes use of a pretrained convolutional neural network (CNN) for patch embedding, and of multivariate Gaussian distributions to get a probabilistic representation of the normal class. It also exploits correlations between the different semantic levels of CNN to better localize anomalies. PaDiM outperforms current state-of-the-art approaches for both anomaly detection and localization on the MVTec AD and STC datasets. To match real-world visual industrial inspection, we extend the evaluation protocol to assess performance of anomaly localization algorithms on non-aligned dataset. The state-of-the-art performance and low complexity of PaDiM make it a good candidate for many industrial applications.

Existing Text Image Forgery Localization (T-IFL) methods often suffer from poor generalization due to the limited scale of real-world datasets and the distribution gap caused by synthetic data that fails to capture the complexity of real-world tampering. To tackle this issue, we propose Fourier Series-based Tampering Synthesis (FSTS), a structured and interpretable framework for synthesizing tampered text images. FSTS first collects 16,750 real-world tampering instances from five representative tampering types, using a structured pipeline that records human-performed editing traces via multi-format logs (e.g., video, PSD, and editing logs). By analyzing these collected parameters and identifying recurring behavioral patterns at both individual and population levels, we formulate a hierarchical modeling framework. Specifically, each individual tampering parameter is represented as a compact combination of basis operation-parameter configurations, while the population-level distribution is constructed by aggregating these behaviors. Since this formulation draws inspiration from the Fourier series, it enables an interpretable approximation using basis functions and their learned weights. By sampling from this modeled distribution, FSTS synthesizes diverse and realistic training data that better reflect real-world forgery traces. Extensive experiments across four evaluation protocols demonstrate that models trained with FSTS data achieve significantly improved generalization on real-world datasets. Dataset is available at https://github.com/ZeqinYu/FSTS{Project Page}.

Precision livestock farming (PLF) increasingly relies on advanced object localization techniques to monitor livestock health and optimize resource management. This study investigates the generalization capabilities of YOLOv8 and YOLOv9 models for cow detection in indoor free-stall barn settings, focusing on varying training data characteristics such as view angles and lighting, and model complexities. Leveraging the newly released public dataset, COws LOcalization (COLO) dataset, we explore three key hypotheses: (1) Model generalization is equally influenced by changes in lighting conditions and camera angles; (2) Higher model complexity guarantees better generalization performance; (3) Fine-tuning with custom initial weights trained on relevant tasks always brings advantages to detection tasks. Our findings reveal considerable challenges in detecting cows in images taken from side views and underscore the importance of including diverse camera angles in building a detection model. Furthermore, our results emphasize that higher model complexity does not necessarily lead to better performance. The optimal model configuration heavily depends on the specific task and dataset. Lastly, while fine-tuning with custom initial weights trained on relevant tasks offers advantages to detection tasks, simpler models do not benefit similarly from this approach. It is more efficient to train a simple model with pre-trained weights without relying on prior relevant information, which can require intensive labor efforts. Future work should focus on adaptive methods and advanced data augmentation to improve generalization and robustness. This study provides practical guidelines for PLF researchers on deploying computer vision models from existing studies, highlights generalization issues, and contributes the COLO dataset containing 1254 images and 11818 cow instances for further research.

The increasing adoption of agentic workflows across diverse domains brings a critical need to scalably and systematically evaluate the complex traces these systems generate. Current evaluation methods depend on manual, domain-specific human analysis of lengthy workflow traces - an approach that does not scale with the growing complexity and volume of agentic outputs. Error analysis in these settings is further complicated by the interplay of external tool outputs and language model reasoning, making it more challenging than traditional software debugging. In this work, we (1) articulate the need for robust and dynamic evaluation methods for agentic workflow traces, (2) introduce a formal taxonomy of error types encountered in agentic systems, and (3) present a set of 148 large human-annotated traces (TRAIL) constructed using this taxonomy and grounded in established agentic benchmarks. To ensure ecological validity, we curate traces from both single and multi-agent systems, focusing on real-world applications such as software engineering and open-world information retrieval. Our evaluations reveal that modern long context LLMs perform poorly at trace debugging, with the best Gemini-2.5-pro model scoring a mere 11% on TRAIL. Our dataset and code are made publicly available to support and accelerate future research in scalable evaluation for agentic workflows.

Driven by Artificial Intelligence-Generated Content (AIGC), the authenticity of audio-visual content is facing severe challenges. Temporal Forgery Localization (TFL) aims to precisely identify manipulated segments within untrimmed sequences. However, existing methods are limited by CNNs' local receptive fields or Transformers' quadratic complexity, while emerging linear models often struggle to balance global authentic context compression with local abrupt forgery perception. To address this, we propose MG-RWKV, a multi-granularity framework that leverages the data-dependent state evolution of RWKV to achieve efficient full-sequence processing with O(T) complexity. Our framework features three core innovations: (1) a Bidirectional RWKV architecture that captures bidirectional temporal contexts without quadratic overhead; (2) a Multi-Granularity Mixture of Experts (MG-MoE) that performs dynamic routing over explicit temporal receptive fields, adaptively selecting granularities based on forgery duration to significantly enhance decision interpretability; and (3) Cross-Granularity Consistency (CGC), which aligns adjacent feature pyramid levels through hierarchical scale-wise pairing and spatial boundary-aware weighting, effectively reducing false positives in authentic regions. Extensive experiments on Lav-DF, TVIL, and Psynd datasets demonstrate that MG-RWKV achieves state-of-the-art performance with low computational cost.

Real-world medical image segmentation has tremendous long-tailed complexity of objects, among which tail conditions correlate with relatively rare diseases and are clinically significant. A trustworthy medical AI algorithm should demonstrate its effectiveness on tail conditions to avoid clinically dangerous damage in these out-of-distribution (OOD) cases. In this paper, we adopt the concept of object queries in Mask Transformers to formulate semantic segmentation as a soft cluster assignment. The queries fit the feature-level cluster centers of inliers during training. Therefore, when performing inference on a medical image in real-world scenarios, the similarity between pixels and the queries detects and localizes OOD regions. We term this OOD localization as MaxQuery. Furthermore, the foregrounds of real-world medical images, whether OOD objects or inliers, are lesions. The difference between them is less than that between the foreground and background, possibly misleading the object queries to focus redundantly on the background. Thus, we propose a query-distribution (QD) loss to enforce clear boundaries between segmentation targets and other regions at the query level, improving the inlier segmentation and OOD indication. Our proposed framework is tested on two real-world segmentation tasks, i.e., segmentation of pancreatic and liver tumors, outperforming previous state-of-the-art algorithms by an average of 7.39% on AUROC, 14.69% on AUPR, and 13.79% on FPR95 for OOD localization. On the other hand, our framework improves the performance of inlier segmentation by an average of 5.27% DSC when compared with the leading baseline nnUNet.

Cross-view geo-localization for Unmanned Aerial Vehicles (UAVs) operating in GNSS-denied environments remains challenging due to the severe geometric discrepancy between oblique UAV imagery and orthogonal satellite maps. Most existing methods address this problem through a decoupled pipeline of place retrieval and pose estimation, implicitly treating perspective distortion as appearance noise rather than an explicit geometric transformation. In this work, we propose a geometry-aware UAV geo-localization framework that explicitly models the 3D scene geometry to unify coarse place recognition and fine-grained pose estimation within a single inference pipeline. Our approach reconstructs a local 3D scene from multi-view UAV image sequences using a Visual Geometry Grounded Transformer (VGGT), and renders a virtual Bird's-Eye View (BEV) representation that orthorectifies the UAV perspective to align with satellite imagery. This BEV serves as a geometric intermediary that enables robust cross-view retrieval and provides spatial priors for accurate 3 Degrees of Freedom (3-DoF) pose regression. To efficiently handle multiple location hypotheses, we introduce a Satellite-wise Attention Block that isolates the interaction between each satellite candidate and the reconstructed UAV scene, preventing inter-candidate interference while maintaining linear computational complexity. In addition, we release a recalibrated version of the University-1652 dataset with precise coordinate annotations and spatial overlap analysis, enabling rigorous evaluation of end-to-end localization accuracy. Extensive experiments on the refined University-1652 benchmark and SUES-200 demonstrate that our method significantly outperforms state-of-the-art baselines, achieving robust meter-level localization accuracy and improved generalization in complex urban environments.

We tackle the problem of localizing 3D point cloud submaps using complex and diverse natural language descriptions, and present Text2Loc++, a novel neural network designed for effective cross-modal alignment between language and point clouds in a coarse-to-fine localization pipeline. To support benchmarking, we introduce a new city-scale dataset covering both color and non-color point clouds from diverse urban scenes, and organize location descriptions into three levels of linguistic complexity. In the global place recognition stage, Text2Loc++ combines a pretrained language model with a Hierarchical Transformer with Max pooling (HTM) for sentence-level semantics, and employs an attention-based point cloud encoder for spatial understanding. We further propose Masked Instance Training (MIT) to filter out non-aligned objects and improve multimodal robustness. To enhance the embedding space, we introduce Modality-aware Hierarchical Contrastive Learning (MHCL), incorporating cross-modal, submap-, text-, and instance-level losses. In the fine localization stage, we completely remove explicit text-instance matching and design a lightweight yet powerful framework based on Prototype-based Map Cloning (PMC) and a Cascaded Cross-Attention Transformer (CCAT). Extensive experiments on the KITTI360Pose dataset show that Text2Loc++ outperforms existing methods by up to 15%. In addition, the proposed model exhibits robust generalization when evaluated on the new dataset, effectively handling complex linguistic expressions and a wide variety of urban environments. The code and dataset will be made publicly available.

Existing deep learning-based cross-view geo-localization methods primarily focus on improving the accuracy of cross-domain image matching, rather than enabling models to comprehensively capture contextual information around the target and minimize the cost of localization errors. To support systematic research into this Distance-Aware Cross-View Geo-Localization (DACVGL) problem, we construct Distance-Aware Campus (DA-Campus), the first benchmark that pairs multi-view imagery with precise distance annotations across three spatial resolutions. Based on DA-Campus, we formulate DACVGL as a hierarchical retrieval problem across different domains. Our study further reveals that, due to the inherent complexity of spatial relationships among buildings, this problem can only be addressed via a contrastive learning paradigm, rather than conventional metric learning. To tackle this challenge, we propose Dynamic Contrastive Learning (DyCL), a novel framework that progressively aligns feature representations according to hierarchical spatial margins. Extensive experiments demonstrate that DyCL is highly complementary to existing multi-scale metric learning methods and yields substantial improvements in both hierarchical retrieval performance and overall cross-view geo-localization accuracy. Our code and benchmark are publicly available at https://github.com/anocodetest1/DyCL.

In Ultrasound Localization Microscopy (ULM),achieving high-resolution images relies on the precise localization of contrast agent particles across consecutive beam-formed frames. However, our study uncovers an enormous potential: The process of delay-and-sum beamforming leads to an irreversible reduction of Radio-Frequency (RF) data, while its implications for localization remain largely unexplored. The rich contextual information embedded within RF wavefronts, including their hyperbolic shape and phase, offers great promise for guiding Deep Neural Networks (DNNs) in challenging localization scenarios. To fully exploit this data, we propose to directly localize scatterers in RF signals. Our approach involves a custom super-resolution DNN using learned feature channel shuffling and a novel semi-global convolutional sampling block tailored for reliable and accurate wavefront localization. Additionally, we introduce a geometric point transformation that facilitates seamless mapping between RF and B-mode coordinate space. To understand the impact of beamforming on ULM, we validate the effectiveness of our method by conducting an extensive comparison with State-Of-The-Art (SOTA) techniques. We present the inaugural in vivo results from an RF-trained DNN, highlighting its real-world practicality. Our findings show that RF-ULM bridges the domain gap between synthetic and real datasets, offering a considerable advantage in terms of precision and complexity. To enable the broader research community to benefit from our findings, our code and the associated SOTA methods are made available at https://github.com/hahnec/rf-ulm.

