Daily Papers

Circular polarization of the Cosmic Microwave Background (CMB) offers the possibility of detecting rotations of the universe and magnetic fields in the primeval universe or in distant clusters of galaxies. We used the Milano Polarimeter (MIPOL) installed at the Testa Grigia Observatory, on the italian Alps, to improve the existing upper limits to the CMB circular polarization at large angular scales. We obtain 95% confidence level upper limits to the degree of the CMB circular polarization ranging between 5.0x10^{-4} and 0.7x10^{-4} at angular scales between 8 and 24 deg, improving by one order of magnitude preexisting upper limits at large angular scales. Our results are still far from the nK region where today expectations place the amplitude of the V Stokes parameter used to characterize circular polarization of the CMB but improve the preexisting limit at similar angular scales. Our observations offered also the opportunity of characterizing the atmospheric emission at 33 GHz at the Testa Grigia Observatory.

Continual Pre-Training (CPT) on Large Language Models (LLMs) has been widely used to expand the model's fundamental understanding of specific downstream domains (e.g., math and code). For the CPT on domain-specific LLMs, one important question is how to choose the optimal mixture ratio between the general-corpus (e.g., Dolma, Slim-pajama) and the downstream domain-corpus. Existing methods usually adopt laborious human efforts by grid-searching on a set of mixture ratios, which require high GPU training consumption costs. Besides, we cannot guarantee the selected ratio is optimal for the specific domain. To address the limitations of existing methods, inspired by the Scaling Law for performance prediction, we propose to investigate the Scaling Law of the Domain-specific Continual Pre-Training (D-CPT Law) to decide the optimal mixture ratio with acceptable training costs for LLMs of different sizes. Specifically, by fitting the D-CPT Law, we can easily predict the general and downstream performance of arbitrary mixture ratios, model sizes, and dataset sizes using small-scale training costs on limited experiments. Moreover, we also extend our standard D-CPT Law on cross-domain settings and propose the Cross-Domain D-CPT Law to predict the D-CPT law of target domains, where very small training costs (about 1% of the normal training costs) are needed for the target domains. Comprehensive experimental results on six downstream domains demonstrate the effectiveness and generalizability of our proposed D-CPT Law and Cross-Domain D-CPT Law.

Database administrators (DBAs) play an important role in managing, maintaining and optimizing database systems. However, it is hard and tedious for DBAs to manage a large number of databases and give timely response (waiting for hours is intolerable in many online cases). In addition, existing empirical methods only support limited diagnosis scenarios, which are also labor-intensive to update the diagnosis rules for database version updates. Recently large language models (LLMs) have shown great potential in various fields. Thus, we propose D-Bot, an LLM-based database diagnosis system that can automatically acquire knowledge from diagnosis documents, and generate reasonable and well-founded diagnosis report (i.e., identifying the root causes and solutions) within acceptable time (e.g., under 10 minutes compared to hours by a DBA). The techniques in D-Bot include (i) offline knowledge extraction from documents, (ii) automatic prompt generation (e.g., knowledge matching, tool retrieval), (iii) root cause analysis using tree search algorithm, and (iv) collaborative mechanism for complex anomalies with multiple root causes. We verify D-Bot on real benchmarks (including 539 anomalies of six typical applications), and the results show that D-Bot can effectively analyze the root causes of unseen anomalies and significantly outperforms traditional methods and vanilla models like GPT-4.

We present AnyHand, a large-scale synthetic dataset designed to advance the state of the art in 3D hand pose estimation from both RGB-only and RGB-D inputs. While recent works with foundation approaches have shown that an increase in the quantity and diversity of training data can markedly improve performance and robustness in hand pose estimation, existing real-world-collected datasets on this task are limited in coverage, and prior synthetic datasets rarely provide occlusions, arm details, and aligned depth together at scale. To address this bottleneck, our AnyHand contains 2.5M single-hand and 4.1M hand-object interaction RGB-D images, with rich geometric annotations. In the RGB-only setting, we show that extending the original training sets of existing baselines with AnyHand yields significant gains on multiple benchmarks (FreiHAND and HO-3D), even when keeping the architecture and training scheme fixed. More impressively, the model trained with AnyHand shows stronger generalization to the out-of-domain HO-Cap dataset, without any fine-tuning. We also contribute a lightweight depth fusion module that can be easily integrated into existing RGB-based models. Trained with AnyHand, the resulting RGB-D model achieves superior performance on the HO-3D benchmark, showing the benefits of depth integration and the effectiveness of our synthetic data.

Large language models (LLMs) have garnered significant attention and widespread usage due to their impressive performance in various tasks. However, they are not without their own set of challenges, including issues such as hallucinations, factual inconsistencies, and limitations in numerical-quantitative reasoning. Evaluating LLMs in miscellaneous reasoning tasks remains an active area of research. Prior to the breakthrough of LLMs, Transformers had already proven successful in the medical domain, effectively employed for various natural language understanding (NLU) tasks. Following this trend, LLMs have also been trained and utilized in the medical domain, raising concerns regarding factual accuracy, adherence to safety protocols, and inherent limitations. In this paper, we focus on evaluating the natural language inference capabilities of popular open-source and closed-source LLMs using clinical trial reports as the dataset. We present the performance results of each LLM and further analyze their performance on a development set, particularly focusing on challenging instances that involve medical abbreviations and require numerical-quantitative reasoning. Gemini, our leading LLM, achieved a test set F1-score of 0.748, securing the ninth position on the task scoreboard. Our work is the first of its kind, offering a thorough examination of the inference capabilities of LLMs within the medical domain.

Accurate and interpretable gait analysis plays a crucial role in the early detection of Parkinsons disease (PD),yet most existing approaches remain limited by single-modality inputs, low robustness, and a lack of clinical transparency. This paper presents an explainable multimodal framework that integrates RGB and Depth (RGB-D) data to recognize Parkinsonian gait patterns under realistic conditions. The proposed system employs dual YOLOv11-based encoders for modality-specific feature extraction, followed by a Multi-Scale Local-Global Extraction (MLGE) module and a Cross-Spatial Neck Fusion mechanism to enhance spatial-temporal representation. This design captures both fine-grained limb motion (e.g., reduced arm swing) and overall gait dynamics (e.g., short stride or turning difficulty), even in challenging scenarios such as low lighting or occlusion caused by clothing. To ensure interpretability, a frozen Large Language Model (LLM) is incorporated to translate fused visual embeddings and structured metadata into clinically meaningful textual explanations. Experimental evaluations on multimodal gait datasets demonstrate that the proposed RGB-D fusion framework achieves higher recognition accuracy, improved robustness to environmental variations, and clear visual-linguistic reasoning compared with single-input baselines. By combining multimodal feature learning with language-based interpretability, this study bridges the gap between visual recognition and clinical understanding, offering a novel vision-language paradigm for reliable and explainable Parkinsons disease gait analysis. Code:https://github.com/manaralnaasan/RGB-D_parkinson-LLM

Traditional approaches for Visual Question Answering (VQA) require large amount of labeled data for training. Unfortunately, such large scale data is usually not available for medical domain. In this paper, we propose a novel medical VQA framework that overcomes the labeled data limitation. The proposed framework explores the use of the unsupervised Denoising Auto-Encoder (DAE) and the supervised Meta-Learning. The advantage of DAE is to leverage the large amount of unlabeled images while the advantage of Meta-Learning is to learn meta-weights that quickly adapt to VQA problem with limited labeled data. By leveraging the advantages of these techniques, it allows the proposed framework to be efficiently trained using a small labeled training set. The experimental results show that our proposed method significantly outperforms the state-of-the-art medical VQA.

This research explores the application of large language models (LLMs) to generate synthetic datasets for Product Desirability Toolkit (PDT) testing, a key component in evaluating user sentiment and product experience. Utilizing gpt-4o-mini, a cost-effective alternative to larger commercial LLMs, three methods, Word+Review, Review+Word, and Supply-Word, were each used to synthesize 1000 product reviews. The generated datasets were assessed for sentiment alignment, textual diversity, and data generation cost. Results demonstrated high sentiment alignment across all methods, with Pearson correlations ranging from 0.93 to 0.97. Supply-Word exhibited the highest diversity and coverage of PDT terms, although with increased generation costs. Despite minor biases toward positive sentiments, in situations with limited test data, LLM-generated synthetic data offers significant advantages, including scalability, cost savings, and flexibility in dataset production.

Advances in deep generative modeling have made it increasingly plausible to train human-level embodied agents. Yet progress has been limited by the absence of large-scale, real-time, multi-modal, and socially interactive datasets that reflect the sensory-motor complexity of natural environments. To address this, we present PLAICraft, a novel data collection platform and dataset capturing multiplayer Minecraft interactions across five time-aligned modalities: video, game output audio, microphone input audio, mouse, and keyboard actions. Each modality is logged with millisecond time precision, enabling the study of synchronous, embodied behaviour in a rich, open-ended world. The dataset comprises over 10,000 hours of gameplay from more than 10,000 global participants. Alongside the dataset, we provide an evaluation suite for benchmarking model capabilities in object recognition, spatial awareness, language grounding, and long-term memory. PLAICraft opens a path toward training and evaluating agents that act fluently and purposefully in real time, paving the way for truly embodied artificial intelligence.

The next Point of Interest (POI) recommendation task is to predict users' immediate next POI visit given their historical data. Location-Based Social Network (LBSN) data, which is often used for the next POI recommendation task, comes with challenges. One frequently disregarded challenge is how to effectively use the abundant contextual information present in LBSN data. Previous methods are limited by their numerical nature and fail to address this challenge. In this paper, we propose a framework that uses pretrained Large Language Models (LLMs) to tackle this challenge. Our framework allows us to preserve heterogeneous LBSN data in its original format, hence avoiding the loss of contextual information. Furthermore, our framework is capable of comprehending the inherent meaning of contextual information due to the inclusion of commonsense knowledge. In experiments, we test our framework on three real-world LBSN datasets. Our results show that the proposed framework outperforms the state-of-the-art models in all three datasets. Our analysis demonstrates the effectiveness of the proposed framework in using contextual information as well as alleviating the commonly encountered cold-start and short trajectory problems.

Large language models (LLMs) pretrained on vast source code have achieved prominent progress in code intelligence. However, existing code LLMs have two main limitations in terms of architecture and pretraining tasks. First, they often adopt a specific architecture (encoder-only or decoder-only) or rely on a unified encoder-decoder network for different downstream tasks. The former paradigm is limited by inflexibility in applications while in the latter, the model is treated as a single system for all tasks, leading to suboptimal performance on a subset of tasks. Secondly, they often employ a limited set of pretraining objectives which might not be relevant to some downstream tasks and hence result in substantial performance degrade. To address these limitations, we propose ``CodeT5+'', a family of encoder-decoder LLMs for code in which component modules can be flexibly combined to suit a wide range of downstream code tasks. Such flexibility is enabled by our proposed mixture of pretraining objectives to mitigate the pretrain-finetune discrepancy. These objectives cover span denoising, contrastive learning, text-code matching, and causal LM pretraining tasks, on both unimodal and bimodal multilingual code corpora. Furthermore, we propose to initialize CodeT5+ with frozen off-the-shelf LLMs without training from scratch to efficiently scale up our models, and explore instruction-tuning to align with natural language instructions. We extensively evaluate CodeT5+ on over 20 code-related benchmarks in different settings, including zero-shot, finetuning, and instruction-tuning. We observe state-of-the-art (SoTA) model performance on various code-related tasks, such as code generation and completion, math programming, and text-to-code retrieval tasks. Particularly, our instruction-tuned CodeT5+ 16B achieves new SoTA results on HumanEval code generation task against other open code LLMs.

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This begs the question: Are these errors incidental, or do they signal more substantial limitations? In an attempt to demystify Transformers, we investigate the limits of these models across three representative compositional tasks -- multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. We formulate compositional tasks as computation graphs to systematically quantify the level of complexity, and break down reasoning steps into intermediate sub-procedures. Our empirical findings suggest that Transformers solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching, without necessarily developing systematic problem-solving skills. To round off our empirical study, we provide theoretical arguments on abstract multi-step reasoning problems that highlight how Transformers' performance will rapidly decay with increased task complexity.