Traditional methods for human localization and pose estimation (HPE), which mainly rely on RGB images as an input modality, confront substantial limitations in real-world applications due to privacy concerns. In contrast, radar-based HPE methods emerge as a promising alternative, characterized by distinctive attributes such as through-wall recognition and privacy-preserving, rendering the method more conducive to practical deployments. This paper presents a Radar Tensor-based human pose (RT-Pose) dataset and an open-source benchmarking framework. The RT-Pose dataset comprises 4D radar tensors, LiDAR point clouds, and RGB images, and is collected for a total of 72k frames across 240 sequences with six different complexity-level actions. The 4D radar tensor provides raw spatio-temporal information, differentiating it from other radar point cloud-based datasets. We develop an annotation process using RGB images and LiDAR point clouds to accurately label 3D human skeletons. In addition, we propose HRRadarPose, the first single-stage architecture that extracts the high-resolution representation of 4D radar tensors in 3D space to aid human keypoint estimation. HRRadarPose outperforms previous radar-based HPE work on the RT-Pose benchmark. The overall HRRadarPose performance on the RT-Pose dataset, as reflected in a mean per joint position error (MPJPE) of 9.91cm, indicates the persistent challenges in achieving accurate HPE in complex real-world scenarios. RT-Pose is available at https://huggingface.co/datasets/uwipl/RT-Pose.

We present PiLoT, a unified framework that tackles UAV-based ego and target geo-localization. Conventional approaches rely on decoupled pipelines that fuse GNSS and Visual-Inertial Odometry (VIO) for ego-pose estimation, and active sensors like laser rangefinders for target localization. However, these methods are susceptible to failure in GNSS-denied environments and incur substantial hardware costs and complexity. PiLoT breaks this paradigm by directly registering live video stream against a geo-referenced 3D map. To achieve robust, accurate, and real-time performance, we introduce three key contributions: 1) a Dual-Thread Engine that decouples map rendering from core localization thread, ensuring both low latency while maintaining drift-free accuracy; 2) a large-scale synthetic dataset with precise geometric annotations (camera pose, depth maps). This dataset enables the training of a lightweight network that generalizes in a zero-shot manner from simulation to real data; and 3) a Joint Neural-Guided Stochastic-Gradient Optimizer (JNGO) that achieves robust convergence even under aggressive motion. Evaluations on a comprehensive set of public and newly collected benchmarks show that PiLoT outperforms state-of-the-art methods while running over 25 FPS on NVIDIA Jetson Orin platform. Our code and dataset is available at: https://github.com/Choyaa/PiLoT.

Unsupervised anomaly detection in brain images is crucial for identifying injuries and pathologies without access to labels. However, the accurate localization of anomalies in medical images remains challenging due to the inherent complexity and variability of brain structures and the scarcity of annotated abnormal data. To address this challenge, we propose a novel approach that incorporates masking within diffusion models, leveraging their generative capabilities to learn robust representations of normal brain anatomy. During training, our model processes only normal brain MRI scans and performs a forward diffusion process in the latent space that adds noise to the features of randomly-selected patches. Following a dual objective, the model learns to identify which patches are noisy and recover their original features. This strategy ensures that the model captures intricate patterns of normal brain structures while isolating potential anomalies as noise in the latent space. At inference, the model identifies noisy patches corresponding to anomalies and generates a normal counterpart for these patches by applying a reverse diffusion process. Our method surpasses existing unsupervised anomaly detection techniques, demonstrating superior performance in generating accurate normal counterparts and localizing anomalies. The code is available at hhttps://github.com/farzad-bz/MAD-AD.

The adoption of fisheye cameras in robotic manipulation, driven by their exceptionally wide Field of View (FoV), is rapidly outpacing a systematic understanding of their downstream effects on policy learning. This paper presents the first comprehensive empirical study to bridge this gap, rigorously analyzing the properties of wrist-mounted fisheye cameras for imitation learning. Through extensive experiments in both simulation and the real world, we investigate three critical research questions: spatial localization, scene generalization, and hardware generalization. Our investigation reveals that: (1) The wide FoV significantly enhances spatial localization, but this benefit is critically contingent on the visual complexity of the environment. (2) Fisheye-trained policies, while prone to overfitting in simple scenes, unlock superior scene generalization when trained with sufficient environmental diversity. (3) While naive cross-camera transfer leads to failures, we identify the root cause as scale overfitting and demonstrate that hardware generalization performance can be improved with a simple Random Scale Augmentation (RSA) strategy. Collectively, our findings provide concrete, actionable guidance for the large-scale collection and effective use of fisheye datasets in robotic learning. More results and videos are available on https://robo-fisheye.github.io/

The fusion of language and vision in large vision-language models (LVLMs) has revolutionized deep learning-based object detection by enhancing adaptability, contextual reasoning, and generalization beyond traditional architectures. This in-depth review presents a structured exploration of the state-of-the-art in LVLMs, systematically organized through a three-step research review process. First, we discuss the functioning of vision language models (VLMs) for object detection, describing how these models harness natural language processing (NLP) and computer vision (CV) techniques to revolutionize object detection and localization. We then explain the architectural innovations, training paradigms, and output flexibility of recent LVLMs for object detection, highlighting how they achieve advanced contextual understanding for object detection. The review thoroughly examines the approaches used in integration of visual and textual information, demonstrating the progress made in object detection using VLMs that facilitate more sophisticated object detection and localization strategies. This review presents comprehensive visualizations demonstrating LVLMs' effectiveness in diverse scenarios including localization and segmentation, and then compares their real-time performance, adaptability, and complexity to traditional deep learning systems. Based on the review, its is expected that LVLMs will soon meet or surpass the performance of conventional methods in object detection. The review also identifies a few major limitations of the current LVLM modes, proposes solutions to address those challenges, and presents a clear roadmap for the future advancement in this field. We conclude, based on this study, that the recent advancement in LVLMs have made and will continue to make a transformative impact on object detection and robotic applications in the future.

Anomaly detection in industrial visual inspection is challenging due to the scarcity of defective samples. Most existing methods rely on unsupervised reconstruction using only normal data, often resulting in overfitting and poor detection of subtle defects. We propose a semi-supervised deep reinforcement learning framework that integrates a neural batch sampler, an autoencoder, and a predictor. The RL-based sampler adaptively selects informative patches by balancing exploration and exploitation through a composite reward. The autoencoder generates loss profiles highlighting abnormal regions, while the predictor performs segmentation in the loss-profile space. This interaction enables the system to effectively learn both normal and defective patterns with limited labeled data. Experiments on the MVTec AD dataset demonstrate that our method achieves higher accuracy and better localization of subtle anomalies than recent state-of-the-art approaches while maintaining low complexity, yielding an average improvement of 0.15 in F1_max and 0.06 in AUC, with a maximum gain of 0.37 in F1_max in the best case.

Vision-Language Models (VLMs) have achieved remarkable progress on a wide range of challenging multimodal understanding and reasoning tasks. However, existing reasoning paradigms, such as the classical Chain-of-Thought (CoT), rely solely on textual information and often underutilize important visual cues. While prior work has incorporated pixel-level visual cues, these representations require precise spatial localization, introducing additional learning complexity. To address this, we propose PatchCue, a novel patch-based visual cue paradigm designed to significantly enhance the visual reasoning capabilities of VLMs. By partitioning images into patches and representing cues at the patch level, PatchCue aligns better with human perceptual habits and leverages the patch-tokenized input of modern VLMs. We train VLMs using a two-stage approach: cold-start supervised fine-tuning to output patch-level cues, followed by reinforcement learning with a process-supervised cue reward that guides intermediate visual reasoning steps. Extensive experiments on multiple VLMs and diverse benchmarks, including general visual question answering, complex reasoning, and document understanding, demonstrate that PatchCue consistently improves overall model performance. Our results show that patch-level cues outperform both pixel-level bounding boxes and point-based cues, providing a more effective and cognitively aligned visual reasoning paradigm.

Time Series Language Models (TSLMs) are emerging as unified models for reasoning over continuous signals in natural language. However, long-context retrieval remains a major limitation: existing models are typically trained and evaluated on short sequences, while real-world time-series sensor streams can span millions of datapoints. This mismatch requires precise temporal localization under strict computational constraints, a regime that is not captured by current benchmarks. We introduce TS-Haystack, a long-context temporal retrieval benchmark comprising ten task types across four categories: direct retrieval, temporal reasoning, multi-step reasoning and contextual anomaly. The benchmark uses controlled needle insertion by embedding short activity bouts into longer longitudinal accelerometer recordings, enabling systematic evaluation across context lengths ranging from seconds to 2 hours per sample. We hypothesize that existing TSLM time series encoders overlook temporal granularity as context length increases, creating a task-dependent effect: compression aids classification but impairs retrieval of localized events. Across multiple model and encoding strategies, we observe a consistent divergence between classification and retrieval behavior. Learned latent compression preserves or improves classification accuracy at compression ratios up to 176times, but retrieval performance degrades with context length, incurring in the loss of temporally localized information. These results highlight the importance of architectural designs that decouple sequence length from computational complexity while preserving temporal fidelity.

Emotional talking-head generation has emerged as a pivotal research area at the intersection of computer vision and multimodal artificial intelligence, with its core value lying in enhancing human-computer interaction through immersive and empathetic engagement.With the advancement of multimodal large language models, the driving signals for emotional talking-head generation has shifted from audio and video to more flexible text. However, current text-driven methods rely on predefined discrete emotion label texts, oversimplifying the dynamic complexity of real facial muscle movements and thus failing to achieve natural emotional expressiveness.This study proposes the Think-Before-Draw framework to address two key challenges: (1) In-depth semantic parsing of emotions--by innovatively introducing Chain-of-Thought (CoT), abstract emotion labels are transformed into physiologically grounded facial muscle movement descriptions, enabling the mapping from high-level semantics to actionable motion features; and (2) Fine-grained expressiveness optimization--inspired by artists' portrait painting process, a progressive guidance denoising strategy is proposed, employing a "global emotion localization--local muscle control" mechanism to refine micro-expression dynamics in generated videos.Our experiments demonstrate that our approach achieves state-of-the-art performance on widely-used benchmarks, including MEAD and HDTF. Additionally, we collected a set of portrait images to evaluate our model's zero-shot generation capability.

This paper introduces GeoChain, a large-scale benchmark for evaluating step-by-step geographic reasoning in multimodal large language models (MLLMs). Leveraging 1.46 million Mapillary street-level images, GeoChain pairs each image with a 21-step chain-of-thought (CoT) question sequence (over 30 million Q&A pairs). These sequences guide models from coarse attributes to fine-grained localization across four reasoning categories - visual, spatial, cultural, and precise geolocation - annotated by difficulty. Images are also enriched with semantic segmentation (150 classes) and a visual locatability score. Our benchmarking of contemporary MLLMs (GPT-4.1 variants, Claude 3.7, Gemini 2.5 variants) on a diverse 2,088-image subset reveals consistent challenges: models frequently exhibit weaknesses in visual grounding, display erratic reasoning, and struggle to achieve accurate localization, especially as the reasoning complexity escalates. GeoChain offers a robust diagnostic methodology, critical for fostering significant advancements in complex geographic reasoning within MLLMs.

Advanced Multimodal Large Language Models (MLLMs) struggle with recent Knowledge-based VQA tasks, such as INFOSEEK and Encyclopedic-VQA, due to their limited and frozen knowledge scope, often leading to ambiguous and inaccurate responses. Thus, multimodal Retrieval-Augmented Generation (mRAG) is naturally introduced to provide MLLMs with comprehensive and up-to-date knowledge, effectively expanding the knowledge scope. However, current mRAG methods have inherent drawbacks, including: 1) Performing retrieval even when external knowledge is not needed. 2) Lacking of identification of evidence that supports the query. 3) Increasing model complexity due to additional information filtering modules or rules. To address these shortcomings, we propose a novel generalized framework called multimodal Retrieval-Reflection-Augmented Generation (mR^2AG), which achieves adaptive retrieval and useful information localization to enable answers through two easy-to-implement reflection operations, preventing high model complexity. In mR^2AG, Retrieval-Reflection is designed to distinguish different user queries and avoids redundant retrieval calls, and Relevance-Reflection is introduced to guide the MLLM in locating beneficial evidence of the retrieved content and generating answers accordingly. In addition, mR^2AG can be integrated into any well-trained MLLM with efficient fine-tuning on the proposed mR^2AG Instruction-Tuning dataset (mR^2AG-IT). mR^2AG significantly outperforms state-of-the-art MLLMs (e.g., GPT-4v/o) and RAG-based MLLMs on INFOSEEK and Encyclopedic-VQA, while maintaining the exceptional capabilities of base MLLMs across a wide range of Visual-dependent tasks.

This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified linear system. We show that the time complexity of such localized methods is upper bounded by min{mathcal{O}(R^2/ε^2), mathcal{O}(m)} to obtain an ε-approximation of the PPR vector, where m denotes the number of edges in the graph and R is a constant defined via nested evolving set processes. Furthermore, the algorithms induced by our framework require solving only mathcal{O}(1/sqrtα) such linear systems, where α is the damping factor. When 1/ε^2ll m, this implies the existence of an algorithm that computes an epsilon -approximation of the PPR vector with an overall time complexity of mathcal{O}left(R^2 / (sqrtαε^2)right), independent of the underlying graph size. Our result resolves an open conjecture from existing literature. Experimental results on real-world graphs validate the efficiency of our methods, demonstrating significant convergence in the early stages.

Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum number of labeled tuples sufficient for getting high generalization accuracy. We give tight bounds on the sample complexity in a variety of settings, focusing on arbitrary distance functions, both general ell_p-distances, and tree metrics. Our main result is an (almost) optimal bound on the sample complexity of learning ell_p-distances for integer p. For any p ge 1 we show that tilde Theta(min(nd,n^2)) labeled tuples are necessary and sufficient for learning d-dimensional representations of n-point datasets. Our results hold for an arbitrary distribution of the input samples and are based on giving the corresponding bounds on the Vapnik-Chervonenkis/Natarajan dimension of the associated problems. We further show that the theoretical bounds on sample complexity obtained via VC/Natarajan dimension can have strong predictive power for experimental results, in contrast with the folklore belief about a substantial gap between the statistical learning theory and the practice of deep learning.

The complexity of learning a concept class under Gaussian marginals in the difficult agnostic model is closely related to its L_1-approximability by low-degree polynomials. For any concept class with Gaussian surface area at most Γ, Klivans et al. (2008) show that degree d = O(Γ^2 / varepsilon^4) suffices to achieve an varepsilon-approximation. This leads to the best-known bounds on the complexity of learning a variety of concept classes. In this note, we improve their analysis by showing that degree d = tilde O (Γ^2 / varepsilon^2) is enough. In light of lower bounds due to Diakonikolas et al. (2021), this yields (near) optimal bounds on the complexity of agnostically learning polynomial threshold functions in the statistical query model. Our proof relies on a direct analogue of a construction of Feldman et al. (2020), who considered L_1-approximation on the Boolean hypercube.

Localizing behaviors of neural networks to a subset of the network's components or a subset of interactions between components is a natural first step towards analyzing network mechanisms and possible failure modes. Existing work is often qualitative and ad-hoc, and there is no consensus on the appropriate way to evaluate localization claims. We introduce path patching, a technique for expressing and quantitatively testing a natural class of hypotheses expressing that behaviors are localized to a set of paths. We refine an explanation of induction heads, characterize a behavior of GPT-2, and open source a framework for efficiently running similar experiments.

We apply a generalized piecewise-linear (PL) version of Morse theory due to Grunert-Kuhnel-Rote to define and study new local and global notions of topological complexity for fully-connected feedforward ReLU neural network functions, F: R^n -> R. Along the way, we show how to construct, for each such F, a canonical polytopal complex K(F) and a deformation retract of the domain onto K(F), yielding a convenient compact model for performing calculations. We also give a construction showing that local complexity can be arbitrarily high.

Geo-localization aims to infer the geographic origin of a given signal. In computer vision, geo-localization has served as a demanding benchmark for compositional reasoning and is relevant to public safety. In contrast, progress on audio geo-localization has been constrained by the lack of high-quality audio-location pairs. To address this gap, we introduce AGL1K, the first audio geo-localization benchmark for audio language models (ALMs), spanning 72 countries and territories. To extract reliably localizable samples from a crowd-sourced platform, we propose the Audio Localizability metric that quantifies the informativeness of each recording, yielding 1,444 curated audio clips. Evaluations on 16 ALMs show that ALMs have emerged with audio geo-localization capability. We find that closed-source models substantially outperform open-source models, and that linguistic clues often dominate as a scaffold for prediction. We further analyze ALMs' reasoning traces, regional bias, error causes, and the interpretability of the localizability metric. Overall, AGL1K establishes a benchmark for audio geo-localization and may advance ALMs with better geospatial reasoning capability.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

State-of-the-art visual localization approaches generally rely on a first image retrieval step whose role is crucial. Yet, retrieval often struggles when facing varying conditions, due to e.g. weather or time of day, with dramatic consequences on the visual localization accuracy. In this paper, we improve this retrieval step and tailor it to the final localization task. Among the several changes we advocate for, we propose to synthesize variants of the training set images, obtained from generative text-to-image models, in order to automatically expand the training set towards a number of nameable variations that particularly hurt visual localization. After expanding the training set, we propose a training approach that leverages the specificities and the underlying geometry of this mix of real and synthetic images. We experimentally show that those changes translate into large improvements for the most challenging visual localization datasets. Project page: https://europe.naverlabs.com/ret4loc

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving the problem exactly in polynomial time. Our analysis identifies structural properties of the input data that influence the integrality of the relaxation. We show that incorporating ordered components introduces additional layers of combinatorial complexity that invalidate the exactness observed in classical (non-ordered) settings. In particular, for certain ordered problems such as the min--max case, the linear relaxation never recovers the integral solution. These results clarify the intrinsic hardness introduced by sorting and reveal that the strength of the relaxation depends critically on the ``proximity'' of the ordered problem to its classical counterpart: problems closer to the non-ordered case tend to admit tighter relaxations, while those further away exhibit substantially weaker behavior. Computational experiments on benchmark instances confirm the predictive value of the integrality conditions and demonstrate the practical implications of exact relaxations for ordered location problems.

An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually is. We systematically assess which papers use which definitions and discuss how they relate to each other. We then analyze the computational complexity of counting the number of such regions for the various definitions. Generally, this turns out to be an intractable problem. We prove NP- and #P-hardness results already for networks with one hidden layer and strong hardness of approximation results for two or more hidden layers. Finally, on the algorithmic side, we demonstrate that counting linear regions can at least be achieved in polynomial space for some common definitions.

As modern microservice systems grow increasingly popular and complex-often consisting of hundreds or even thousands of fine-grained, interdependent components-they are becoming more susceptible to frequent and subtle failures. Ensuring system reliability therefore hinges on accurate and efficient failure localization. Traditional failure localization approaches based on small models lack the flexibility to adapt to diverse failure scenarios, while recent LLM-based methods suffer from two major limitations: they often rely on rigid invocation workflows that constrain the model's ability to dynamically explore optimal localization paths, and they require resource-intensive inference, making them cost-prohibitive for real-world deployment. To address these challenges, we explore the use of reinforcement fine-tuning to equip lightweight LLMs with reasoning and self-refinement capabilities, significantly improving the cost-effectiveness and adaptability of LLM-based failure localization. We begin with an empirical study to identify three key capabilities essential for accurate localization. Building on these insights, we propose a progressive multi-stage GRPO fine-tuning framework, which integrates a multi-factor failure localization grader and a recursion-of-thought actor module. The resulting model, ThinkFL, not only outperforms existing state-of-the-art LLMs and baseline methods in localization accuracy but also reduces end-to-end localization latency from minutes to seconds, demonstrating strong potential for real-world applications.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

Pre-trained language models can be fine-tuned to solve diverse NLP tasks, including in few-shot settings. Thus fine-tuning allows the model to quickly pick up task-specific ``skills,'' but there has been limited study of where these newly-learnt skills reside inside the massive model. This paper introduces the term skill localization for this problem and proposes a solution. Given the downstream task and a model fine-tuned on that task, a simple optimization is used to identify a very small subset of parameters (sim0.01% of model parameters) responsible for (>95%) of the model's performance, in the sense that grafting the fine-tuned values for just this tiny subset onto the pre-trained model gives performance almost as well as the fine-tuned model. While reminiscent of recent works on parameter-efficient fine-tuning, the novel aspects here are that: (i) No further re-training is needed on the subset (unlike, say, with lottery tickets). (ii) Notable improvements are seen over vanilla fine-tuning with respect to calibration of predictions in-distribution (40-90% error reduction) as well as the quality of predictions out-of-distribution (OOD). In models trained on multiple tasks, a stronger notion of skill localization is observed, where the sparse regions corresponding to different tasks are almost disjoint, and their overlap (when it happens) is a proxy for task similarity. Experiments suggest that localization via grafting can assist certain forms of continual learning.

Hallucinations in large language models (LLMs) remain a central obstacle to trustworthy deployment, motivating detectors that are accurate, lightweight, and broadly applicable. Since an LLM with a prompt defines a conditional distribution, we argue that the complexity of the distribution is an indicator of hallucination. However, the density of the distribution is unknown and the samples (i.e., responses generated for the prompt) are discrete distributions, which leads to a significant challenge in quantifying the complexity of the distribution. We propose to compute the optimal-transport distances between the sets of token embeddings of pairwise samples, which yields a Wasserstein distance matrix measuring the costs of transforming between the samples. This Wasserstein distance matrix provides a means to quantify the complexity of the distribution defined by the LLM with the prompt. Based on the Wasserstein distance matrix, we derive two complementary signals: AvgWD, measuring the average cost, and EigenWD, measuring the cost complexity. This leads to a training-free detector for hallucinations in LLMs. We further extend the framework to black-box LLMs via teacher forcing with an accessible teacher model. Experiments show that AvgWD and EigenWD are competitive with strong uncertainty baselines and provide complementary behavior across models and datasets, highlighting distribution complexity as an effective signal for LLM truthfulness.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward g(gamma, v) depends on the proposed threshold gamma and latent value v and it can be only achieved if the threshold is lower than or equal to the unknown latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most epsilon smaller than the optimum and prove that the number of queries needed can be infinitely large even when g(gamma, v) is monotone with respect to both gamma and v. On the positive side, we provide a tight query complexity Theta(1/epsilon^3) when g is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight Theta(1/epsilon^3) query complexity can be achieved as long as g satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight Theta(T^{2/3}) regret bound using continuous-arm bandit techniques and the aforementioned query complexity results.

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below. With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error. When such an upper bound is not known, we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019]. These two algorithms can then be combined to prepare a ground state without knowing an upper bound of the ground energy. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem.