Large Language Models (LLMs) are increasingly becoming ubiquitous, yet their ability to reason about and retain temporal information remains limited. This hinders their application in real-world scenarios where understanding the sequential nature of events is crucial. This paper experiments with state-of-the-art models on a novel, large-scale temporal dataset, TempUN, to reveal significant limitations in temporal retention and reasoning abilities. Interestingly, closed-source models indicate knowledge gaps more frequently, potentially suggesting a trade-off between uncertainty awareness and incorrect responses. Further, exploring various fine-tuning approaches yielded no major performance improvements. The associated dataset and code are available at the following URL (https://github.com/lingoiitgn/TempUN).

The generality of pretrained large language models (LLMs) has prompted increasing interest in their use as in-context learning agents. To be successful, such agents must form beliefs about how to achieve their goals based on limited interaction with their environment, resulting in uncertainty about the best action to take at each step. In this paper, we study how LLM agents form and act on these beliefs by conducting experiments in controlled sequential decision-making tasks. To begin, we find that LLM agents are overconfident: They draw strong conclusions about what to do based on insufficient evidence, resulting in inadequately explorative behavior. We dig deeper into this phenomenon and show how it emerges from a collapse in the entropy of the action distribution implied by sampling from the LLM. We then demonstrate that existing token-level sampling techniques are by themselves insufficient to make the agent explore more. Motivated by this fact, we introduce Entropic Activation Steering (EAST), an activation steering method for in-context LLM agents. EAST computes a steering vector as an entropy-weighted combination of representations, and uses it to manipulate an LLM agent's uncertainty over actions by intervening on its activations during the forward pass. We show that EAST can reliably increase the entropy in an LLM agent's actions, causing more explorative behavior to emerge. Finally, EAST modifies the subjective uncertainty an LLM agent expresses, paving the way to interpreting and controlling how LLM agents represent uncertainty about their decisions.

As the research community aims to build better AI assistants that are more dynamic and personalized to the diversity of humans that they interact with, there is increased interest in evaluating the theory of mind capabilities of large language models (LLMs). Indeed, several recent studies suggest that LLM theory of mind capabilities are quite impressive, approximating human-level performance. Our paper aims to rebuke this narrative and argues instead that past studies were not directly measuring agent performance, potentially leading to findings that are illusory in nature as a result. We draw a strong distinction between what we call literal theory of mind i.e. measuring the agent's ability to predict the behavior of others and functional theory of mind i.e. adapting to agents in-context based on a rational response to predictions of their behavior. We find that top performing open source LLMs may display strong capabilities in literal theory of mind, depending on how they are prompted, but seem to struggle with functional theory of mind -- even when partner policies are exceedingly simple. Our work serves to highlight the double sided nature of inductive bias in LLMs when adapting to new situations. While this bias can lead to strong performance over limited horizons, it often hinders convergence to optimal long-term behavior.

We present a re-discovery of G278.94+1.35 as possibly one of the largest known Galactic supernova remnants (SNR) - that we name Diprotodon. While previously established as a Galactic SNR, Diprotodon is visible in our new EMU and GLEAM radio continuum images at an angular size of 3.33x3.23 deg, much larger than previously measured. At the previously suggested distance of 2.7 kpc, this implies a diameter of 157x152 pc. This size would qualify Diprotodon as the largest known SNR and pushes our estimates of SNR sizes to the upper limits. We investigate the environment in which the SNR is located and examine various scenarios that might explain such a large and relatively bright SNR appearance. We find that Diprotodon is most likely at a much closer distance of sim1 kpc, implying its diameter is 58x56 pc and it is in the radiative evolutionary phase. We also present a new Fermi-LAT data analysis that confirms the angular extent of the SNR in gamma-rays. The origin of the high-energy emission remains somewhat puzzling, and the scenarios we explore reveal new puzzles, given this unexpected and unique observation of a seemingly evolved SNR having a hard GeV spectrum with no breaks. We explore both leptonic and hadronic scenarios, as well as the possibility that the high-energy emission arises from the leftover particle population of a historic pulsar wind nebula.

Audio pattern recognition is an important research topic in the machine learning area, and includes several tasks such as audio tagging, acoustic scene classification, music classification, speech emotion classification and sound event detection. Recently, neural networks have been applied to tackle audio pattern recognition problems. However, previous systems are built on specific datasets with limited durations. Recently, in computer vision and natural language processing, systems pretrained on large-scale datasets have generalized well to several tasks. However, there is limited research on pretraining systems on large-scale datasets for audio pattern recognition. In this paper, we propose pretrained audio neural networks (PANNs) trained on the large-scale AudioSet dataset. These PANNs are transferred to other audio related tasks. We investigate the performance and computational complexity of PANNs modeled by a variety of convolutional neural networks. We propose an architecture called Wavegram-Logmel-CNN using both log-mel spectrogram and waveform as input feature. Our best PANN system achieves a state-of-the-art mean average precision (mAP) of 0.439 on AudioSet tagging, outperforming the best previous system of 0.392. We transfer PANNs to six audio pattern recognition tasks, and demonstrate state-of-the-art performance in several of those tasks. We have released the source code and pretrained models of PANNs: https://github.com/qiuqiangkong/audioset_tagging_cnn.

Automatic evaluation is an integral aspect of dialogue system research. The traditional reference-based NLG metrics are generally found to be unsuitable for dialogue assessment. Consequently, recent studies have suggested various unique, reference-free neural metrics that better align with human evaluations. Notably among them, large language models (LLMs), particularly the instruction-tuned variants like ChatGPT, are shown to be promising substitutes for human judges. Yet, existing works on utilizing LLMs for automatic dialogue evaluation are limited in their scope in terms of the number of meta-evaluation datasets, mode of evaluation, coverage of LLMs, etc. Hence, it remains inconclusive how effective these LLMs are. To this end, we conduct a comprehensive study on the application of LLMs for automatic dialogue evaluation. Specifically, we analyze the multi-dimensional evaluation capability of 30 recently emerged LLMs at both turn and dialogue levels, using a comprehensive set of 12 meta-evaluation datasets. Additionally, we probe the robustness of the LLMs in handling various adversarial perturbations at both turn and dialogue levels. Finally, we explore how model-level and dimension-level ensembles impact the evaluation performance. All resources are available at https://github.com/e0397123/comp-analysis.

Foundation models and vision-language pre-training have significantly advanced Vision-Language Models (VLMs), enabling multimodal processing of visual and linguistic data. However, their application in domain-specific agricultural tasks, such as plant pathology, remains limited due to the lack of large-scale, comprehensive multimodal image--text datasets and benchmarks. To address this gap, we introduce LeafNet, a comprehensive multimodal dataset, and LeafBench, a visual question-answering benchmark developed to systematically evaluate the capabilities of VLMs in understanding plant diseases. The dataset comprises 186,000 leaf digital images spanning 97 disease classes, paired with metadata, generating 13,950 question-answer pairs spanning six critical agricultural tasks. The questions assess various aspects of plant pathology understanding, including visual symptom recognition, taxonomic relationships, and diagnostic reasoning. Benchmarking 12 state-of-the-art VLMs on our LeafBench dataset, we reveal substantial disparity in their disease understanding capabilities. Our study shows performance varies markedly across tasks: binary healthy--diseased classification exceeds 90% accuracy, while fine-grained pathogen and species identification remains below 65%. Direct comparison between vision-only models and VLMs demonstrates the critical advantage of multimodal architectures: fine-tuned VLMs outperform traditional vision models, confirming that integrating linguistic representations significantly enhances diagnostic precision. These findings highlight critical gaps in current VLMs for plant pathology applications and underscore the need for LeafBench as a rigorous framework for methodological advancement and progress evaluation toward reliable AI-assisted plant disease diagnosis. Code is available at https://github.com/EnalisUs/LeafBench.

The strong intervening absorption system at redshift 1.15 towards the very bright quasar HE 0515-4414 is the most studied absorber for measuring possible cosmological variations in the fine-structure constant, α. We observed HE 0515-4414 for 16.1,h with the Very Large Telescope and present here the first constraint on relative variations in α with parts-per-million (ppm) precision from the new ESPRESSO spectrograph: Δα/α= 1.3 pm 1.3_{rm stat} pm 0.4_{rm sys},{rm ppm}. The statistical uncertainty (1σ) is similar to the ensemble precision of previous large samples of absorbers, and derives from the high S/N achieved (approx105 per 0.4,km,s^{-1} pixel). ESPRESSO's design, and calibration of our observations with its laser frequency comb, effectively removed wavelength calibration errors from our measurement. The high resolving power of our ESPRESSO spectrum (R=145000) enabled the identification of very narrow components within the absorption profile, allowing a more robust analysis of Δα/α. The evidence for the narrow components is corroborated by their correspondence with previously detected molecular hydrogen and neutral carbon. The main remaining systematic errors arise from ambiguities in the absorption profile modelling, effects from redispersing the individual quasar exposures, and convergence of the parameter estimation algorithm. All analyses of the spectrum, including systematic error estimates, were initially blinded to avoid human biases. We make our reduced ESPRESSO spectrum of HE 0515-4414 publicly available for further analysis. Combining our ESPRESSO result with 28 measurements, from other spectrographs, in which wavelength calibration errors have been mitigated, yields a weighted mean Δα/α= -0.5 pm 0.5_{rm stat} pm 0.4_{rm sys},ppm at redshifts 0.6-2.4.

Biomedical data and benchmarks are highly valuable yet very limited in low-resource languages other than English such as Vietnamese. In this paper, we make use of a state-of-the-art translation model in English-Vietnamese to translate and produce both pretrained as well as supervised data in the biomedical domains. Thanks to such large-scale translation, we introduce ViPubmedT5, a pretrained Encoder-Decoder Transformer model trained on 20 million translated abstracts from the high-quality public PubMed corpus. ViPubMedT5 demonstrates state-of-the-art results on two different biomedical benchmarks in summarization and acronym disambiguation. Further, we release ViMedNLI - a new NLP task in Vietnamese translated from MedNLI using the recently public En-vi translation model and carefully refined by human experts, with evaluations of existing methods against ViPubmedT5.

Understanding entailment and contradiction is fundamental to understanding natural language, and inference about entailment and contradiction is a valuable testing ground for the development of semantic representations. However, machine learning research in this area has been dramatically limited by the lack of large-scale resources. To address this, we introduce the Stanford Natural Language Inference corpus, a new, freely available collection of labeled sentence pairs, written by humans doing a novel grounded task based on image captioning. At 570K pairs, it is two orders of magnitude larger than all other resources of its type. This increase in scale allows lexicalized classifiers to outperform some sophisticated existing entailment models, and it allows a neural network-based model to perform competitively on natural language inference benchmarks for the first time.

Over the last decades, excellent computational chemistry tools have been developed. Their full potential has not yet been reached as most are challenging to learn and exist in isolation. Recently, large-language models (LLMs) have shown strong performance in tasks across domains, but struggle with chemistry-related problems. Moreover, these models lack access to external knowledge sources, limiting their usefulness in scientific applications. In this study, we introduce ChemCrow, an LLM chemistry agent designed to accomplish tasks across organic synthesis, drug discovery, and materials design. By integrating 17 expert-designed tools, ChemCrow augments the LLM performance in chemistry, and new capabilities emerge. Our agent autonomously planned the syntheses of an insect repellent, three organocatalysts, as well as other relevant molecules. Our evaluation, including both LLM and expert assessments, demonstrates ChemCrow's effectiveness in automating a diverse set of chemical tasks. Surprisingly, we find that GPT-4 as an evaluator cannot distinguish between clearly wrong GPT-4 completions and Chemcrow's performance. There is a significant risk of misuse of tools like ChemCrow, and we discuss their potential harms. Employed responsibly, our work not only aids expert chemists and lowers barriers for non-experts, but also fosters scientific advancement by bridging the gap between experimental and computational chemistry. A subset of the code is publicly available at https://github.com/ur-whitelab/chemcrow-public.

Layering information spaces is a promising strategy to design intuitive and engaging interactive experiences. Although multi-layer displays enable promising interaction techniques through limited depth perception - achieved via slight separation between layers - it remains unclear how to fully design experiences that leverage the unique affordances of layered information. To address this, we introduce Proscenium, a dual-layer, large transparent display workspace setup with an adjustable separation between the layers. We demonstrate our preliminary design space focusing on how rendered information can be transitioned and linked across displays, and showcase 14 speculative experience prototypes across six categories.

Evidence to guide healthcare decisions is often limited by a lack of relevant and trustworthy literature as well as difficulty in contextualizing existing research for a specific patient. Large language models (LLMs) could potentially address both challenges by either summarizing published literature or generating new studies based on real-world data (RWD). We evaluated the ability of five LLM-based systems in answering 50 clinical questions and had nine independent physicians review the responses for relevance, reliability, and actionability. As it stands, general-purpose LLMs (ChatGPT-4, Claude 3 Opus, Gemini Pro 1.5) rarely produced answers that were deemed relevant and evidence-based (2% - 10%). In contrast, retrieval augmented generation (RAG)-based and agentic LLM systems produced relevant and evidence-based answers for 24% (OpenEvidence) to 58% (ChatRWD) of questions. Only the agentic ChatRWD was able to answer novel questions compared to other LLMs (65% vs. 0-9%). These results suggest that while general-purpose LLMs should not be used as-is, a purpose-built system for evidence summarization based on RAG and one for generating novel evidence working synergistically would improve availability of pertinent evidence for patient care.

The development of Large Language Models (LLMs) has predominantly focused on high-resource languages, leaving extremely low-resource languages like Irish with limited representation. This work presents UCCIX, a pioneering effort on the development of an open-source Irish-based LLM. We propose a novel framework for continued pre-training of LLMs specifically adapted for extremely low-resource languages, requiring only a fraction of the textual data typically needed for training LLMs according to scaling laws. Our model, based on Llama 2-13B, outperforms much larger models on Irish language tasks with up to 12% performance improvement, showcasing the effectiveness and efficiency of our approach. We also contribute comprehensive Irish benchmarking datasets, including IrishQA, a question-answering dataset, and Irish version of MT-bench. These datasets enable rigorous evaluation and facilitate future research in Irish LLM systems. Our work aims to preserve and promote the Irish language, knowledge, and culture of Ireland in the digital era while providing a framework for adapting LLMs to other indigenous languages.

In this study, we introduce ANGST, a novel, first-of-its kind benchmark for depression-anxiety comorbidity classification from social media posts. Unlike contemporary datasets that often oversimplify the intricate interplay between different mental health disorders by treating them as isolated conditions, ANGST enables multi-label classification, allowing each post to be simultaneously identified as indicating depression and/or anxiety. Comprising 2876 meticulously annotated posts by expert psychologists and an additional 7667 silver-labeled posts, ANGST posits a more representative sample of online mental health discourse. Moreover, we benchmark ANGST using various state-of-the-art language models, ranging from Mental-BERT to GPT-4. Our results provide significant insights into the capabilities and limitations of these models in complex diagnostic scenarios. While GPT-4 generally outperforms other models, none achieve an F1 score exceeding 72% in multi-class comorbid classification, underscoring the ongoing challenges in applying language models to mental health diagnostics.

Large Language Models (LLMs) based on transformer architectures have revolutionized a variety of domains, with tokenization playing a pivotal role in their pre-processing and fine-tuning stages. In multilingual models, particularly those tailored for Indic languages, effective tokenization is crucial for optimizing performance. This paper presents a comprehensive evaluation of tokenizers used by 12 LLMs across all 22 official languages of India, with a focus on comparing the efficiency of their tokenization processes. We employed the Normalized Sequence Length (NSL) as a key metric in our analysis. Our findings reveal that the SUTRA tokenizer outperforms all other models, including several Indic-specific models, excelling in 14 languages. Notable insights include the SUTRA tokenizer's superior handling of Indic languages, GPT-4o's advancement over its predecessor GPT-4 in processing Indian languages, and the limited performance of Project Indus in certain languages. This study underscores the critical importance of developing targeted tokenization strategies for multilingual and Indic-centric models, laying the groundwork for future improvements in tokenizer design to enhance linguistic coverage and model efficiency.

With the advent of large multimodal language models, science is now at a threshold of an AI-based technological transformation. Recently, a plethora of new AI models and tools has been proposed, promising to empower researchers and academics worldwide to conduct their research more effectively and efficiently. This includes all aspects of the research cycle, especially (1) searching for relevant literature; (2) generating research ideas and conducting experimentation; generating (3) text-based and (4) multimodal content (e.g., scientific figures and diagrams); and (5) AI-based automatic peer review. In this survey, we provide an in-depth overview over these exciting recent developments, which promise to fundamentally alter the scientific research process for good. Our survey covers the five aspects outlined above, indicating relevant datasets, methods and results (including evaluation) as well as limitations and scope for future research. Ethical concerns regarding shortcomings of these tools and potential for misuse (fake science, plagiarism, harms to research integrity) take a particularly prominent place in our discussion. We hope that our survey will not only become a reference guide for newcomers to the field but also a catalyst for new AI-based initiatives in the area of "AI4Science".

Automation in agriculture plays a vital role in addressing challenges related to crop monitoring and disease management, particularly through early detection systems. This study investigates the effectiveness of combining multimodal Large Language Models (LLMs), specifically GPT-4o, with Convolutional Neural Networks (CNNs) for automated plant disease classification using leaf imagery. Leveraging the PlantVillage dataset, we systematically evaluate model performance across zero-shot, few-shot, and progressive fine-tuning scenarios. A comparative analysis between GPT-4o and the widely used ResNet-50 model was conducted across three resolutions (100, 150, and 256 pixels) and two plant species (apple and corn). Results indicate that fine-tuned GPT-4o models achieved slightly better performance compared to the performance of ResNet-50, achieving up to 98.12% classification accuracy on apple leaf images, compared to 96.88% achieved by ResNet-50, with improved generalization and near-zero training loss. However, zero-shot performance of GPT-4o was significantly lower, underscoring the need for minimal training. Additional evaluations on cross-resolution and cross-plant generalization revealed the models' adaptability and limitations when applied to new domains. The findings highlight the promise of integrating multimodal LLMs into automated disease detection pipelines, enhancing the scalability and intelligence of precision agriculture systems while reducing the dependence on large, labeled datasets and high-resolution sensor infrastructure. Large Language Models, Vision Language Models, LLMs and CNNs, Disease Detection with Vision Language Models, VLMs

Purpose: Accurate segmentation of clinical target volumes (CTV) and organs-at-risk is crucial for optimizing gynecologic brachytherapy (GYN-BT) treatment planning. However, anatomical variability, low soft-tissue contrast in CT imaging, and limited annotated datasets pose significant challenges. This study presents GynBTNet, a novel multi-stage learning framework designed to enhance segmentation performance through self-supervised pretraining and hierarchical fine-tuning strategies. Methods: GynBTNet employs a three-stage training strategy: (1) self-supervised pretraining on large-scale CT datasets using sparse submanifold convolution to capture robust anatomical representations, (2) supervised fine-tuning on a comprehensive multi-organ segmentation dataset to refine feature extraction, and (3) task-specific fine-tuning on a dedicated GYN-BT dataset to optimize segmentation performance for clinical applications. The model was evaluated against state-of-the-art methods using the Dice Similarity Coefficient (DSC), 95th percentile Hausdorff Distance (HD95), and Average Surface Distance (ASD). Results: Our GynBTNet achieved superior segmentation performance, significantly outperforming nnU-Net and Swin-UNETR. Notably, it yielded a DSC of 0.837 +/- 0.068 for CTV, 0.940 +/- 0.052 for the bladder, 0.842 +/- 0.070 for the rectum, and 0.871 +/- 0.047 for the uterus, with reduced HD95 and ASD compared to baseline models. Self-supervised pretraining led to consistent performance improvements, particularly for structures with complex boundaries. However, segmentation of the sigmoid colon remained challenging, likely due to anatomical ambiguities and inter-patient variability. Statistical significance analysis confirmed that GynBTNet's improvements were significant compared to baseline models.

Gaussian Splatting has emerged as a high-performance technique for novel view synthesis, enabling real-time rendering and high-quality reconstruction of small scenes. However, scaling to larger environments has so far relied on partitioning the scene into chunks -- a strategy that introduces artifacts at chunk boundaries, complicates training across varying scales, and is poorly suited to unstructured scenarios such as city-scale flyovers combined with street-level views. Moreover, rendering remains fundamentally limited by GPU memory, as all visible chunks must reside in VRAM simultaneously. We introduce A LoD of Gaussians, a framework for training and rendering ultra-large-scale Gaussian scenes on a single consumer-grade GPU -- without partitioning. Our method stores the full scene out-of-core (e.g., in CPU memory) and trains a Level-of-Detail (LoD) representation directly, dynamically streaming only the relevant Gaussians. A hybrid data structure combining Gaussian hierarchies with Sequential Point Trees enables efficient, view-dependent LoD selection, while a lightweight caching and view scheduling system exploits temporal coherence to support real-time streaming and rendering. Together, these innovations enable seamless multi-scale reconstruction and interactive visualization of complex scenes -- from broad aerial views to fine-grained ground-level details.

Vision-threatening eye diseases pose a major global health burden, with timely diagnosis limited by workforce shortages and restricted access to specialized care. While multimodal large language models (MLLMs) show promise for medical image interpretation, advancing MLLMs for ophthalmology is hindered by the lack of comprehensive benchmark datasets suitable for evaluating generative models. We present a large-scale multimodal ophthalmology benchmark comprising 32,633 instances with multi-granular annotations across 12 common ophthalmic conditions and 5 imaging modalities. The dataset integrates imaging, anatomical structures, demographics, and free-text annotations, supporting anatomical structure recognition, disease screening, disease staging, and demographic prediction for bias evaluation. This work extends our preliminary LMOD benchmark with three major enhancements: (1) nearly 50% dataset expansion with substantial enlargement of color fundus photography; (2) broadened task coverage including binary disease diagnosis, multi-class diagnosis, severity classification with international grading standards, and demographic prediction; and (3) systematic evaluation of 24 state-of-the-art MLLMs. Our evaluations reveal both promise and limitations. Top-performing models achieved ~58% accuracy in disease screening under zero-shot settings, and performance remained suboptimal for challenging tasks like disease staging. We will publicly release the dataset, curation pipeline, and leaderboard to potentially advance ophthalmic AI applications and reduce the global burden of vision-threatening diseases.

Providing high-quality feedback is crucial for student success but is constrained by time, cost, and limited data availability. We introduce Synthetic Educational Feedback Loops (SEFL), a novel framework designed to deliver immediate, on-demand feedback at scale without relying on extensive, real-world student data. In SEFL, two large language models (LLMs) operate in teacher--student roles to simulate assignment completion and formative feedback, generating abundant synthetic pairs of student work and corresponding critiques. We then fine-tune smaller, more computationally efficient LLMs on these synthetic pairs, enabling them to replicate key features of high-quality, goal-oriented feedback. Unlike personalized tutoring approaches that offer multi-turn, individualized instruction, SEFL specifically focuses on replicating the teacher-->student feedback loop for diverse assignments. Through both LLM-as-a-judge and human evaluations, we demonstrate that SEFL-tuned models outperform their non-tuned counterparts in feedback quality, clarity, and timeliness. These findings reveal SEFL's potential to transform feedback processes for higher education and beyond, offering an ethical and scalable alternative to conventional manual feedback cycles.