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

Neural networks are capable of translating between languages -- in some cases even between two languages where there is little or no access to parallel translations, in what is known as Unsupervised Machine Translation (UMT). Given this progress, it is intriguing to ask whether machine learning tools can ultimately enable understanding animal communication, particularly that of highly intelligent animals. We propose a theoretical framework for analyzing UMT when no parallel translations are available and when it cannot be assumed that the source and target corpora address related subject domains or posses similar linguistic structure. We exemplify this theory with two stylized models of language, for which our framework provides bounds on necessary sample complexity; the bounds are formally proven and experimentally verified on synthetic data. These bounds show that the error rates are inversely related to the language complexity and amount of common ground. This suggests that unsupervised translation of animal communication may be feasible if the communication system is sufficiently complex.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

We study the representation complexity of model-based and model-free reinforcement learning (RL) in the context of circuit complexity. We prove theoretically that there exists a broad class of MDPs such that their underlying transition and reward functions can be represented by constant depth circuits with polynomial size, while the optimal Q-function suffers an exponential circuit complexity in constant-depth circuits. By drawing attention to the approximation errors and building connections to complexity theory, our theory provides unique insights into why model-based algorithms usually enjoy better sample complexity than model-free algorithms from a novel representation complexity perspective: in some cases, the ground-truth rule (model) of the environment is simple to represent, while other quantities, such as Q-function, appear complex. We empirically corroborate our theory by comparing the approximation error of the transition kernel, reward function, and optimal Q-function in various Mujoco environments, which demonstrates that the approximation errors of the transition kernel and reward function are consistently lower than those of the optimal Q-function. To the best of our knowledge, this work is the first to study the circuit complexity of RL, which also provides a rigorous framework for future research.

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

We present ModularSubsetSelection (MSS), a new algorithm for locally differentially private (LDP) frequency estimation. Given a universe of size k and n users, our varepsilon-LDP mechanism encodes each input via a Residue Number System (RNS) over ell pairwise-coprime moduli m_0, ldots, m_{ell-1}, and reports a randomly chosen index j in [ell] along with the perturbed residue using the statistically optimal SubsetSelection (SS) (Wang et al. 2016). This design reduces the user communication cost from Θbigl(ωlog_2(k/ω)bigr) bits required by standard SS (with ωapprox k/(e^varepsilon+1)) down to lceil log_2 ell rceil + lceil log_2 m_j rceil bits, where m_j < k. Server-side decoding runs in Θ(n + r k ell) time, where r is the number of LSMR (Fong and Saunders 2011) iterations. In practice, with well-conditioned moduli (i.e., constant r and ell = Θ(log k)), this becomes Θ(n + k log k). We prove that MSS achieves worst-case MSE within a constant factor of state-of-the-art protocols such as SS and ProjectiveGeometryResponse (PGR) (Feldman et al. 2022) while avoiding the algebraic prerequisites and dynamic-programming decoder required by PGR. Empirically, MSS matches the estimation accuracy of SS, PGR, and RAPPOR (Erlingsson, Pihur, and Korolova 2014) across realistic (k, varepsilon) settings, while offering faster decoding than PGR and shorter user messages than SS. Lastly, by sampling from multiple moduli and reporting only a single perturbed residue, MSS achieves the lowest reconstruction-attack success rate among all evaluated LDP protocols.

Code based Language Models (LMs) have shown very promising results in the field of software engineering with applications such as code refinement, code completion and generation. However, the task of time and space complexity classification from code has not been extensively explored due to a lack of datasets, with prior endeavors being limited to Java. In this project, we aim to address these gaps by creating a labelled dataset of code snippets spanning multiple languages (Python and C++ datasets currently, with C, C#, and JavaScript datasets being released shortly). We find that existing time complexity calculation libraries and tools only apply to a limited number of use-cases. The lack of a well-defined rule based system motivates the application of several recently proposed code-based LMs. We demonstrate the effectiveness of dead code elimination and increasing the maximum sequence length of LMs. In addition to time complexity, we propose to use LMs to find space complexities from code, and to the best of our knowledge, this is the first attempt to do so. Furthermore, we introduce a novel code comprehension task, called cross-language transfer, where we fine-tune the LM on one language and run inference on another. Finally, we visualize the activation of the attention fed classification head of our LMs using Non-negative Matrix Factorization (NMF) to interpret our results.

Vision-language models (VLMs) commonly formulate visual grounding and detection as a coordinate-token generation problem, serializing each 2D box into multiple 1D tokens that are learned and decoded largely independently. This token-by-token decoding mismatches the coupled structure of box geometry and creates a practical inference bottleneck due to strictly sequential generation. We introduce LocateAnything, a unified generative grounding and detection framework based on Parallel Box Decoding (PBD). By decoding geometric elements such as bounding boxes and points as atomic units in a single step, LocateAnything preserves intra-box geometric coherence and unlocks substantial parallelism. We show that PBD improves both decoding throughput and localization accuracy. We further develop a scalable data engine and curate LocateAnything-Data, a large-scale dataset with more than 138 million training samples, substantially increasing data diversity for high-precision localization. Extensive evaluations show that LocateAnything advances the speed-accuracy frontier, achieving significantly higher decoding throughput while improving high-IoU localization quality across diverse benchmarks. The results highlight the complementary benefits of Parallel Box Decoding and large-scale training data in enabling efficient and precise unified visual grounding and detection.

Large-scale visual localization systems continue to rely on 3D point clouds built from image collections using structure-from-motion. While the 3D points in these models are represented using local image features, directly matching a query image's local features against the point cloud is challenging due to the scale of the nearest-neighbor search problem. Many recent approaches to visual localization have thus proposed a hybrid method, where first a global (per image) embedding is used to retrieve a small subset of database images, and local features of the query are matched only against those. It seems to have become common belief that global embeddings are critical for said image-retrieval in visual localization, despite the significant downside of having to compute two feature types for each query image. In this paper, we take a step back from this assumption and propose Constrained Approximate Nearest Neighbors (CANN), a joint solution of k-nearest-neighbors across both the geometry and appearance space using only local features. We first derive the theoretical foundation for k-nearest-neighbor retrieval across multiple metrics and then showcase how CANN improves visual localization. Our experiments on public localization benchmarks demonstrate that our method significantly outperforms both state-of-the-art global feature-based retrieval and approaches using local feature aggregation schemes. Moreover, it is an order of magnitude faster in both index and query time than feature aggregation schemes for these datasets. Code will be released.

Localizing objects in an unsupervised manner poses significant challenges due to the absence of key visual information such as the appearance, type and number of objects, as well as the lack of labeled object classes typically available in supervised settings. While recent approaches to unsupervised object localization have demonstrated significant progress by leveraging self-supervised visual representations, they often require computationally intensive training processes, resulting in high resource demands in terms of computation, learnable parameters, and data. They also lack explicit modeling of visual context, potentially limiting their accuracy in object localization. To tackle these challenges, we propose a single-stage learning framework, dubbed PEEKABOO, for unsupervised object localization by learning context-based representations at both the pixel- and shape-level of the localized objects through image masking. The key idea is to selectively hide parts of an image and leverage the remaining image information to infer the location of objects without explicit supervision. The experimental results, both quantitative and qualitative, across various benchmark datasets, demonstrate the simplicity, effectiveness and competitive performance of our approach compared to state-of-the-art methods in both single object discovery and unsupervised salient object detection tasks. Code and pre-trained models are available at: https://github.com/hasibzunair/peekaboo

In the context of distributed synchronous computing, processors perform in rounds, and the time-complexity of a distributed algorithm is classically defined as the number of rounds before all computing nodes have output. Hence, this complexity measure captures the running time of the slowest node(s). In this paper, we are interested in the running time of the ordinary nodes, to be compared with the running time of the slowest nodes. The node-averaged time-complexity of a distributed algorithm on a given instance is defined as the average, taken over every node of the instance, of the number of rounds before that node output. We compare the node-averaged time-complexity with the classical one in the standard LOCAL model for distributed network computing. We show that there can be an exponential gap between the node-averaged time-complexity and the classical time-complexity, as witnessed by, e.g., leader election. Our first main result is a positive one, stating that, in fact, the two time-complexities behave the same for a large class of problems on very sparse graphs. In particular, we show that, for LCL problems on cycles, the node-averaged time complexity is of the same order of magnitude as the slowest node time-complexity. In addition, in the LOCAL model, the time-complexity is computed as a worst case over all possible identity assignments to the nodes of the network. In this paper, we also investigate the ID-averaged time-complexity, when the number of rounds is averaged over all possible identity assignments. Our second main result is that the ID-averaged time-complexity is essentially the same as the expected time-complexity of randomized algorithms (where the expectation is taken over all possible random bits used by the nodes, and the number of rounds is measured for the worst-case identity assignment). Finally, we study the node-averaged ID-averaged time-complexity.

The superficial alignment hypothesis (SAH) posits that large language models learn most of their knowledge during pre-training, and that post-training merely surfaces this knowledge. The SAH, however, lacks a precise definition, which has led to (i) different and seemingly orthogonal arguments supporting it, and (ii) important critiques to it. We propose a new metric called task complexity: the length of the shortest program that achieves a target performance on a task. In this framework, the SAH simply claims that pre-trained models drastically reduce the complexity of achieving high performance on many tasks. Our definition unifies prior arguments supporting the SAH, interpreting them as different strategies to find such short programs. Experimentally, we estimate the task complexity of mathematical reasoning, machine translation, and instruction following; we then show that these complexities can be remarkably low when conditioned on a pre-trained model. Further, we find that pre-training enables access to strong performances on our tasks, but it can require programs of gigabytes of length to access them. Post-training, on the other hand, collapses the complexity of reaching this same performance by several orders of magnitude. Overall, our results highlight that task adaptation often requires surprisingly little information -- often just a few kilobytes.

Graph-based learning has emerged as a transformative approach for modeling complex relationships across diverse domains, yet its potential in wireless security remains largely unexplored. In this work, we introduce the first application of graph-based learning for jamming source localization, addressing the imminent threat of jamming attacks in wireless networks. Unlike geometric optimization techniques that struggle under environmental uncertainties and dense interference, we reformulate localization as an inductive graph regression task. Our approach integrates structured node representations that encode local and global signal aggregation, ensuring spatial coherence and adaptive signal fusion. To enhance robustness, we incorporate an attention-based graph neural network that adaptively refines neighborhood influence and introduces a confidence-guided estimation mechanism that dynamically balances learned predictions with domain-informed priors. We evaluate our approach under complex radio frequency environments with varying sampling densities and signal propagation conditions, conducting comprehensive ablation studies on graph construction, feature selection, and pooling strategies. Results demonstrate that our novel graph-based learning framework significantly outperforms established localization baselines, particularly in challenging scenarios with sparse and obfuscated signal information. Code is available at [https://github.com/daniaherzalla/gnn-jamming-source-localization](https://github.com/daniaherzalla/gnn-jamming-source-localization).

Given the damping factor α and precision tolerance ε, andersen2006local introduced Approximate Personalized PageRank (APPR), the de facto local method for approximating the PPR vector, with runtime bounded by Θ(1/(αε)) independent of the graph size. Recently, fountoulakis2022open asked whether faster local algorithms could be developed using O(1/(sqrtαε)) operations. By noticing that APPR is a local variant of Gauss-Seidel, this paper explores the question of whether standard iterative solvers can be effectively localized. We propose to use the locally evolving set process, a novel framework to characterize the algorithm locality, and demonstrate that many standard solvers can be effectively localized. Let operatorname{vol}{ (S_t)} and overlineγ_{t} be the running average of volume and the residual ratio of active nodes textstyle S_{t} during the process. We show operatorname{vol}{ (S_t)}/overlineγ_{t} leq 1/ε and prove APPR admits a new runtime bound O(operatorname{vol}(S_t)/(αoverlineγ_{t})) mirroring the actual performance. Furthermore, when the geometric mean of residual reduction is Θ(sqrtα), then there exists c in (0,2) such that the local Chebyshev method has runtime O(operatorname{vol}(S_{t})/(sqrtα(2-c))) without the monotonicity assumption. Numerical results confirm the efficiency of this novel framework and show up to a hundredfold speedup over corresponding standard solvers on real-world graphs.