Extracting structured information from unstructured text is crucial for modeling real-world processes, but traditional schema mining relies on semi-structured data, limiting scalability. This paper introduces schema-miner, a novel tool that combines large language models with human feedback to automate and refine schema extraction. Through an iterative workflow, it organizes properties from text, incorporates expert input, and integrates domain-specific ontologies for semantic depth. Applied to materials science--specifically atomic layer deposition--schema-miner demonstrates that expert-guided LLMs generate semantically rich schemas suitable for diverse real-world applications.

Recent advancements in Large Language Models (LLMs) have shown significant potential in enhancing recommender systems. However, addressing the cold-start recommendation problem, where users lack historical data, remains a considerable challenge. In this paper, we introduce KALM4Rec (Keyword-driven Retrieval-Augmented Large Language Models for Cold-start User Recommendations), a novel framework specifically designed to tackle this problem by requiring only a few input keywords from users in a practical scenario of cold-start user restaurant recommendations. KALM4Rec operates in two main stages: candidates retrieval and LLM-based candidates re-ranking. In the first stage, keyword-driven retrieval models are used to identify potential candidates, addressing LLMs' limitations in processing extensive tokens and reducing the risk of generating misleading information. In the second stage, we employ LLMs with various prompting strategies, including zero-shot and few-shot techniques, to re-rank these candidates by integrating multiple examples directly into the LLM prompts. Our evaluation, using a Yelp restaurant dataset with user reviews from three English-speaking cities, shows that our proposed framework significantly improves recommendation quality. Specifically, the integration of in-context instructions with LLMs for re-ranking markedly enhances the performance of the cold-start user recommender system.

Autonomous medical robots hold promise to improve patient outcomes, reduce provider workload, democratize access to care, and enable superhuman precision. However, autonomous medical robotics has been limited by a fundamental data problem: existing medical robotic datasets are small, single-embodiment, and rarely shared openly, restricting the development of foundation models that the field needs to advance. We introduce Open-H-Embodiment, the largest open dataset of medical robotic video with synchronized kinematics to date, spanning more than 49 institutions and multiple robotic platforms including the CMR Versius, Intuitive Surgical's da Vinci, da Vinci Research Kit (dVRK), Rob Surgical BiTrack, Virtual Incision's MIRA, Moon Surgical Maestro, and a variety of custom systems, spanning surgical manipulation, robotic ultrasound, and endoscopy procedures. We demonstrate the research enabled by this dataset through two foundation models. GR00T-H is the first open foundation vision-language-action model for medical robotics, which is the only evaluated model to achieve full end-to-end task completion on a structured suturing benchmark (25% of trials vs. 0% for all others) and achieves 64% average success across a 29-step ex vivo suturing sequence. We also train Cosmos-H-Surgical-Simulator, the first action-conditioned world model to enable multi-embodiment surgical simulation from a single checkpoint, spanning nine robotic platforms and supporting in silico policy evaluation and synthetic data generation for the medical domain. These results suggest that open, large-scale medical robot data collection can serve as critical infrastructure for the research community, enabling advances in robot learning, world modeling, and beyond.

Medical ultrasound is a widely accessible, real-time imaging modality, yet progress in data-driven ultrasound research is constrained by the scarcity of large, open collections of raw channel data. Existing public datasets are predominantly based on reconstructed images, while the smaller number of open raw channel datasets is generally specialized to individual reconstruction or imaging tasks, limiting the development of general-purpose methods and foundation models that operate directly on ultrasound signals. While interpretive tasks can be performed on reconstructed images, many of the key technical challenges in ultrasound imaging, such as aberration correction and reverberation reduction, require the raw channel data itself. We introduce OpenH-RF, a community-driven open dataset initiative comprising approximately 40 TB of medical ultrasound raw channel data in 19,332 acquisitions, contributed by 38 institutions across academia and industry, spanning in-vivo, phantom, and simulated data. Each dataset is annotated with a number of supported tasks, ranging from generalized reconstruction, speed-of-sound estimation, and aberration correction to blood flow imaging, motion estimation, quantitative ultrasound, and image interpretation. OpenH-RF provides a unified, self-contained data format that captures raw channel data together with the acquisition, probe, metadata, and reconstruction information required for reproducible processing across scanners and acquisition schemes. The corpus is publicly hosted under a permissive CC BY 4.0 license and can be streamed programmatically and selectively at scale. By bringing heterogeneous ultrasound data into a common representation, backed by modern data infrastructure, OpenH-RF lowers the barrier to working with raw channel data and aims to open medical ultrasound research to new communities. See https://open-h.github.io/OpenH-RF.

Recent advancements in large language models (LLMs) have underscored their importance in the evolution of artificial intelligence. However, despite extensive pretraining on multilingual datasets, available open-sourced LLMs exhibit limited effectiveness in processing Vietnamese. The challenge is exacerbated by the absence of systematic benchmark datasets and metrics tailored for Vietnamese LLM evaluation. To mitigate these issues, we have finetuned LLMs specifically for Vietnamese and developed a comprehensive evaluation framework encompassing 10 common tasks and 31 metrics. Our evaluation results reveal that the fine-tuned LLMs exhibit enhanced comprehension and generative capabilities in Vietnamese. Moreover, our analysis indicates that models with more parameters can introduce more biases and uncalibrated outputs and the key factor influencing LLM performance is the quality of the training or fine-tuning datasets. These insights underscore the significance of meticulous fine-tuning with high-quality datasets in enhancing LLM performance.

Large language models (LLMs) are transforming automated program repair (APR) through agent-based approaches that localize bugs, generate patches, and verify fixes. However, the lack of high-quality, scalable training datasets, especially those with verifiable outputs and intermediate reasoning traces-limits progress, particularly for open-source models. In this work, we present SWE-Synth, a framework for synthesizing realistic, verifiable, and process-aware bug-fix datasets at the repository level. SWE-Synth leverages LLM agents to simulate debugging workflows, producing not only bug-fix pairs but also test cases and structured repair trajectories. Compared to manually curated datasets, our method scales with minimal human effort while preserving contextual richness and correctness. Experiments show that models trained on SWE-Synth outperform those trained on real-world datasets by 2.3% on SWE-Bench Lite. Our results highlight the potential of synthetic, agent-generated data to advance the state of the art in APR and software engineering automation.

The widespread adoption of long-horizon agents has made model workloads increasingly input-heavy. Although prior work has substantially reduced the cost of long-context computation, prefill remains computationally expensive, and large KV caches continue to strain HBM and SSD capacity and data-transfer bandwidth. Together, these compute, storage, and bandwidth demands constitute the primary bottleneck to further lowering deployment costs. To address this challenge, we introduce DeepSeek-V4.1-Flash, a multimodal Mixture-of-Experts (MoE) model with 552B backbone parameters and support for contexts of up to one million tokens. With its Causal Encoder-Decoder (CED) architecture, the model activates 16B parameters per token during decode but only 8B parameters during prefill, substantially improving cost efficiency for agentic workloads. To push the limits of KV cache compression, DeepSeek-V4.1-Flash combines cross-layer KV cache reuse in Compressed Sparse Attention 2 (CSA2) with FP4 KV caching. These designs reduce its global KV cache footprint (always in HBM) to 890 bytes per token, roughly 1/4 of the corresponding footprint of DeepSeek-V4-Flash. Further, through a dedicated deployment optimization known as SWA Bounded Replay, DeepSeek-V4.1-Flash reduces its persistent KV cache footprint (always on SSD or in host memory) to roughly 1/8 of that of DeepSeek-V4-Flash. Despite its much smaller KV cache footprint, the model delivers substantially better performance than the baseline. In addition, we streamline the DeepSeek-V4 architecture and introduce several efficient architectural extensions. We pretrain DeepSeek-V4.1-Flash on a multimodal corpus comprising 45T tokens and conduct comprehensive post-training, yielding strong performance across diverse text-based and multimodal agentic scenarios. Model checkpoints are available at https://huggingface.co/deepseek-ai/DeepSeek-V4.1-Flash.

We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling compartments that have a permeable boundary. Each cell secretes a signaling chemical into the bulk region at a constant rate and receives a feedback of the bulk chemical from the entire collection of cells. This global feedback, which activates signaling pathways within the cells, modifies the intracellular dynamics according to the external environment. The cell secretion and global feedback are regulated by permeability parameters across the cell membrane. For arbitrary reaction-kinetics within each cell, the method of matched asymptotic expansions is used in the limit of small cell radius to construct steady-state solutions of the PDE-ODE model, and to derive a globally coupled nonlinear matrix eigenvalue problem (GCEP) that characterizes the linear stability properties of the steady-states. In the limit of large bulk diffusivity an asymptotic analysis of the PDE-ODE model leads to a limiting ODE system for the spatial average of the concentration in the bulk region that is coupled to the intracellular dynamics within the cells. Results from the linear stability theory and ODE dynamics are illustrated for Sel'kov reaction-kinetics, where the kinetic parameters are chosen so that each cell is quiescent when uncoupled from the bulk medium. For various specific spatial configurations of cells, the linear stability theory is used to construct phase diagrams in parameter space characterizing where a switch-like emergence of intracellular oscillations can occur through a Hopf bifurcation.

Financial markets pose fundamental challenges for asset return prediction due to their high dimensionality, non-stationarity, and persistent volatility. Despite advances in large language models and multi-agent systems, current quantitative research pipelines suffer from limited automation, weak interpretability, and fragmented coordination across key components such as factor mining and model innovation. In this paper, we propose R&D-Agent for Quantitative Finance, in short RD-Agent(Q), the first data-centric multi-agent framework designed to automate the full-stack research and development of quantitative strategies via coordinated factor-model co-optimization. RD-Agent(Q) decomposes the quant process into two iterative stages: a Research stage that dynamically sets goal-aligned prompts, formulates hypotheses based on domain priors, and maps them to concrete tasks, and a Development stage that employs a code-generation agent, Co-STEER, to implement task-specific code, which is then executed in real-market backtests. The two stages are connected through a feedback stage that thoroughly evaluates experimental outcomes and informs subsequent iterations, with a multi-armed bandit scheduler for adaptive direction selection. Empirically, RD-Agent(Q) achieves up to 2X higher annualized returns than classical factor libraries using 70% fewer factors, and outperforms state-of-the-art deep time-series models on real markets. Its joint factor-model optimization delivers a strong balance between predictive accuracy and strategy robustness. Our code is available at: https://github.com/microsoft/RD-Agent.

Marcinkiewicz strong law of large numbers, {n^{-frac1p}}sum_{k=1}^{n} (d_{k}- d)rightarrow 0 almost surely with pin(1,2), are developed for products d_k=prod_{r=1}^s x_k^{(r)}, where the x_k^{(r)} = sum_{l=-infty}^{infty}c_{k-l}^{(r)}xi_l^{(r)} are two-sided linear processes with coefficients {c_l^{(r)}}_{lin Z} and i.i.d. zero-mean innovations {xi_l^{(r)}}_{lin Z}. The decay of the coefficients c_l^{(r)} as |l|toinfty, can be slow enough for {x_k^{(r)}} to have long memory while {d_k} can have heavy tails. The long-range dependence and heavy tails for {d_k} are handled simultaneously and a decoupling property shows the convergence rate is dictated by the worst of long-range dependence and heavy tails, but not their combination. The Marcinkiewicz strong law of large numbers is also extended to the multivariate linear process case.

This paper studies Kernel density estimation for a high-dimensional distribution rho(x). Traditional approaches have focused on the limit of large number of data points n and fixed dimension d. We analyze instead the regime where both the number n of data points y_i and their dimensionality d grow with a fixed ratio alpha=(log n)/d. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density hat rho_h^{D}(x)=1{n h^d}sum_{i=1}^n Kleft(x-y_i{h}right), depending on the bandwidth h: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches. Below a certain value of the bandwidth, h_{CLT}(alpha), we find that the CLT breaks down. The statistics of hat rho_h^{D}(x) for a fixed x drawn from rho(x) is given by a heavy-tailed distribution (an alpha-stable distribution). In particular below a value h_G(alpha), we find that hat rho_h^{D}(x) is governed by extreme value statistics: only a few points in the database matter and give the dominant contribution to the density estimator. We provide a detailed analysis for high-dimensional multivariate Gaussian data. We show that the optimal bandwidth threshold based on Kullback-Leibler divergence lies in the new statistical regime identified in this paper. Our findings reveal limitations of classical approaches, show the relevance of these new statistical regimes, and offer new insights for Kernel density estimation in high-dimensional settings.