Standard continuous-time generative models rely on monolithic architectures that must navigate vastly different signal regimes, from isotropic noise to intricate data distributions. While scaling model capacity improves performance, deploying a massive network uniformly across the entire generative timeline is inherently inefficient. In this work, we propose Complexity-Balanced Splitting (CBS), a principled framework for temporal capacity allocation that distributes the generative workload across multiple specialized sub-networks. Grounded in function approximation theory and de Boor's equidistribution principle, CBS partitions the diffusion timeline into segments of equal approximation burden, allocating more representational capacity to regions where the generative dynamics are more difficult to model. To estimate this local complexity, we introduce two complementary and tractable monitor functions: a spatial measure based on the flow's Dirichlet energy, and a geometric measure based on the acceleration of the sampling trajectories. Using a lightweight auxiliary model to estimate these complexity profiles, our approach eliminates the need for heuristic temporal splits or computationally expensive search procedures. Extensive evaluation across multiple architectures (SiT, JiT, and UNet) and datasets demonstrates that CBS consistently improves synthesis quality without increasing per-step inference cost. In particular, CBS improves FID by ~35% on SiT-XL with CFG relative to naive temporal partitioning. Project page is available at https://noamissachar.github.io/CBS/.

We propose a novel unsupervised object localization method that allows us to explain the predictions of the model by utilizing self-supervised pre-trained models without additional finetuning. Existing unsupervised and self-supervised object localization methods often utilize class-agnostic activation maps or self-similarity maps of a pre-trained model. Although these maps can offer valuable information for localization, their limited ability to explain how the model makes predictions remains challenging. In this paper, we propose a simple yet effective unsupervised object localization method based on representer point selection, where the predictions of the model can be represented as a linear combination of representer values of training points. By selecting representer points, which are the most important examples for the model predictions, our model can provide insights into how the model predicts the foreground object by providing relevant examples as well as their importance. Our method outperforms the state-of-the-art unsupervised and self-supervised object localization methods on various datasets with significant margins and even outperforms recent weakly supervised and few-shot methods.

Cross-view geo-localization is a promising solution for large-scale localization problems, requiring the sequential execution of retrieval and metric localization tasks to achieve fine-grained predictions. However, existing methods typically focus on designing standalone models for these two tasks, resulting in inefficient collaboration and increased training overhead. In this paper, we propose UnifyGeo, a novel unified hierarchical geo-localization framework that integrates retrieval and metric localization tasks into a single network. Specifically, we first employ a unified learning strategy with shared parameters to jointly learn multi-granularity representation, facilitating mutual reinforcement between these two tasks. Subsequently, we design a re-ranking mechanism guided by a dedicated loss function, which enhances geo-localization performance by improving both retrieval accuracy and metric localization references. Extensive experiments demonstrate that UnifyGeo significantly outperforms the state-of-the-arts in both task-isolated and task-associated settings. Remarkably, on the challenging VIGOR benchmark, which supports fine-grained localization evaluation, the 1-meter-level localization recall rate improves from 1.53\% to 39.64\% and from 0.43\% to 25.58\% under same-area and cross-area evaluations, respectively. Code will be made publicly available.

Recent progress has pushed AI frontiers from pattern recognition tasks toward problems that require step by step, System2 style reasoning, especially with large language models. Yet, unlike learning, where generalization and out of distribution (OoD) evaluation concepts are well formalized, there is no clear, consistent definition or metric for reasoning ability. We propose Complexity Out of Distribution (Complexity OoD) generalization as a framework and problem setting to define and measure reasoning. A model exhibits Complexity OoD generalization when it maintains performance on test instances whose minimal required solution complexity, either representational (richer solution structure) or computational (more reasoning steps/program length), exceeds that of all training examples. We formalize complexity via solution description Kolmogorov complexity and operational proxies (e.g., object/relation counts; reasoning step counts), clarifying how Complexity OoD differs from length and compositional OoD. This lens unifies learning and reasoning: many cases solvable with System1 like processing at low complexity become System2 like under complexity pressure, while System2 can be viewed as generalization over solution structures. We translate this perspective into practice with recommendations for operationalizing Complexity OoD across the stack: incorporating complexity into benchmark and evaluation metric design, rethinking supervision to target solution traces, seeking and designing inductive biases for Complexity OoD generalization, addressing learning to reason spillovers such as spurious shortcuts, semantic robustness, catastrophic forgetting, and step wise calibration. Because Complexity OoD cannot be solved by scaling data alone, progress toward robust reasoning will require architectures and training regimes that explicitly model and allocate computation with respect to complexity.

Recent studies suggest that deep learning models inductive bias towards favoring simpler features may be one of the sources of shortcut learning. Yet, there has been limited focus on understanding the complexity of the myriad features that models learn. In this work, we introduce a new metric for quantifying feature complexity, based on V-information and capturing whether a feature requires complex computational transformations to be extracted. Using this V-information metric, we analyze the complexities of 10,000 features, represented as directions in the penultimate layer, that were extracted from a standard ImageNet-trained vision model. Our study addresses four key questions: First, we ask what features look like as a function of complexity and find a spectrum of simple to complex features present within the model. Second, we ask when features are learned during training. We find that simpler features dominate early in training, and more complex features emerge gradually. Third, we investigate where within the network simple and complex features flow, and find that simpler features tend to bypass the visual hierarchy via residual connections. Fourth, we explore the connection between features complexity and their importance in driving the networks decision. We find that complex features tend to be less important. Surprisingly, important features become accessible at earlier layers during training, like a sedimentation process, allowing the model to build upon these foundational elements.

LiDAR-based global localization is a fundamental problem for mobile robots. It consists of two stages, place recognition and pose estimation, which yields the current orientation and translation, using only the current scan as query and a database of map scans. Inspired by the definition of a recognized place, we consider that a good global localization solution should keep the pose estimation accuracy with a lower place density. Following this idea, we propose a novel framework towards sparse place-based global localization, which utilizes a unified and learning-free representation, Radon sinogram (RING), for all sub-tasks. Based on the theoretical derivation, a translation invariant descriptor and an orientation invariant metric are proposed for place recognition, achieving certifiable robustness against arbitrary orientation and large translation between query and map scan. In addition, we also utilize the property of RING to propose a global convergent solver for both orientation and translation estimation, arriving at global localization. Evaluation of the proposed RING based framework validates the feasibility and demonstrates a superior performance even under a lower place density.

In this paper, we study the localization problem in dense urban settings. In such environments, Global Navigation Satellite Systems fail to provide good accuracy due to low likelihood of line-of-sight (LOS) links between the receiver (Rx) to be located and the satellites, due to the presence of obstacles like the buildings. Thus, one has to resort to other technologies, which can reliably operate under non-line-of-sight (NLOS) conditions. Recently, we proposed a Received Signal Strength (RSS) fingerprint and convolutional neural network-based algorithm, LocUNet, and demonstrated its state-of-the-art localization performance with respect to the widely adopted k-nearest neighbors (kNN) algorithm, and to state-of-the-art time of arrival (ToA) ranging-based methods. In the current work, we first recognize LocUNet's ability to learn the underlying prior distribution of the Rx position or Rx and transmitter (Tx) association preferences from the training data, and attribute its high performance to these. Conversely, we demonstrate that classical methods based on probabilistic approach, can greatly benefit from an appropriate incorporation of such prior information. Our studies also numerically prove LocUNet's close to optimal performance in many settings, by comparing it with the theoretically optimal formulations.

The capacity of existing human keypoint localization models is limited by keypoint priors provided by the training data. To alleviate this restriction and pursue more general model, this work studies keypoint localization from a different perspective by reasoning locations based on keypiont clues in text descriptions. We propose LocLLM, the first Large-Language Model (LLM) based keypoint localization model that takes images and text instructions as inputs and outputs the desired keypoint coordinates. LocLLM leverages the strong reasoning capability of LLM and clues of keypoint type, location, and relationship in textual descriptions for keypoint localization. To effectively tune LocLLM, we construct localization-based instruction conversations to connect keypoint description with corresponding coordinates in input image, and fine-tune the whole model in a parameter-efficient training pipeline. LocLLM shows remarkable performance on standard 2D/3D keypoint localization benchmarks. Moreover, incorporating language clues into the localization makes LocLLM show superior flexibility and generalizable capability in cross dataset keypoint localization, and even detecting novel type of keypoints unseen during training.

This paper re-examines a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials. Next, focusing on a one-parameter-per-edge setting, it is shown that the Karush-Kuhn-Tucker (KKT) optimality conditions for the NOTEARS formulation cannot be satisfied except in a trivial case, which explains a behavior of the associated algorithm. We then derive the KKT conditions for an equivalent reformulation, show that they are indeed necessary, and relate them to explicit constraints that certain edges be absent from the graph. If the score function is convex, these KKT conditions are also sufficient for local minimality despite the non-convexity of the constraint. Informed by the KKT conditions, a local search post-processing algorithm is proposed and shown to substantially and universally improve the structural Hamming distance of all tested algorithms, typically by a factor of 2 or more. Some combinations with local search are both more accurate and more efficient than the original NOTEARS.

The advent of autonomous agents is transforming interactions with Graphical User Interfaces (GUIs) by employing natural language as a powerful intermediary. Despite the predominance of Supervised Fine-Tuning (SFT) methods in current GUI agents for achieving spatial localization, these methods face substantial challenges due to their limited capacity to accurately perceive positional data. Existing strategies, such as reinforcement learning, often fail to assess positional accuracy effectively, thereby restricting their utility. In response, we introduce Location Preference Optimization (LPO), a novel approach that leverages locational data to optimize interaction preferences. LPO uses information entropy to predict interaction positions by focusing on zones rich in information. Besides, it further introduces a dynamic location reward function based on physical distance, reflecting the varying importance of interaction positions. Supported by Group Relative Preference Optimization (GRPO), LPO facilitates an extensive exploration of GUI environments and significantly enhances interaction precision. Comprehensive experiments demonstrate LPO's superior performance, achieving SOTA results across both offline benchmarks and real-world online evaluations. Our code will be made publicly available soon, at https://github.com/AIDC-AI/LPO.

We propose a novel method for geolocalizing Unmanned Aerial Vehicles (UAVs) in environments lacking Global Navigation Satellite Systems (GNSS). Current state-of-the-art techniques employ an offline-trained encoder to generate a vector representation (embedding) of the UAV's current view, which is then compared with pre-computed embeddings of geo-referenced images to determine the UAV's position. Here, we demonstrate that the performance of these methods can be significantly enhanced by preprocessing the images to extract their edges, which exhibit robustness to seasonal and illumination variations. Furthermore, we establish that utilizing edges enhances resilience to orientation and altitude inaccuracies. Additionally, we introduce a confidence criterion for localization. Our findings are substantiated through synthetic experiments.

Improvements in language models' capabilities have pushed their applications towards longer contexts, making long-context evaluation and development an active research area. However, many disparate use-cases are grouped together under the umbrella term of "long-context", defined simply by the total length of the model's input, including - for example - Needle-in-a-Haystack tasks, book summarization, and information aggregation. Given their varied difficulty, in this position paper we argue that conflating different tasks by their context length is unproductive. As a community, we require a more precise vocabulary to understand what makes long-context tasks similar or different. We propose to unpack the taxonomy of long-context based on the properties that make them more difficult with longer contexts. We propose two orthogonal axes of difficulty: (I) Diffusion: How hard is it to find the necessary information in the context? (II) Scope: How much necessary information is there to find? We survey the literature on long-context, provide justification for this taxonomy as an informative descriptor, and situate the literature with respect to it. We conclude that the most difficult and interesting settings, whose necessary information is very long and highly diffused within the input, is severely under-explored. By using a descriptive vocabulary and discussing the relevant properties of difficulty in long-context, we can implement more informed research in this area. We call for a careful design of tasks and benchmarks with distinctly long context, taking into account the characteristics that make it qualitatively different from shorter context.

Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood. In this work, we seek to understand how high-level human-interpretable features are represented within the internal neuron activations of LLMs. We train k-sparse linear classifiers (probes) on these internal activations to predict the presence of features in the input; by varying the value of k we study the sparsity of learned representations and how this varies with model scale. With k=1, we localize individual neurons which are highly relevant for a particular feature, and perform a number of case studies to illustrate general properties of LLMs. In particular, we show that early layers make use of sparse combinations of neurons to represent many features in superposition, that middle layers have seemingly dedicated neurons to represent higher-level contextual features, and that increasing scale causes representational sparsity to increase on average, but there are multiple types of scaling dynamics. In all, we probe for over 100 unique features comprising 10 different categories in 7 different models spanning 70 million to 6.9 billion parameters.

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

A fundamental problem in quantum many-body physics is that of finding ground states of local Hamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithms for learning ground states. Specifically, [Huang et al. Science 2022], introduced an approach for learning properties of the ground state of an n-qubit gapped local Hamiltonian H from only n^{O(1)} data points sampled from Hamiltonians in the same phase of matter. This was subsequently improved by [Lewis et al. Nature Communications 2024], to O(log n) samples when the geometry of the n-qubit system is known. In this work, we introduce two approaches that achieve a constant sample complexity, independent of system size n, for learning ground state properties. Our first algorithm consists of a simple modification of the ML model used by Lewis et al. and applies to a property of interest known beforehand. Our second algorithm, which applies even if a description of the property is not known, is a deep neural network model. While empirical results showing the performance of neural networks have been demonstrated, to our knowledge, this is the first rigorous sample complexity bound on a neural network model for predicting ground state properties. We also perform numerical experiments that confirm the improved scaling of our approach compared to earlier results.

Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5) multimodal misalignment. While existing surveys describe these phenomena empirically, they lack a rigorous theoretical synthesis connecting them to the foundational limits of computation, information, and learning. This work closes that gap by presenting a unified, proof-informed framework that formalizes the innate theoretical ceilings of LLM scaling. First, computability and uncomputability imply an irreducible residue of error: for any computably enumerable model family, diagonalization guarantees inputs on which some model must fail, and undecidable queries (e.g., halting-style tasks) induce infinite failure sets for all computable predictors. Second, information-theoretic and statistical constraints bound attainable accuracy even on decidable tasks, finite description length enforces compression error, and long-tail factual knowledge requires prohibitive sample complexity. Third, geometric and computational effects compress long contexts far below their nominal size due to positional under-training, encoding attenuation, and softmax crowding. We further show how likelihood-based training favors pattern completion over inference, how retrieval under token limits suffers from semantic drift and coupling noise, and how multimodal scaling inherits shallow cross-modal alignment. Across sections, we pair theorems and empirical evidence to outline where scaling helps, where it saturates, and where it cannot progress, providing both theoretical foundations and practical mitigation paths like bounded-oracle retrieval, positional curricula, and sparse or hierarchical attention.

Transfer learning is an essential technique for many machine learning/AI models of complex structures such as large language models and generative AI. The essence of transfer learning is to leverage knowledge from resolved source tasks for a new target task, especially when the sample size m of the training data for the latter is low. In this work, we rigorously analyze the potential benefit of transfer learning in terms of sample efficiency. Specifically, taking an optimal transport viewpoint of transfer learning, we find that when the data dimension d is higher than 3, the sample complexity for transfer learning is O(m^{-(α+1)/d}), with α indicating the smoothness of the data distribution, as opposed to the O(m^{-p/d}) sample complexity for direct learning with p indicating the smoothness of the optimal target model. Our finding theoretically supports a better sample efficiency for transfer learning, when the target task is optimizing over a family of not-so-smooth models (i.e., highly complex networks with the possible use of non-smooth activation functions). Using image classification as an example, we numerically demonstrate the sample efficiency for transfer learning, that is, in the data hungry regime, the model performance can be significantly improved by transfer learning.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

We tackle the problem of 3D point cloud localization based on a few natural linguistic descriptions and introduce a novel neural network, Text2Loc, that fully interprets the semantic relationship between points and text. Text2Loc follows a coarse-to-fine localization pipeline: text-submap global place recognition, followed by fine localization. In global place recognition, relational dynamics among each textual hint are captured in a hierarchical transformer with max-pooling (HTM), whereas a balance between positive and negative pairs is maintained using text-submap contrastive learning. Moreover, we propose a novel matching-free fine localization method to further refine the location predictions, which completely removes the need for complicated text-instance matching and is lighter, faster, and more accurate than previous methods. Extensive experiments show that Text2Loc improves the localization accuracy by up to 2times over the state-of-the-art on the KITTI360Pose dataset. Our project page is publicly available at https://yan-xia.github.io/projects/text2loc/.

Worldwide Geo-localization aims to pinpoint the precise location of images taken anywhere on Earth. This task has considerable challenges due to immense variation in geographic landscapes. The image-to-image retrieval-based approaches fail to solve this problem on a global scale as it is not feasible to construct a large gallery of images covering the entire world. Instead, existing approaches divide the globe into discrete geographic cells, transforming the problem into a classification task. However, their performance is limited by the predefined classes and often results in inaccurate localizations when an image's location significantly deviates from its class center. To overcome these limitations, we propose GeoCLIP, a novel CLIP-inspired Image-to-GPS retrieval approach that enforces alignment between the image and its corresponding GPS locations. GeoCLIP's location encoder models the Earth as a continuous function by employing positional encoding through random Fourier features and constructing a hierarchical representation that captures information at varying resolutions to yield a semantically rich high-dimensional feature suitable to use even beyond geo-localization. To the best of our knowledge, this is the first work employing GPS encoding for geo-localization. We demonstrate the efficacy of our method via extensive experiments and ablations on benchmark datasets. We achieve competitive performance with just 20% of training data, highlighting its effectiveness even in limited-data settings. Furthermore, we qualitatively demonstrate geo-localization using a text query by leveraging CLIP backbone of our image encoder. The project webpage is available at: https://vicentevivan.github.io/GeoCLIP

We prove that any Turing machine running on inputs of arbitrary length can be simulated by a constant bit-size transformer, as long as the context window is sufficiently long. This improves previous works, which require scaling up either the model's precision or the number of parameters on longer inputs. Furthermore, we prove that the complexity class SPACE[s(n)] exactly characterizes the expressive power of a constant bit-size transformer with a context window of length s(n). Our approach relies on simulating Post machines, a Turing-complete computational model. Post machines can be modeled as automata equipped with a queue, exhibiting computational behaviors naturally aligned with those of transformers. The behavioral similarity between transformers and Post machines may offer new insights into the mechanisms underlying the reasoning abilities of transformers.

Hallucination has been widely recognized to be a significant drawback for large language models (LLMs). There have been many works that attempt to reduce the extent of hallucination. These efforts have mostly been empirical so far, which cannot answer the fundamental question whether it can be completely eliminated. In this paper, we formalize the problem and show that it is impossible to eliminate hallucination in LLMs. Specifically, we define a formal world where hallucination is defined as inconsistencies between a computable LLM and a computable ground truth function. By employing results from learning theory, we show that LLMs cannot learn all of the computable functions and will therefore always hallucinate. Since the formal world is a part of the real world which is much more complicated, hallucinations are also inevitable for real world LLMs. Furthermore, for real world LLMs constrained by provable time complexity, we describe the hallucination-prone tasks and empirically validate our claims. Finally, using the formal world framework, we discuss the possible mechanisms and efficacies of existing hallucination mitigators as well as the practical implications on the safe deployment of LLMs.

Planet-scale image geolocalization remains a challenging problem due to the diversity of images originating from anywhere in the world. Although approaches based on vision transformers have made significant progress in geolocalization accuracy, success in prior literature is constrained to narrow distributions of images of landmarks, and performance has not generalized to unseen places. We present a new geolocalization system that combines semantic geocell creation, multi-task contrastive pretraining, and a novel loss function. Additionally, our work is the first to perform retrieval over location clusters for guess refinements. We train two models for evaluations on street-level data and general-purpose image geolocalization; the first model, PIGEON, is trained on data from the game of Geoguessr and is capable of placing over 40% of its guesses within 25 kilometers of the target location globally. We also develop a bot and deploy PIGEON in a blind experiment against humans, ranking in the top 0.01% of players. We further challenge one of the world's foremost professional Geoguessr players to a series of six matches with millions of viewers, winning all six games. Our second model, PIGEOTTO, differs in that it is trained on a dataset of images from Flickr and Wikipedia, achieving state-of-the-art results on a wide range of image geolocalization benchmarks, outperforming the previous SOTA by up to 7.7 percentage points on the city accuracy level and up to 38.8 percentage points on the country level. Our findings suggest that PIGEOTTO is the first image geolocalization model that effectively generalizes to unseen places and that our approach can pave the way for highly accurate, planet-scale image geolocalization systems. Our code is available on GitHub.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of n variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the problem of learning the best polytree is NP-hard, we study which restrictions make it more tractable by considering for example in-degree bounds, properties of score functions measuring the quality of a polytree, and approximation algorithms. We devise an algorithm that finds the optimal polytree in time O((2+ε)^n) for arbitrarily small ε> 0 and any constant in-degree bound k, improving over the fastest previously known algorithm of time complexity O(3^n). We further give polynomial-time algorithms for finding a polytree whose score is within a factor of k from the optimal one for arbitrary scores and a factor of 2 for additive ones. Many of the results are complemented by (nearly) tight lower bounds for either the time complexity or the approximation factors.

We show that a variety of modern deep learning tasks exhibit a "double-descent" phenomenon where, as we increase model size, performance first gets worse and then gets better. Moreover, we show that double descent occurs not just as a function of model size, but also as a function of the number of training epochs. We unify the above phenomena by defining a new complexity measure we call the effective model complexity and conjecture a generalized double descent with respect to this measure. Furthermore, our notion of model complexity allows us to identify certain regimes where increasing (even quadrupling) the number of train samples actually hurts test performance.

We consider the task of mapping pseudocode to long programs that are functionally correct. Given test cases as a mechanism to validate programs, we search over the space of possible translations of the pseudocode to find a program that passes the validation. However, without proper credit assignment to localize the sources of program failures, it is difficult to guide search toward more promising programs. We propose to perform credit assignment based on signals from compilation errors, which constitute 88.7% of program failures. Concretely, we treat the translation of each pseudocode line as a discrete portion of the program, and whenever a synthesized program fails to compile, an error localization method tries to identify the portion of the program responsible for the failure. We then focus search over alternative translations of the pseudocode for those portions. For evaluation, we collected the SPoC dataset (Search-based Pseudocode to Code) containing 18,356 programs with human-authored pseudocode and test cases. Under a budget of 100 program compilations, performing search improves the synthesis success rate over using the top-one translation of the pseudocode from 25.6% to 44.7%.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which provides intermediate reasoning steps together with the final output, has emerged as a powerful empirical technique, underpinning much of the recent progress in the reasoning capabilities of large language models. This paper develops a statistical theory of learning under CoT supervision. A key characteristic of the CoT setting, in contrast to standard supervision, is the mismatch between the training objective (CoT risk) and the test objective (end-to-end risk). A central part of our analysis, distinguished from prior work, is explicitly linking those two types of risk to achieve sharper sample complexity bounds. This is achieved via the *CoT information measure* I_{D, h_star}^{CoT}(epsilon; calH), which quantifies the additional discriminative power gained from observing the reasoning process. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard E2E supervision. Specifically, it is shown that the sample complexity required to achieve a target E2E error epsilon scales as d/I_{D, h_star}^{CoT}(epsilon; calH), where d is a measure of hypothesis class complexity, which can be much faster than standard d/epsilon rates. Information-theoretic lower bounds in terms of the CoT information are also obtained. Together, these results suggest that CoT information is a fundamental measure of statistical complexity for learning under chain-of-thought supervision.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

Previous methods for image geo-localization have typically treated the task as either classification or retrieval, often relying on black-box decisions that lack interpretability. The rise of large vision-language models (LVLMs) has enabled a rethinking of geo-localization as a reasoning-driven task grounded in visual cues. However, two major challenges persist. On the data side, existing reasoning-focused datasets are primarily based on street-view imagery, offering limited scene diversity and constrained viewpoints. On the modeling side, current approaches predominantly rely on supervised fine-tuning, which yields only marginal improvements in reasoning capabilities. To address these challenges, we propose a novel pipeline that constructs a reasoning-oriented geo-localization dataset, MP16-Reason, using diverse social media images. We introduce GLOBE, Group-relative policy optimization for Localizability assessment and Optimized visual-cue reasoning, yielding Bi-objective geo-Enhancement for the VLM in recognition and reasoning. GLOBE incorporates task-specific rewards that jointly enhance localizability assessment, visual-cue reasoning, and geolocation accuracy. Both qualitative and quantitative results demonstrate that GLOBE outperforms state-of-the-art open-source LVLMs on geo-localization tasks, particularly in diverse visual scenes, while also generating more insightful and interpretable reasoning trajectories. The data and code are available at https://github.com/lingli1996/GLOBE.