Machine learning-based computer-generated holography (ML-CGH) has advanced rapidly in recent years, yet progress is constrained by the limited availability of high-quality, large-scale hologram datasets. To address this, we present KOREATECH-CGH, a publicly available dataset comprising 6,000 pairs of RGB-D images and complex holograms across resolutions ranging from 256*256 to 2048*2048, with depth ranges extending to the theoretical limits of the angular spectrum method for wide 3D scene coverage. To improve hologram quality at large depth ranges, we introduce amplitude projection, a post-processing technique that replaces amplitude components of hologram wavefields at each depth layer while preserving phase. This approach enhances reconstruction fidelity, achieving 27.01 dB PSNR and 0.87 SSIM, surpassing a recent optimized silhouette-masking layer-based method by 2.03 dB and 0.04 SSIM, respectively. We further validate the utility of KOREATECH-CGH through experiments on hologram generation and super-resolution using state-of-the-art ML models, confirming its applicability for training and evaluating next-generation ML-CGH systems.

Distributed as an open source library since 2013, RTAB-Map started as an appearance-based loop closure detection approach with memory management to deal with large-scale and long-term online operation. It then grew to implement Simultaneous Localization and Mapping (SLAM) on various robots and mobile platforms. As each application brings its own set of contraints on sensors, processing capabilities and locomotion, it raises the question of which SLAM approach is the most appropriate to use in terms of cost, accuracy, computation power and ease of integration. Since most of SLAM approaches are either visual or lidar-based, comparison is difficult. Therefore, we decided to extend RTAB-Map to support both visual and lidar SLAM, providing in one package a tool allowing users to implement and compare a variety of 3D and 2D solutions for a wide range of applications with different robots and sensors. This paper presents this extended version of RTAB-Map and its use in comparing, both quantitatively and qualitatively, a large selection of popular real-world datasets (e.g., KITTI, EuRoC, TUM RGB-D, MIT Stata Center on PR2 robot), outlining strengths and limitations of visual and lidar SLAM configurations from a practical perspective for autonomous navigation applications.

De-identification of clinical text is a prerequisite for the secondary use of electronic health records. Existing public benchmarks such as the i2b2 2006 and 2014 corpora are over a decade old and lack the semantic and demographic diversity of modern clinical narratives. Large Language Models (LLMs) reach state-of-the-art zero-shot extraction, but their use at enterprise scale is limited by computational cost and by hospital data governance that restricts sending Protected Health Information (PHI) to cloud APIs. We introduce SHIELD (Synthetic Human-annotated Identifier-replaced Entries for Learning and De-identification), a diverse clinical note dataset of 1,381 notes with 10,229 gold-standard PHI spans across 9 categories, built with set-cover diversity sampling across demographic and document-type strata and human-in-the-loop adjudication. We evaluate four LLMs (two proprietary, two open-weight) to establish a performance ceiling on SHIELD, then show that a teacher-student distillation framework transfers these capabilities into locally deployable Small Language Models. Our best distilled model reaches micro-averaged span-level precision of 0.89 and recall of 0.88 while running on standard workstation hardware. It trails its cloud teacher on per-category recall (0.90 vs. 0.81 macro-averaged) but remains competitive given its lower cost and on-premise deployability. Cross-dataset evaluation shows that diversity-trained models generalize well on universal structured PHI categories, while institution-specific entities remain hard to transfer in both directions, which suggests pairing broad-coverage models with specialized models for high-volume, semi-structured note types. We publicly release the SHIELD dataset and the distilled DeBERTa v3 model to provide an accurate, cost-effective de-identification pipeline deployable entirely behind institutional firewalls.

Large Language Models (LLMs) often struggle with producing factually consistent answers due to limitations in their parametric memory. Retrieval-Augmented Generation (RAG) paradigms mitigate this issue by incorporating external knowledge at inference time. However, such methods typically handle knowledge as unstructured text, which reduces retrieval accuracy, hinders compositional reasoning, and amplifies the influence of irrelevant information on the factual consistency of LLM outputs. To overcome these limitations, we propose a novel framework that dynamically constructs and expands knowledge graphs (KGs) during inference, integrating both internal knowledge extracted from LLMs and external knowledge retrieved from external sources. Our method begins by extracting a seed KG from the question via prompting, followed by iterative expansion using the LLM's internal knowledge. The KG is then selectively refined through external retrieval, enhancing factual coverage and correcting inaccuracies. We evaluate our approach on three diverse Factual QA benchmarks, demonstrating consistent gains in factual accuracy over baselines. Our findings reveal that inference-time KG construction is a promising direction for enhancing LLM factuality in a structured, interpretable, and scalable manner.

We examine whether the perturbative renormalization group (RG) regime of stochastic turbulence can be continued from small varepsilon to the physical value varepsilon_{phys}=2, corresponding to large-scale forcing. Exploiting the simplifications of the large-d limit, we calculate the correction exponent ω to five-loop order and find a simple structure suggesting a closed analytic form. This form implies that the fixed point stable near varepsilon=0 ceases to be simultaneously real and infrared stable before reaching varepsilon_{phys}=2, pointing to a possible change of infrared regime rather than a controlled perturbative RG extrapolation.

The inference process in Large Language Models (LLMs) is often limited due to the absence of parallelism in the auto-regressive decoding process, resulting in most operations being restricted by the memory bandwidth of accelerators. While methods such as speculative decoding have been suggested to address this issue, their implementation is impeded by the challenges associated with acquiring and maintaining a separate draft model. In this paper, we present Medusa, an efficient method that augments LLM inference by adding extra decoding heads to predict multiple subsequent tokens in parallel. Using a tree-based attention mechanism, Medusa constructs multiple candidate continuations and verifies them simultaneously in each decoding step. By leveraging parallel processing, Medusa introduces only minimal overhead in terms of single-step latency while substantially reducing the number of decoding steps required. We present two levels of fine-tuning procedures for Medusa to meet the needs of different use cases: Medusa-1: Medusa is directly fine-tuned on top of a frozen backbone LLM, enabling lossless inference acceleration. Medusa-2: Medusa is fine-tuned together with the backbone LLM, enabling better prediction accuracy of Medusa heads and higher speedup but needing a special training recipe that preserves the backbone model's capabilities. Moreover, we propose several extensions that improve or expand the utility of Medusa, including a self-distillation to handle situations where no training data is available and a typical acceptance scheme to boost the acceptance rate while maintaining generation quality. We evaluate Medusa on models of various sizes and training procedures. Our experiments demonstrate that Medusa-1 can achieve over 2.2x speedup without compromising generation quality, while Medusa-2 further improves the speedup to 2.3-3.6x.

Traditional POI recommendation systems often lack transparency, interpretability, and scrutability due to their reliance on dense vector-based user embeddings. Furthermore, the cold-start problem -- where systems have insufficient data for new users -- limits their ability to generate accurate recommendations. Existing methods often address this by leveraging similar trajectories from other users, but this approach can be computationally expensive and increases the context length for LLM-based methods, making them difficult to scale. To address these limitations, we propose a method that generates natural language (NL) user profiles from large-scale, location-based social network (LBSN) check-ins, utilizing robust personality assessments and behavioral theories. These NL profiles capture user preferences, routines, and behaviors, improving POI prediction accuracy while offering enhanced transparency. By incorporating NL profiles as system prompts to LLMs, our approach reduces reliance on extensive historical data, while remaining flexible, easily updated, and computationally efficient. Our method is not only competitive with other LLM-based and complex agentic frameworks but is also more scalable for real-world scenarios and on-device POI recommendations. Results demonstrate that our approach consistently outperforms baseline methods, offering a more interpretable and resource-efficient solution for POI recommendation systems. Our source code is available at: https://github.com/w11wo/GenUP.

We present an experimental implementation of the multiplayer Quantum Volunteer's Dilemma on noisy intermediate-scale quantum (NISQ) hardware, executed on the ibm_kingston backend via Qiskit Runtime. The game is evaluated for N = 2 to 9 players under four transpiler optimization levels, with 20 independent repetitions per configuration and 2048 shots per circuit, including post-processing readout error correction via mthree. Target-state fidelity decays with system size but remains above 70% (corrected) through N = 9. With readout correction, the global average payoff reproduces the quantum theoretical benchmark exactly for N <= 6 and exceeds the classical Nash equilibrium across the full tested range. Optimization level 2 is selected as the reference configuration after gate count analysis reveals that levels 2 and 3 produce identical transpiled circuits, with level 2 achieving superior fidelity stability. A Hamming distance analysis of raw measurement counts shows that single-qubit errors dominate at small N, with multi-qubit contributions growing beyond N = 6. A calibration-based digital twin captures global payoff trends but exhibits a linear fidelity decay profile that diverges from the hardware behavior at large N, exposing the limits of first-order independent per-qubit noise models. These results demonstrate that aggregate quantum advantage in multiplayer games is robust to NISQ noise conditions across the full tested range, while the practical observability of state-level advantage is constrained to N <= 8 under post-processed readout correction.

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 442 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.

Popularized by the Differentiable Search Index, the emerging paradigm of generative retrieval re-frames the classic information retrieval problem into a sequence-to-sequence modeling task, forgoing external indices and encoding an entire document corpus within a single Transformer. Although many different approaches have been proposed to improve the effectiveness of generative retrieval, they have only been evaluated on document corpora on the order of 100k in size. We conduct the first empirical study of generative retrieval techniques across various corpus scales, ultimately scaling up to the entire MS MARCO passage ranking task with a corpus of 8.8M passages and evaluating model sizes up to 11B parameters. We uncover several findings about scaling generative retrieval to millions of passages; notably, the central importance of using synthetic queries as document representations during indexing, the ineffectiveness of existing proposed architecture modifications when accounting for compute cost, and the limits of naively scaling model parameters with respect to retrieval performance. While we find that generative retrieval is competitive with state-of-the-art dual encoders on small corpora, scaling to millions of passages remains an important and unsolved challenge. We believe these findings will be valuable for the community to clarify the current state of generative retrieval, highlight the unique challenges, and inspire new research directions.

Due to the cumbersome nature of human evaluation and limitations of code-based evaluation, Large Language Models (LLMs) are increasingly being used to assist humans in evaluating LLM outputs. Yet LLM-generated evaluators simply inherit all the problems of the LLMs they evaluate, requiring further human validation. We present a mixed-initiative approach to ``validate the validators'' -- aligning LLM-generated evaluation functions (be it prompts or code) with human requirements. Our interface, EvalGen, provides automated assistance to users in generating evaluation criteria and implementing assertions. While generating candidate implementations (Python functions, LLM grader prompts), EvalGen asks humans to grade a subset of LLM outputs; this feedback is used to select implementations that better align with user grades. A qualitative study finds overall support for EvalGen but underscores the subjectivity and iterative process of alignment. In particular, we identify a phenomenon we dub criteria drift: users need criteria to grade outputs, but grading outputs helps users define criteria. What is more, some criteria appears dependent on the specific LLM outputs observed (rather than independent criteria that can be defined a priori), raising serious questions for approaches that assume the independence of evaluation from observation of model outputs. We present our interface and implementation details, a comparison of our algorithm with a baseline approach, and implications for the design of future LLM evaluation assistants.

As robots become increasingly capable of operating over extended periods -- spanning days, weeks, and even months -- they are expected to accumulate knowledge of their environments and leverage this experience to assist humans more effectively. This paper studies the problem of Long-term Active Embodied Question Answering (LA-EQA), a new task in which a robot must both recall past experiences and actively explore its environment to answer complex, temporally-grounded questions. Unlike traditional EQA settings, which typically focus either on understanding the present environment alone or on recalling a single past observation, LA-EQA challenges an agent to reason over past, present, and possible future states, deciding when to explore, when to consult its memory, and when to stop gathering observations and provide a final answer. Standard EQA approaches based on large models struggle in this setting due to limited context windows, absence of persistent memory, and an inability to combine memory recall with active exploration. To address this, we propose a structured memory system for robots, inspired by the mind palace method from cognitive science. Our method encodes episodic experiences as scene-graph-based world instances, forming a reasoning and planning algorithm that enables targeted memory retrieval and guided navigation. To balance the exploration-recall trade-off, we introduce value-of-information-based stopping criteria that determines when the agent has gathered sufficient information. We evaluate our method on real-world experiments and introduce a new benchmark that spans popular simulation environments and actual industrial sites. Our approach significantly outperforms state-of-the-art baselines, yielding substantial gains in both answer accuracy and exploration efficiency.

In recent years, Deep Learning models have shown a great performance in complex optimization problems. They generally require large training datasets, which is a limitation in most practical cases. Transfer learning allows importing the first layers of a pre-trained architecture and connecting them to fully-connected layers to adapt them to a new problem. Consequently, the configuration of the these layers becomes crucial for the performance of the model. Unfortunately, the optimization of these models is usually a computationally demanding task. One strategy to optimize Deep Learning models is the pruning scheme. Pruning methods are focused on reducing the complexity of the network, assuming an expected performance penalty of the model once pruned. However, the pruning could potentially be used to improve the performance, using an optimization algorithm to identify and eventually remove unnecessary connections among neurons. This work proposes EvoPruneDeepTL, an evolutionary pruning model for Transfer Learning based Deep Neural Networks which replaces the last fully-connected layers with sparse layers optimized by a genetic algorithm. Depending on its solution encoding strategy, our proposed model can either perform optimized pruning or feature selection over the densely connected part of the neural network. We carry out different experiments with several datasets to assess the benefits of our proposal. Results show the contribution of EvoPruneDeepTL and feature selection to the overall computational efficiency of the network as a result of the optimization process. In particular, the accuracy is improved, reducing at the same time the number of active neurons in the final layers.

Low-rank adaptation (LoRA) has become the standard approach for parameter-efficient fine-tuning of large language models (LLM), but our theoretical understanding of LoRA has been limited. In this work, we theoretically analyze LoRA fine-tuning in the neural tangent kernel (NTK) regime with N data points, showing: (i) full fine-tuning (without LoRA) admits a low-rank solution of rank rlesssim N; (ii) using LoRA with rank rgtrsim N eliminates spurious local minima, allowing gradient descent to find the low-rank solutions; (iii) the low-rank solution found using LoRA generalizes well.

Motion sensor time-series are central to human activity recognition (HAR), with applications in health, sports, and smart devices. However, existing methods are trained for fixed activity sets and require costly retraining when new behaviours or sensor setups appear. Recent attempts to use large language models (LLMs) for HAR, typically by converting signals into text or images, suffer from limited accuracy and lack verifiable interpretability. We propose ZARA, the first agent-based framework for zero-shot, explainable HAR directly from raw motion time-series. ZARA integrates an automatically derived pair-wise feature knowledge base that captures discriminative statistics for every activity pair, a multi-sensor retrieval module that surfaces relevant evidence, and a hierarchical agent pipeline that guides the LLM to iteratively select features, draw on this evidence, and produce both activity predictions and natural-language explanations. ZARA enables flexible and interpretable HAR without any fine-tuning or task-specific classifiers. Extensive experiments on 8 HAR benchmarks show that ZARA achieves SOTA zero-shot performance, delivering clear reasoning while exceeding the strongest baselines by 2.53x in macro F1. Ablation studies further confirm the necessity of each module, marking ZARA as a promising step toward trustworthy, plug-and-play motion time-series analysis. Our codes are available at https://github.com/zechenli03/ZARA.

Despite the increasing prevalence of large language models (LLMs), we still have a limited understanding of how their representational spaces are structured. This limits our ability to interpret how and what they learn or relate them to learning in humans. We argue LLMs are best seen as an instance of lossy compression, where over training they learn by retaining only information in their training data relevant to their objective(s). We show pre-training results in models that are optimally compressed for next-sequence prediction, approaching the Information Bottleneck bound on compression. Across an array of open weights models, each compresses differently, likely due to differences in the data and training recipes used. However even across different families of LLMs the optimality of a model's compression, and the information present in it, can predict downstream performance on across a wide array of benchmarks, letting us directly link representational structure to actionable insights about model performance. In the general case the work presented here offers a unified Information-Theoretic framing for how these models learn that is deployable at scale.

Video Moment Retrieval (VMR) is a task to localize the temporal moment in untrimmed video specified by natural language query. For VMR, several methods that require full supervision for training have been proposed. Unfortunately, acquiring a large number of training videos with labeled temporal boundaries for each query is a labor-intensive process. This paper explores methods for performing VMR in a weakly-supervised manner (wVMR): training is performed without temporal moment labels but only with the text query that describes a segment of the video. Existing methods on wVMR generate multi-scale proposals and apply query-guided attention mechanisms to highlight the most relevant proposal. To leverage the weak supervision, contrastive learning is used which predicts higher scores for the correct video-query pairs than for the incorrect pairs. It has been observed that a large number of candidate proposals, coarse query representation, and one-way attention mechanism lead to blurry attention maps which limit the localization performance. To handle this issue, Video-Language Alignment Network (VLANet) is proposed that learns sharper attention by pruning out spurious candidate proposals and applying a multi-directional attention mechanism with fine-grained query representation. The Surrogate Proposal Selection module selects a proposal based on the proximity to the query in the joint embedding space, and thus substantially reduces candidate proposals which leads to lower computation load and sharper attention. Next, the Cascaded Cross-modal Attention module considers dense feature interactions and multi-directional attention flow to learn the multi-modal alignment. VLANet is trained end-to-end using contrastive loss which enforces semantically similar videos and queries to gather. The experiments show that the method achieves state-of-the-art performance on Charades-STA and DiDeMo datasets.

Foundation models in computational pathology promise to unlock the development of new clinical decision support systems and models for precision medicine. However, there is a mismatch between most clinical analysis, which is defined at the level of one or more whole slide images, and foundation models to date, which process the thousands of image tiles contained in a whole slide image separately. The requirement to train a network to aggregate information across a large number of tiles in multiple whole slide images limits these models' impact. In this work, we present a slide-level foundation model for H&E-stained histopathology, PRISM, that builds on Virchow tile embeddings and leverages clinical report text for pre-training. Using the tile embeddings, PRISM produces slide-level embeddings with the ability to generate clinical reports, resulting in several modes of use. Using text prompts, PRISM achieves zero-shot cancer detection and sub-typing performance approaching and surpassing that of a supervised aggregator model. Using the slide embeddings with linear classifiers, PRISM surpasses supervised aggregator models. Furthermore, we demonstrate that fine-tuning of the PRISM slide encoder yields label-efficient training for biomarker prediction, a task that typically suffers from low availability of training data; an aggregator initialized with PRISM and trained on as little as 10% of the training data can outperform a supervised baseline that uses all of the data.

Despite recent advances, frontier large language model (LLM) agents remain limited in discovering and patching complex vulnerabilities in real-world software. Generally available agents can already aid attackers, who only need to find one exploitable weakness, while defenders must continuously identify and patch all vulnerabilities across fast-growing codebases. Stronger defensive agents would help close this gap, yet the scarcity of security training data with reproducible build and execution environments remains a bottleneck. We present CyberForge, a framework that synthesizes executable, repository-level security training data by injecting vulnerabilities into real C/C++ projects. It validates each instance dynamically: the injected build must pass the project's unit tests, and generated proof-of-vulnerability (PoV) must trigger on the injected build and not on the clean one. CyberForge is not limited by the availability of disclosed vulnerabilities, therefore it can scale in comparison to data augmentation techniques which rely on historic CVE data. The resulting corpus holds 1034 validated vulnerabilities across 80 projects and 63 weakness categories, with edit locality similar to real CVE patches under a real-versus-real noise floor. Fine-tuning on trajectories collected over this corpus improves SEC-bench patch repair by +3.3 to +14.7 points, in all six configurations of three model scales and two teachers, with the 31B student reaching its GPT-5.4-mini teacher, 72.7% against 74.0%. These gains generalize out of distribution to PatchEval, a corpus containing other programming languages, where every configuration also improves and the 31B student passes its teacher.

Forced alignment evaluation typically requires manually annotated timestamps, limiting large-scale and multilingual analysis. We introduce two corpus-level metrics based on self-supervised (SSL) speech representations for reference-free forced alignment evaluation: Phoneme-Cluster Mutual Information (PCMI) and Word Acoustic Consistency Score (WACS). PCMI measures agreement between aligned phoneme labels and clusters induced from SSL-speech representations, while WACS measures consistency of repeated word realizations using dynamic time warping similarity between word representation sequences. Using both random and systematic perturbations, we show that PCMI and WACS degrade consistently under alignment perturbations. We further analyze the metrics across multiple alignment systems on 85 languages from FLEURS, validate them against manually annotated alignments from 45 languages in DoReCo, and evaluate them on two phonologically complex low-resource languages. The metrics effectively separate high- and low-quality alignments and correlate strongly with timestamp-based alignment quality measures. Our results demonstrate that SSL-speech representations enable scalable, reference-free forced alignment evaluation. The metrics are available as an open-source Python package at https://github.com/mahesh-ak/forced-aligner-metrics.

Machine Unlearning methods for Large Language Models typically assume pre-specified forget and retain sets. In realistic settings, however, requests may provide only a few examples of undesired behavior, requiring forget and retain sets to be inferred from heterogeneous corpora. We study this data-selection problem and propose GRACE , a gradient-guided coreset selection method that constructs both forget and retain sets for LLM unlearning. GRACE first computes a forget direction from seed examples that elicit the undesired behavior, then selects a compact forget coreset whose gradients approximate this direction using non-negative orthogonal matching pursuit. To preserve model utility, it selects retain examples after projecting out the forget direction and applying clustered orthogonal matching pursuit in the remaining gradient space. Across two target domains, two model families, and four unlearning algorithms, GRACE improves model utility while maintaining comparable forget quality, with particularly consistent gains over prior gradient-based selection methods.

Language models (LMs) are becoming the foundation for almost all major language technologies, but their capabilities, limitations, and risks are not well understood. We present Holistic Evaluation of Language Models (HELM) to improve the transparency of language models. First, we taxonomize the vast space of potential scenarios (i.e. use cases) and metrics (i.e. desiderata) that are of interest for LMs. Then we select a broad subset based on coverage and feasibility, noting what's missing or underrepresented (e.g. question answering for neglected English dialects, metrics for trustworthiness). Second, we adopt a multi-metric approach: We measure 7 metrics (accuracy, calibration, robustness, fairness, bias, toxicity, and efficiency) for each of 16 core scenarios when possible (87.5% of the time). This ensures metrics beyond accuracy don't fall to the wayside, and that trade-offs are clearly exposed. We also perform 7 targeted evaluations, based on 26 targeted scenarios, to analyze specific aspects (e.g. reasoning, disinformation). Third, we conduct a large-scale evaluation of 30 prominent language models (spanning open, limited-access, and closed models) on all 42 scenarios, 21 of which were not previously used in mainstream LM evaluation. Prior to HELM, models on average were evaluated on just 17.9% of the core HELM scenarios, with some prominent models not sharing a single scenario in common. We improve this to 96.0%: now all 30 models have been densely benchmarked on the same core scenarios and metrics under standardized conditions. Our evaluation surfaces 25 top-level findings. For full transparency, we release all raw model prompts and completions publicly for further analysis, as well as a general modular toolkit. We intend for HELM to be a living benchmark for the community, continuously updated with new scenarios, metrics, and models.