We study the memorization power of feedforward ReLU neural networks. We show that such networks can memorize any N points that satisfy a mild separability assumption using Oleft(Nright) parameters. Known VC-dimension upper bounds imply that memorizing N samples requires Omega(N) parameters, and hence our construction is optimal up to logarithmic factors. We also give a generalized construction for networks with depth bounded by 1 leq L leq N, for memorizing N samples using O(N/L) parameters. This bound is also optimal up to logarithmic factors. Our construction uses weights with large bit complexity. We prove that having such a large bit complexity is both necessary and sufficient for memorization with a sub-linear number of parameters.

Minimum Bayes Risk (MBR) decoding is a text generation technique that has been shown to improve the quality of machine translations, but is expensive, even if a sampling-based approximation is used. Besides requiring a large number of sampled sequences, it requires the pairwise calculation of a utility metric, which has quadratic complexity. In this paper, we propose to approximate pairwise metric scores with scores calculated against aggregated reference representations. This changes the complexity of utility estimation from O(n^2) to O(n), while empirically preserving most of the quality gains of MBR decoding. We release our source code at https://github.com/ZurichNLP/mbr

Understanding when learning is statistically possible yet computationally hard is a central challenge in high-dimensional statistics. In this work, we investigate this question in the context of single- and multi-index models, classes of functions widely studied as benchmarks to probe the ability of machine learning methods to discover features in high-dimensional data. Our main contribution is to show that a Noise Sensitivity Exponent (NSE) - a simple quantity determined by the activation function - governs the existence and magnitude of statistical-to-computational gaps within a broad regime of these models. We first establish that, in single-index models with large additive noise, the onset of a computational bottleneck is fully characterized by the NSE. We then demonstrate that the same exponent controls a statistical-computational gap in the specialization transition of large separable multi-index models, where individual components become learnable. Finally, in hierarchical multi-index models, we show that the NSE governs the optimal computational rate in which different directions are sequentially learned. Taken together, our results identify the NSE as a unifying property linking noise robustness, computational hardness, and feature specialization in high-dimensional learning.

According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple encodings to find the most predictive one. Inspired by Kolmogorov Complexity principles, we propose a single-pass adaptive tokenizer, KARL, which predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL's training procedure closely resembles the Upside-Down Reinforcement Learning paradigm, as it learns to conditionally predict token halting based on a desired reconstruction quality. KARL matches the performance of recent adaptive tokenizers while operating in a single pass. We present scaling laws for KARL, analyzing the role of encoder/decoder size, continuous vs. discrete tokenization and more. Additionally, we offer a conceptual study drawing an analogy between Adaptive Image Tokenization and Algorithmic Information Theory, examining the predicted image complexity (KC) across axes such as structure vs. noise and in- vs. out-of-distribution familiarity -- revealing alignment with human intuition.

Image geolocalization, in which, traditionally, an AI model predicts the precise GPS coordinates of an image is a challenging task with many downstream applications. However, the user cannot utilize the model to further their knowledge other than the GPS coordinate; the model lacks an understanding of the location and the conversational ability to communicate with the user. In recent days, with tremendous progress of large multimodal models (LMMs) proprietary and open-source researchers have attempted to geolocalize images via LMMs. However, the issues remain unaddressed; beyond general tasks, for more specialized downstream tasks, one of which is geolocalization, LMMs struggle. In this work, we propose to solve this problem by introducing a conversational model GAEA that can provide information regarding the location of an image, as required by a user. No large-scale dataset enabling the training of such a model exists. Thus we propose a comprehensive dataset GAEA with 800K images and around 1.6M question answer pairs constructed by leveraging OpenStreetMap (OSM) attributes and geographical context clues. For quantitative evaluation, we propose a diverse benchmark comprising 4K image-text pairs to evaluate conversational capabilities equipped with diverse question types. We consider 11 state-of-the-art open-source and proprietary LMMs and demonstrate that GAEA significantly outperforms the best open-source model, LLaVA-OneVision by 25.69% and the best proprietary model, GPT-4o by 8.28%. Our dataset, model and codes are available

We present algorithms for diffusion model sampling which obtain δ-error in polylog(1/δ) steps, given access to widetilde O(δ)-accurate score estimates in L^2. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is widetilde O(d_star polylog(1/δ)) where d_star is the intrinsic dimension of the data. Further, under a non-uniform L-Lipschitz condition, the complexity reduces to widetilde O(L polylog(1/δ)). Our approach also yields the first polylog(1/δ) complexity sampler for general log-concave distributions using only gradient evaluations.

We present a scalable 3D reconstruction model that addresses a critical limitation in offline feed-forward methods: their computational and memory requirements grow quadratically w.r.t. the number of input images. Our approach is built on the key insight that this bottleneck stems from the varying-length Key-Value (KV) space representation of scene geometry, which we distill into a fixed-size Multi-Layer Perceptron (MLP) via test-time training. VGG-T^3 (Visual Geometry Grounded Test Time Training) scales linearly w.r.t. the number of input views, similar to online models, and reconstructs a 1k image collection in just 54 seconds, achieving a 11.6times speed-up over baselines that rely on softmax attention. Since our method retains global scene aggregation capability, our point map reconstruction error outperforming other linear-time methods by large margins. Finally, we demonstrate visual localization capabilities of our model by querying the scene representation with unseen images.

We revisit the I/O complexity of attention in large language models. Given query-key-value matrices Q,K,VinR^{ntimes d}, and a machine with fast memory size M, the goal is to compute the "attention matrix" A=softmax(Q K ^{top}/d) V with the minimal number of data transfers between fast and slow memory. Existing methods in the literature, most notably FlashAttention and its variants, incur an I/O cost that depends quadratically on n, while a trivial lower bound only requires Ω(nd) I/O's to read the inputs and write the output. In this work, we present a technique for computing attention where the I/O cost only depends almost-linearly on n in most parameter regimes. This is achieved by developing I/O-efficient algorithms inspired by the recent approximate attention framework of Alman and Song. We also prove corresponding lower bounds in each parameter regime to show that our algorithms are indeed close to I/O-optimal.

What are the root causes of hallucinations in large language models (LLMs)? We use Communication Complexity to prove that the Transformer layer is incapable of composing functions (e.g., identify a grandparent of a person in a genealogy) if the domains of the functions are large enough; we show through examples that this inability is already empirically present when the domains are quite small. We also point out that several mathematical tasks that are at the core of the so-called compositional tasks thought to be hard for LLMs are unlikely to be solvable by Transformers, for large enough instances and assuming that certain well accepted conjectures in the field of Computational Complexity are true.

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

In this paper, we propose new randomized algorithms for estimating the two-to-infinity and one-to-two norms in a matrix-free setting, using only matrix-vector multiplications. Our methods are based on appropriate modifications of Hutchinson's diagonal estimator and its Hutch++ version. We provide oracle complexity bounds for both modifications. We further illustrate the practical utility of our algorithms for Jacobian-based regularization in deep neural network training on image classification tasks. We also demonstrate that our methodology can be applied to mitigate the effect of adversarial attacks in the domain of recommender systems.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

We address the problem of optimizing a Brownian motion. We consider a (random) realization W of a Brownian motion with input space in [0,1]. Given W, our goal is to return an ε-approximation of its maximum using the smallest possible number of function evaluations, the sample complexity of the algorithm. We provide an algorithm with sample complexity of order log^2(1/ε). This improves over previous results of Al-Mharmah and Calvin (1996) and Calvin et al. (2017) which provided only polynomial rates. Our algorithm is adaptive---each query depends on previous values---and is an instance of the optimism-in-the-face-of-uncertainty principle.

Localizing individuals in crowds is more in accordance with the practical demands of subsequent high-level crowd analysis tasks than simply counting. However, existing localization based methods relying on intermediate representations (i.e., density maps or pseudo boxes) serving as learning targets are counter-intuitive and error-prone. In this paper, we propose a purely point-based framework for joint crowd counting and individual localization. For this framework, instead of merely reporting the absolute counting error at image level, we propose a new metric, called density Normalized Average Precision (nAP), to provide more comprehensive and more precise performance evaluation. Moreover, we design an intuitive solution under this framework, which is called Point to Point Network (P2PNet). P2PNet discards superfluous steps and directly predicts a set of point proposals to represent heads in an image, being consistent with the human annotation results. By thorough analysis, we reveal the key step towards implementing such a novel idea is to assign optimal learning targets for these proposals. Therefore, we propose to conduct this crucial association in an one-to-one matching manner using the Hungarian algorithm. The P2PNet not only significantly surpasses state-of-the-art methods on popular counting benchmarks, but also achieves promising localization accuracy. The codes will be available at: https://github.com/TencentYoutuResearch/CrowdCounting-P2PNet.

The end-to-end nature of neural machine translation (NMT) removes many ways of manually guiding the translation process that were available in older paradigms. Recent work, however, has introduced a new capability: lexically constrained or guided decoding, a modification to beam search that forces the inclusion of pre-specified words and phrases in the output. However, while theoretically sound, existing approaches have computational complexities that are either linear (Hokamp and Liu, 2017) or exponential (Anderson et al., 2017) in the number of constraints. We present a algorithm for lexically constrained decoding with a complexity of O(1) in the number of constraints. We demonstrate the algorithms remarkable ability to properly place these constraints, and use it to explore the shaky relationship between model and BLEU scores. Our implementation is available as part of Sockeye.

Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where good belief representations and heuristics are critical for scaling up. In this work, a different formulation is introduced for conformant problems with deterministic actions where they are automatically converted into classical ones and solved by an off-the-shelf classical planner. The translation maps literals L and sets of assumptions t about the initial situation, into new literals KL/t that represent that L must be true if t is initially true. We lay out a general translation scheme that is sound and establish the conditions under which the translation is also complete. We show that the complexity of the complete translation is exponential in a parameter of the problem called the conformant width, which for most benchmarks is bounded. The planner based on this translation exhibits good performance in comparison with existing planners, and is the basis for T0, the best performing planner in the Conformant Track of the 2006 International Planning Competition.