Vision and vision-language applications of neural networks, such as image classification and captioning, rely on large-scale annotated datasets that require non-trivial data-collecting processes. This time-consuming endeavor hinders the emergence of large-scale datasets, limiting researchers and practitioners to a small number of choices. Therefore, we seek more efficient ways to collect and annotate images. Previous initiatives have gathered captions from HTML alt-texts and crawled social media postings, but these data sources suffer from noise, sparsity, or subjectivity. For this reason, we turn to commercial shopping websites whose data meet three criteria: cleanliness, informativeness, and fluency. We introduce the Let's Go Shopping (LGS) dataset, a large-scale public dataset with 15 million image-caption pairs from publicly available e-commerce websites. When compared with existing general-domain datasets, the LGS images focus on the foreground object and have less complex backgrounds. Our experiments on LGS show that the classifiers trained on existing benchmark datasets do not readily generalize to e-commerce data, while specific self-supervised visual feature extractors can better generalize. Furthermore, LGS's high-quality e-commerce-focused images and bimodal nature make it advantageous for vision-language bi-modal tasks: LGS enables image-captioning models to generate richer captions and helps text-to-image generation models achieve e-commerce style transfer.

Ultrasound imaging is one of the most widely used diagnostic modalities, offering real-time, radiation-free assessment across diverse clinical domains. However, interpretation of ultrasound images remains challenging due to high noise levels, operator dependence, and limited field of view, resulting in substantial inter-observer variability. Current Deep Learning approaches are hindered by the scarcity of large labeled datasets and the domain gap between general and sonographic images, which limits the transferability of models pretrained on non-medical data. To address these challenges, we introduce the Ultrasound Self-Supervised Foundation Model with Masked Autoencoding (USF-MAE), the first large-scale self-supervised MAE framework pretrained exclusively on ultrasound data. The model was pre-trained on 370,000 2D and 3D ultrasound images curated from 46 open-source datasets, collectively termed OpenUS-46, spanning over twenty anatomical regions. This curated dataset has been made publicly available to facilitate further research and reproducibility. Using a Vision Transformer encoder-decoder architecture, USF-MAE reconstructs masked image patches, enabling it to learn rich, modality-specific representations directly from unlabeled data. The pretrained encoder was fine-tuned on three public downstream classification benchmarks: BUS-BRA (breast cancer), MMOTU-2D (ovarian tumors), and GIST514-DB (gastrointestinal stromal tumors). Across all tasks, USF-MAE consistently outperformed conventional CNN and ViT baselines, achieving F1-scores of 81.6%, 79.6%, and 82.4%, respectively. Despite not using labels during pretraining, USF-MAE approached the performance of the supervised foundation model UltraSam on breast cancer classification and surpassed it on the other tasks, demonstrating strong cross-anatomical generalization.

Despite their ability to understand chemical knowledge, large language models (LLMs) remain limited in their capacity to propose novel molecules with desired functions (e.g., drug-like properties). In addition, the molecules that LLMs propose can often be challenging to make, and are almost never compatible with automated synthesis approaches. To better enable the discovery of functional small molecules, LLMs need to learn a new molecular language that is more effective in predicting properties and inherently synced with automated synthesis technology. Current molecule LLMs are limited by representing molecules based on atoms. In this paper, we argue that just like tokenizing texts into meaning-bearing (sub-)word tokens instead of characters, molecules should be tokenized at the level of functional building blocks, i.e., parts of molecules that bring unique functions and serve as effective building blocks for real-world automated laboratory synthesis. This motivates us to propose mCLM, a modular Chemical-Language Model that comprises a bilingual language model that understands both natural language descriptions of functions and molecular blocks. mCLM front-loads synthesizability considerations while improving the predicted functions of molecules in a principled manner. mCLM, with only 3B parameters, achieves improvements in synthetic accessibility relative to 7 other leading generative AI methods including GPT-5. When tested on 122 out-of-distribution medicines using only building blocks/tokens that are compatible with automated modular synthesis, mCLM outperforms all baselines in property scores and synthetic accessibility. mCLM can also reason on multiple functions and iteratively self-improve to rescue drug candidates that failed late in clinical trials ("fallen angels").

Hepatocellular carcinoma (HCC) is the third leading cause of cancer-related mortality worldwide, with early detection improving survival from <20% to >70%. The standardized Liver Imaging Reporting and Data System (LI-RADS) criteria provide an imaging-based diagnostic framework to evaluate liver lesions for HCC, serving as a foundation for automating HCC detection with artificial intelligence (AI). However, the lack of large, publicly available datasets with high-quality annotations has limited the development and evaluation of AI models for automated LI-RADS assessment. We introduce AMPLIFAI dataset, the first public dataset of 590 multiphase abdominal CT studies annotated with LI-RADS categories, lesion size, and voxel-level segmentations for three major LI-RADS features: arterial phase hyperenhancement, washout, and enhancing capsule. The dataset was curated and harmonized from four public datasets and augmented with expert annotations from five board-certified radiologists and one resident. Following the Datasheets for Datasets format, this paper details the dataset's composition, curation and harmonization process, and annotation workflow to support transparent, reproducible research in medical imaging AI.

We present The Vault, an open-source, large-scale code-text dataset designed to enhance the training of code-focused large language models (LLMs). Existing open-source datasets for training code-based LLMs often face challenges in terms of size, quality (due to noisy signals), and format (only containing code function and text explanation pairings). The Vault overcomes these limitations by providing 40 million code-text pairs across 10 popular programming languages, thorough cleaning for 10+ prevalent issues, and various levels of code-text pairings, including class, function, and line levels. Researchers and practitioners can utilize The Vault for training diverse code-focused LLMs or incorporate the provided data cleaning methods and scripts to improve their datasets. By employing The Vault as the training dataset for code-centric LLMs, we anticipate significant advancements in code understanding and generation tasks, fostering progress in both artificial intelligence research and software development practices.

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our multiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

Clinical deployment of automated brain MRI analysis faces a fundamental challenge: clinical data is heterogeneous and noisy, and high-quality labels are prohibitively costly to obtain. Self-supervised learning (SSL) can address this by leveraging the vast amounts of unlabeled data produced in clinical workflows to train robust foundation models that adapt out-of-domain with minimal supervision. However, the development of foundation models for brain MRI has been limited by small pretraining datasets and in-domain benchmarking focused on high-quality, research-grade data. To address this gap, we organized the FOMO25 challenge as a satellite event at MICCAI 2025. FOMO25 provided participants with a large pretraining dataset, FOMO60K, and evaluated models on data sourced directly from clinical workflows in few-shot and out-of-domain settings. Tasks covered infarct classification, meningioma segmentation, and brain age regression, and considered both models trained on FOMO60K (method track) and any data (open track). Nineteen foundation models from sixteen teams were evaluated using a standardized containerized pipeline. Results show that (a) self-supervised pretraining improves generalization on clinical data under domain shift, with the strongest models trained out-of-domain surpassing supervised baselines trained in-domain. (b) No single pretraining objective benefits all tasks: MAE favors segmentation, hybrid reconstruction-contrastive objectives favor classification, and (c) strong performance was achieved by small pretrained models, and improvements from scaling model size and training duration did not yield reliable benefits.

In "Embers of Autoregression" (McCoy et al., 2023), we showed that several large language models (LLMs) have some important limitations that are attributable to their origins in next-word prediction. Here we investigate whether these issues persist with o1, a new system from OpenAI that differs from previous LLMs in that it is optimized for reasoning. We find that o1 substantially outperforms previous LLMs in many cases, with particularly large improvements on rare variants of common tasks (e.g., forming acronyms from the second letter of each word in a list, rather than the first letter). Despite these quantitative improvements, however, o1 still displays the same qualitative trends that we observed in previous systems. Specifically, o1 - like previous LLMs - is sensitive to the probability of examples and tasks, performing better and requiring fewer "thinking tokens" in high-probability settings than in low-probability ones. These results show that optimizing a language model for reasoning can mitigate but might not fully overcome the language model's probability sensitivity.

Scenario simulation is central to testing autonomous driving systems. Scenic, a domain-specific language (DSL) for CARLA, enables precise and reproducible scenarios, but NL-to-Scenic generation with large language models (LLMs) suffers from scarce data, limited reproducibility, and inconsistent metrics. We introduce NL2Scenic, an open dataset and framework with 146 NL/Scenic pairs, a difficulty-stratified 30-case test split, an Example Retriever, and 14 prompting variants (ZS, FS, CoT, SP, MoT). We evaluate 13 models: four proprietary (GPT-4o, GPT-5, Claude-Sonnet-4, Gemini-2.5-pro) and nine open-source code models (Qwen2.5Coder 0.5B-32B; CodeLlama 7B/13B/34B), using text metrics (BLEU, ChrF, EDIT-SIM, CrystalBLEU) and execution metrics (compilation and generation), and compare them with an expert study (n=11). EDIT-SIM correlates best with human judgments; we also propose EDIT-COMP (F1 of EDIT-SIM and compilation) as a robust dataset-level proxy that improves ranking fidelity. GPT-4o performs best overall, while Qwen2.5Coder-14B reaches about 88 percent of its expert score on local hardware. Retrieval-augmented prompting, Few-Shot with Example Retriever (FSER), consistently boosts smaller models, and scaling shows diminishing returns beyond mid-size, with Qwen2.5Coder outperforming CodeLlama at comparable scales. NL2Scenic and EDIT-COMP offer a standardized, reproducible basis for evaluating Scenic code generation and indicate that mid-size open-source models are practical, cost-effective options for autonomous-driving scenario programming.

Ongoing and upcoming galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) survey, will observe vast regions of sky and a wide range of redshifts. In order to model the observations and address various systematic uncertainties, N-body simulations are routinely adopted, however, the number of large simulations with sufficiently high mass resolution is usually limited by available computing time. Therefore, achieving a simulation volume with the effective statistical errors significantly smaller than those of the observations becomes prohibitively expensive. In this study, we apply the Convergence Acceleration by Regression and Pooling (CARPool) method to mitigate the sample variance of the DESI-like galaxy clustering in the AbacusSummit simulations, with the assistance of the quasi-N-body simulations FastPM. Based on the halo occupation distribution (HOD) models, we construct different FastPM galaxy catalogs, including the luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasars, with their number densities and two-point clustering statistics well matched to those of AbacusSummit. We also employ the same initial conditions between AbacusSummit and FastPM to achieve high cross-correlation, as it is useful in effectively suppressing the variance. Our method of reducing noise in clustering is equivalent to performing a simulation with volume larger by a factor of 5 and 4 for LRGs and ELGs, respectively. We also mitigate the standard deviation of the LRG bispectrum with the triangular configurations k_2=2k_1=0.2 h/Mpc by a factor of 1.6. With smaller sample variance on galaxy clustering, we are able to constrain the baryon acoustic oscillations (BAO) scale parameters to higher precision. The CARPool method will be beneficial to better constrain the theoretical systematics of BAO, redshift space distortions (RSD) and primordial non-Gaussianity (NG).

We study a set of four-dimensional N=2 superconformal field theories (SCFTs) widehatΓ(G) labeled by a pair of simply-laced Lie groups Γ and G. They are constructed out of gauging a number of D_p(G) and (G, G) conformal matter SCFTs; therefore they do not have Lagrangian descriptions in general. For Γ= D_4, E_6, E_7, E_8 and some special choices of G, the resulting theories have identical central charges (a=c) without taking any large N limit. Moreover, we find that the Schur indices for such theories can be written in terms of that of N=4 super Yang--Mills theory upon rescaling fugacities. Especially, we find that the Schur index of D_4(SU(N)) theory for N odd is written in terms of MacMahon's generalized sum-of-divisor function, which is quasi-modular. For generic choices of Γ and G, it can be regarded as a generalization of the affine quiver gauge theory obtained from D3-branes probing an ALE singularity of type Γ. We also comment on a tantalizing connection regarding the theories labeled by Γ in the Deligne--Cvitanović exceptional series.

We introduce the Series-Parallel Workflow Decomposition (SP\-WD) heuristic algorithm for the Workflow Scheduling Problem (WSP) decomposition. We demonstrate that the SPWD algorithm facilitates the scheduling of large WSP instances with the hybrid D-Wave Constrained Quadratic Model solver, enabling the scheduling of instances that would otherwise exceed its capacity limitations. We also describe the accompanying execution environment used to obtain the results of the experiments with real-life workflow instances available in the WfCommons standardization initiative repository.