Text-to-image models give rise to workflows which often begin with an exploration step, where users sift through a large collection of generated images. The global nature of the text-to-image generation process prevents users from narrowing their exploration to a particular object in the image. In this paper, we present a technique to generate a collection of images that depicts variations in the shape of a specific object, enabling an object-level shape exploration process. Creating plausible variations is challenging as it requires control over the shape of the generated object while respecting its semantics. A particular challenge when generating object variations is accurately localizing the manipulation applied over the object's shape. We introduce a prompt-mixing technique that switches between prompts along the denoising process to attain a variety of shape choices. To localize the image-space operation, we present two techniques that use the self-attention layers in conjunction with the cross-attention layers. Moreover, we show that these localization techniques are general and effective beyond the scope of generating object variations. Extensive results and comparisons demonstrate the effectiveness of our method in generating object variations, and the competence of our localization techniques.

Geolocation, the task of identifying an image's location, requires complex reasoning and is crucial for navigation, monitoring, and cultural preservation. However, current methods often produce coarse, imprecise, and non-interpretable localization. A major challenge lies in the quality and scale of existing geolocation datasets. These datasets are typically small-scale and automatically constructed, leading to noisy data and inconsistent task difficulty, with images that either reveal answers too easily or lack sufficient clues for reliable inference. To address these challenges, we introduce a comprehensive geolocation framework with three key components: GeoComp, a large-scale dataset; GeoCoT, a novel reasoning method; and GeoEval, an evaluation metric, collectively designed to address critical challenges and drive advancements in geolocation research. At the core of this framework is GeoComp (Geolocation Competition Dataset), a large-scale dataset collected from a geolocation game platform involving 740K users over two years. It comprises 25 million entries of metadata and 3 million geo-tagged locations spanning much of the globe, with each location annotated thousands to tens of thousands of times by human users. The dataset offers diverse difficulty levels for detailed analysis and highlights key gaps in current models. Building on this dataset, we propose Geographical Chain-of-Thought (GeoCoT), a novel multi-step reasoning framework designed to enhance the reasoning capabilities of Large Vision Models (LVMs) in geolocation tasks. GeoCoT improves performance by integrating contextual and spatial cues through a multi-step process that mimics human geolocation reasoning. Finally, using the GeoEval metric, we demonstrate that GeoCoT significantly boosts geolocation accuracy by up to 25% while enhancing interpretability.

In-context localization (ICL) seeks to localize a target object specified by a small set of support examples in a query image, operating on the fly without training or parameter updates. Despite rapid advances in vision-language models (VLMs), achieving category-agnostic and visually grounded ICL remains an open problem, even though it is essential for applications such as image editing, personalized visual search, and retrieval. Existing methods are fragile and rely on explicit category supervision, which not only limits applicability in realistic settings with unnamed or instance-specific objects but also introduces category bias that steers predictions toward semantic priors rather than visual evidence. We introduce a two-stage training framework that explicitly optimizes in-context attention between support bounding boxes and query images without category supervision. We further refine localization via reinforcement learning using Group Relative Policy Optimization (GRPO) to directly minimize localization error. This formulation enforces visual correspondence over semantic priors, yielding robust instance-level localization. Empirically, a 7B-parameter model trained with our objectives outperforms models up to 72B parameters, demonstrating that context-aware localization objectives can surpass scaling alone. Comprehensive ablations validate the contribution of each component.

We present a novel framework for training large language models with continuously adjustable internal representations that span the full spectrum from localist (interpretable, rule-based) to distributed (generalizable, efficient) encodings. The key innovation is a locality dial, a tunable parameter that dynamically controls the degree of localization during both training and inference without requiring model retraining. This is achieved through group sparsity penalties on attention mechanisms, information-theoretic anchor design, and dynamic rule injection. We provide rigorous mathematical proofs establishing explicit threshold conditions under which attention provably concentrates on semantically relevant blocks, with exponential bounds on attention entropy and pointer fidelity. Specifically, we prove that when group sparsity penalties exceed certain threshold values, the model's attention mechanisms concentrate on semantically relevant blocks, achieving low entropy and high fidelity with negligible error. This framework enables practitioners to continuously interpolate between interpretable and high-performance modes, supporting applications in regulated domains requiring both transparency and capability.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of epsilon-optimal policies reaching a set S_L^{rightarrow} of incrementally L-controllable states. We introduce a novel layered decomposition of the set of incrementally L-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of mathcal{O}(LS^{rightarrow}_{L(1+epsilon)}Gamma_{L(1+epsilon)} A ln^{12}(S^{rightarrow}_{L(1+epsilon)})/epsilon^2), where S^{rightarrow}_{L(1+epsilon)} is the number of states that are incrementally L(1+epsilon)-controllable, A is the number of actions, and Gamma_{L(1+epsilon)} is the branching factor of the transitions over such states. LAE improves over the algorithm of Tarbouriech et al. (2020a) by a factor of L^2 and it is the first algorithm for AX that works in a countably-infinite state space. Moreover, we show that, under a certain identifiability assumption, LAE achieves minimax-optimal sample complexity of mathcal{O}(LS^{rightarrow}_{L}Aln^{12}(S^{rightarrow}_{L})/epsilon^2), outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

Worldwide geolocalization aims to locate the precise location at the coordinate level of photos taken anywhere on the Earth. It is very challenging due to 1) the difficulty of capturing subtle location-aware visual semantics, and 2) the heterogeneous geographical distribution of image data. As a result, existing studies have clear limitations when scaled to a worldwide context. They may easily confuse distant images with similar visual contents, or cannot adapt to various locations worldwide with different amounts of relevant data. To resolve these limitations, we propose G3, a novel framework based on Retrieval-Augmented Generation (RAG). In particular, G3 consists of three steps, i.e., Geo-alignment, Geo-diversification, and Geo-verification to optimize both retrieval and generation phases of worldwide geolocalization. During Geo-alignment, our solution jointly learns expressive multi-modal representations for images, GPS and textual descriptions, which allows us to capture location-aware semantics for retrieving nearby images for a given query. During Geo-diversification, we leverage a prompt ensembling method that is robust to inconsistent retrieval performance for different image queries. Finally, we combine both retrieved and generated GPS candidates in Geo-verification for location prediction. Experiments on two well-established datasets IM2GPS3k and YFCC4k verify the superiority of G3 compared to other state-of-the-art methods.

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 models on data with different corruption levels across three datasets ranging from 30,000 to approx 1.3M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~10% of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse than that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

Large language models exhibit a puzzling inconsistency: they solve complex problems yet frequently fail on seemingly simpler ones. We investigate whether LLMs internally encode problem difficulty in a way that aligns with human judgment, and whether this representation tracks generalization during reinforcement learning post-training. We train linear probes across layers and token positions on 60 models, evaluating on mathematical and coding subsets of Easy2HardBench. We find that human-labeled difficulty is strongly linearly decodable (AMC: rho approx 0.88) and exhibits clear model-size scaling, whereas LLM-derived difficulty is substantially weaker and scales poorly. Steering along the difficulty direction reveals that pushing models toward "easier" representations reduces hallucination and improves accuracy. During GRPO training on Qwen2.5-Math-1.5B, the human-difficulty probe strengthens and positively correlates with test accuracy across training steps, while the LLM-difficulty probe degrades and negatively correlates with performance. These results suggest that human annotations provide a stable difficulty signal that RL amplifies, while automated difficulty estimates derived from model performance become misaligned precisely as models improve. We release probe code and evaluation scripts to facilitate replication.

Weakly supervised object localization (WSOL) aims at predicting object locations in an image using only image-level category labels. Common challenges that image classification models encounter when localizing objects are, (a) they tend to look at the most discriminative features in an image that confines the localization map to a very small region, (b) the localization maps are class agnostic, and the models highlight objects of multiple classes in the same image and, (c) the localization performance is affected by background noise. To alleviate the above challenges we introduce the following simple changes through our proposed method ViTOL. We leverage the vision-based transformer for self-attention and introduce a patch-based attention dropout layer (p-ADL) to increase the coverage of the localization map and a gradient attention rollout mechanism to generate class-dependent attention maps. We conduct extensive quantitative, qualitative and ablation experiments on the ImageNet-1K and CUB datasets. We achieve state-of-the-art MaxBoxAcc-V2 localization scores of 70.47% and 73.17% on the two datasets respectively. Code is available on https://github.com/Saurav-31/ViTOL

In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with respect to diamond distance. For the former, we present an efficient average-case algorithm along with a nearly matching lower bound with respect to the number of observables to be predicted. For the latter, we present average-case query complexity lower bounds for learning classes of unitaries. We obtain an exponential lower bound for learning unitary 2-designs and a doubly exponential lower bound for Haar-random unitaries. Finally, we demonstrate the practical relevance of our access model by applying our learning algorithm to attack an authentication protocol using Classical-Readout Quantum Physically Unclonable Functions, partially addressing an important open question in quantum hardware security.

Large language models are typically trained by treating text as a single global distribution, often resulting in geographically homogenized behavior. We study metadata conditioning as a lightweight approach for localization, pre-training 31 models (at 0.5B and 1B parameter scales) from scratch on large-scale English news data annotated with verified URLs, country tags, and continent tags, covering 4 continents and 17 countries. Across four controlled experiments, we show that metadata conditioning consistently improves in-region performance without sacrificing cross-region generalization, enables global models to recover localization comparable to region-specific models, and improves learning efficiency. Our ablation studies demonstrate that URL-level metadata alone captures much of the geographic signal, while balanced regional data coverage remains essential, as metadata cannot fully compensate for missing regions. Finally, we introduce a downstream benchmark of 800 localized news MCQs and show that after instruction tuning, metadata conditioned global models achieve accuracy comparable to LLaMA-3.2-1B-Instruct, despite being trained on substantially less data. Together, these results establish metadata conditioning as a practical and compute-efficient approach for localization of language models.

Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we propose algorithmic enhancements and a topological hardness measure with implications for a broad class of search problems. As part of our study, we also address several open mathematical questions. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut-Kirby series (1981), and resolve various potential counterexamples in the Miller-Schupp series (1991), including three infinite subfamilies.

Language models learn a great quantity of factual information during pretraining, and recent work localizes this information to specific model weights like mid-layer MLP weights. In this paper, we find that we can change how a fact is stored in a model by editing weights that are in a different location than where existing methods suggest that the fact is stored. This is surprising because we would expect that localizing facts to specific model parameters would tell us where to manipulate knowledge in models, and this assumption has motivated past work on model editing methods. Specifically, we show that localization conclusions from representation denoising (also known as Causal Tracing) do not provide any insight into which model MLP layer would be best to edit in order to override an existing stored fact with a new one. This finding raises questions about how past work relies on Causal Tracing to select which model layers to edit. Next, we consider several variants of the editing problem, including erasing and amplifying facts. For one of our editing problems, editing performance does relate to localization results from representation denoising, but we find that which layer we edit is a far better predictor of performance. Our results suggest, counterintuitively, that better mechanistic understanding of how pretrained language models work may not always translate to insights about how to best change their behavior. Our code is available at https://github.com/google/belief-localization

Methods for knowledge editing and unlearning in large language models seek to edit or remove undesirable knowledge or capabilities without compromising general language modeling performance. This work investigates how mechanistic interpretability -- which, in part, aims to identify model components (circuits) associated to specific interpretable mechanisms that make up a model capability -- can improve the precision and effectiveness of editing and unlearning. We find a stark difference in unlearning and edit robustness when training components localized by different methods. We highlight an important distinction between methods that localize components based primarily on preserving outputs, and those finding high level mechanisms with predictable intermediate states. In particular, localizing edits/unlearning to components associated with the lookup-table mechanism for factual recall 1) leads to more robust edits/unlearning across different input/output formats, and 2) resists attempts to relearn the unwanted information, while also reducing unintended side effects compared to baselines, on both a sports facts dataset and the CounterFact dataset across multiple models. We also find that certain localized edits disrupt the latent knowledge in the model more than any other baselines, making unlearning more robust to various attacks.