Consider a random uniform sample of n points in a compact region A of Euclidean d-space, d geq 2, with a smooth or (when d=2) polygonal boundary. Fix k bf N. Let T_{n,k} be the threshold r at which the geometric graph on these n vertices with distance parameter r becomes k-connected. We show that if d=2 then n (pi/|A|) T_{n,1}^2 - log n is asymptotically standard Gumbel. For (d,k) neq (2,1), it is n (theta_d/|A|) T_{n,k}^d - (2-2/d) log n - (4-2k-2/d) log log n that converges in distribution to a nondegenerate limit, where theta_d is the volume of the unit ball. The limit is Gumbel with scale parameter 2 except when (d,k)=(2,2) where the limit is two component extreme value distributed. The different cases reflect the fact that boundary effects are more more important in some cases than others. We also give similar results for the largest k-nearest neighbour link U_{n,k} in the sample, and show T_{n,k}=U_{n,k} with high probability. We provide estimates on rates of convergence and give similar results for Poisson samples in A. Finally, we give similar results even for non-uniform samples, with a less explicit sequence of centring constants.

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some scenarios where stronger results are needed in order to establish an asymptotic normal approximation uniformly over a family of probability measures. In this note we collect some results in this direction. We restrict ourselves to weak convergence in mathbb R^d with continuous limit measures.

Scaling limits, such as infinite-width limits, serve as promising theoretical tools to study large-scale models. However, it is widely believed that existing infinite-width theory does not faithfully explain the behavior of practical networks, especially those trained in standard parameterization (SP) meaning He initialization with a global learning rate. For instance, existing theory for SP predicts instability at large learning rates and vanishing feature learning at stable ones. In practice, however, optimal learning rates decay slower than theoretically predicted and networks exhibit both stable training and non-trivial feature learning, even at very large widths. Here, we show that this discrepancy is not fully explained by finite-width phenomena. Instead, we find a resolution through a finer-grained analysis of the regime previously considered unstable and therefore uninteresting. In particular, we show that, under cross-entropy (CE) loss, the unstable regime comprises two distinct sub-regimes: a catastrophically unstable regime and a more benign controlled divergence regime, where logits diverge but gradients and activations remain stable. Moreover, under large learning rates at the edge of the controlled divergence regime, there exists a well-defined infinite width limit where features continue to evolve in all the hidden layers. In experiments across optimizers, architectures, and data modalities, we validate that neural networks operate in this controlled divergence regime under CE loss but not under MSE loss. Our empirical evidence suggests that width-scaling considerations are surprisingly useful for predicting empirically maximal stable learning rate exponents which provide useful guidance on optimal learning rate exponents. Finally, our analysis clarifies the effectiveness and limitations of recently proposed layerwise learning rate scaling for standard initialization.

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of which the gradient flow is described by a partial differential equation in the large-neural network limit, i.e., the mean-field regime. To derive the generalization bounds under this setting, our analysis necessitates a shift from the conventional time-invariant Gram matrix employed in the lazy training regime to a time-variant, distribution-dependent version. To this end, we provide a global lower bound on the minimum eigenvalue of the Gram matrix under the mean-field regime. Besides, for the traceability of the dynamic of Kullback-Leibler (KL) divergence, we establish the linear convergence of the empirical error and estimate the upper bound of the KL divergence over parameters distribution. Finally, we build the uniform convergence for generalization bound via Rademacher complexity. Our results offer new insights into the generalization ability of deep ResNet beyond the lazy training regime and contribute to advancing the understanding of the fundamental properties of deep neural networks.

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of Λ = 2.14 pm 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% pm 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 pm 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 μs at distance-5 up to a million cycles, with a cycle time of 1.1 μs. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 times 10^9 cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.

The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of and connects these scaling laws. We identify variance-limited and resolution-limited scaling behavior for both dataset and model size, for a total of four scaling regimes. The variance-limited scaling follows simply from the existence of a well-behaved infinite data or infinite width limit, while the resolution-limited regime can be explained by positing that models are effectively resolving a smooth data manifold. In the large width limit, this can be equivalently obtained from the spectrum of certain kernels, and we present evidence that large width and large dataset resolution-limited scaling exponents are related by a duality. We exhibit all four scaling regimes in the controlled setting of large random feature and pretrained models and test the predictions empirically on a range of standard architectures and datasets. We also observe several empirical relationships between datasets and scaling exponents under modifications of task and architecture aspect ratio. Our work provides a taxonomy for classifying different scaling regimes, underscores that there can be different mechanisms driving improvements in loss, and lends insight into the microscopic origins of and relationships between scaling exponents.

In this work we study static neutron stars in the context of several inflationary models which are popular in cosmology. These inflationary models are non-minimally coupled scalar theories which yield a viable inflationary phenomenology in both Jordan and Einstein frames. By considering the constraints from inflationary theories, which basically determine the values of the potential strength, usually considered as a free parameter in astrophysical neutron star works, we construct and solve the Tolman-Oppenheimer-Volkoff equations using a solid python-3 LSODA integrator. For our study we consider several popular inflationary models, such as the universal attractors, the R^p attractors (three distinct model values), the induced inflation, the quadratic inflation, the Higgs inflation and the a-attractors (two distinct model values) and for the following popular equations of state the WFF1, the SLy, the APR, the MS1, the AP3, the AP4, the ENG, the MPA1 and the MS1b. We construct the M-R diagram and we confront the resulting theory with theoretical and observational constraints. As we demonstrate, remarkably, all the neutron stars produced by all the inflationary models we considered are compatible with all the constraints for the MPA1 equation of state. It is notable that for this particular equation of state, the maximum masses of the neutron stars are in the mass-gap region with M>2.5M_{odot}, but lower than the 3 solar masses causal limit. We also make the observation that as the NICER constraints are pushed towards larger radii, as for example in the case of the black widow pulsar PSR J0952-0607, it seems that equations of state that produce neutron stars with maximum masses in the mass gap region, with M>2.5M_{odot}, but lower than the 3 solar masses causal limit, are favored and are compatible with the modified NICER constraints.

We consider the problem of learning a target function corresponding to a single hidden layer neural network, with a quadratic activation function after the first layer, and random weights. We consider the asymptotic limit where the input dimension and the network width are proportionally large. Recent work [Cui & al '23] established that linear regression provides Bayes-optimal test error to learn such a function when the number of available samples is only linear in the dimension. That work stressed the open challenge of theoretically analyzing the optimal test error in the more interesting regime where the number of samples is quadratic in the dimension. In this paper, we solve this challenge for quadratic activations and derive a closed-form expression for the Bayes-optimal test error. We also provide an algorithm, that we call GAMP-RIE, which combines approximate message passing with rotationally invariant matrix denoising, and that asymptotically achieves the optimal performance. Technically, our result is enabled by establishing a link with recent works on optimal denoising of extensive-rank matrices and on the ellipsoid fitting problem. We further show empirically that, in the absence of noise, randomly-initialized gradient descent seems to sample the space of weights, leading to zero training loss, and averaging over initialization leads to a test error equal to the Bayes-optimal one.

In this paper, we study the infinite-depth limit of finite-width residual neural networks with random Gaussian weights. With proper scaling, we show that by fixing the width and taking the depth to infinity, the pre-activations converge in distribution to a zero-drift diffusion process. Unlike the infinite-width limit where the pre-activation converge weakly to a Gaussian random variable, we show that the infinite-depth limit yields different distributions depending on the choice of the activation function. We document two cases where these distributions have closed-form (different) expressions. We further show an intriguing change of regime phenomenon of the post-activation norms when the width increases from 3 to 4. Lastly, we study the sequential limit infinite-depth-then-infinite-width and compare it with the more commonly studied infinite-width-then-infinite-depth limit.

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.

In this paper, we introduce a novel approach for bounding the cumulant generating function (CGF) of a Dirichlet process (DP) X sim DP(αν_0), using superadditivity. In particular, our key technical contribution is the demonstration of the superadditivity of αmapsto log E_{X sim DP(αν_0)}[exp( E_X[αf])], where E_X[f] = int f dX. This result, combined with Fekete's lemma and Varadhan's integral lemma, converts the known asymptotic large deviation principle into a practical upper bound on the CGF logE_{Xsim DP(αν_0)}{exp(E_{X}{[f]})} for any α> 0. The bound is given by the convex conjugate of the scaled reversed Kullback-Leibler divergence αKL(ν_0Vert cdot). This new bound provides particularly effective confidence regions for sums of independent DPs, making it applicable across various fields.

We consider N classical particles interacting via the Coulomb potential in spatial dimension d and in the presence of an external trap, at equilibrium at inverse temperature beta. In the large N limit, the particles are confined within a droplet of finite size. We study smooth linear statistics, i.e. the fluctuations of sums of the form {cal L}_N = sum_{i=1}^N f({bf x}_i), where {bf x}_i's are the positions of the particles and where f({bf x}_i) is a sufficiently regular function. There exists at present standard results for the first and second moments of {cal L}_N in the large N limit, as well as associated Central Limit Theorems in general dimension and for a wide class of confining potentials. Here we obtain explicit expressions for the higher order cumulants of {cal L}_N at large N, when the function f({bf x})=f(|{bf x}|) and the confining potential are both rotationnally invariant. A remarkable feature of our results is that these higher cumulants depend only on the value of f'(|{bf x}|) and its higher order derivatives evaluated exactly at the boundary of the droplet, which in this case is a d-dimensional sphere. In the particular two-dimensional case d=2 at the special value beta=2, a connection to the Ginibre ensemble allows us to derive these results in an alternative way using the tools of determinantal point processes. Finally we also obtain the large deviation form of the full probability distribution function of {cal L}_N.

Underdamped Langevin dynamics (ULD) is a widely-used sampler for Gibbs distributions πpropto e^{-V}, and is often empirically effective in high dimensions. However, existing non-asymptotic convergence guarantees for discretized ULD typically scale polynomially with the ambient dimension d, leading to vacuous bounds when d is large. The main known dimension-free result concerns the randomized midpoint discretization in Wasserstein-2 distance (Liu et al.,2023), while dimension-independent guarantees for ULD discretizations in KL divergence have remained open. We close this gap by proving the first dimension-free KL divergence bounds for discretized ULD. Our analysis refines the KL local error framework (Altschuler et al., 2025) to a dimension-free setting and yields bounds that depend on tr(H), where H upper bounds the Hessian of V, rather than on d. As a consequence, we obtain improved iteration complexity for underdamped Langevin Monte Carlo relative to overdamped Langevin methods in regimes where tr(H)ll d.

The Universal Approximation Theorem posits that neural networks can theoretically possess unlimited approximation capacity with a suitable activation function and a freely chosen or trained set of parameters. However, a more practical scenario arises when these neural parameters, especially the nonlinear weights and biases, are bounded. This leads us to question: Does the approximation capacity of a neural network remain universal, or does it have a limit when the parameters are practically bounded? And if it has a limit, how can it be measured? Our theoretical study indicates that while universal approximation is theoretically feasible, in practical numerical scenarios, Deep Neural Networks (DNNs) with any analytic activation functions (such as Tanh and Sigmoid) can only be approximated by a finite-dimensional vector space under a bounded nonlinear parameter space (NP space), whether in a continuous or discrete sense. Based on this study, we introduce the concepts of ε outer measure and Numerical Span Dimension (NSdim) to quantify the approximation capacity limit of a family of networks both theoretically and practically. Furthermore, drawing on our new theoretical study and adopting a fresh perspective, we strive to understand the relationship between back-propagation neural networks and random parameter networks (such as the Extreme Learning Machine (ELM)) with both finite and infinite width. We also aim to provide fresh insights into regularization, the trade-off between width and depth, parameter space, width redundancy, condensation, and other related important issues.

We consider an existing conjecture addressing the asymptotic behavior of neural networks in the large width limit. The results that follow from this conjecture include tight bounds on the behavior of wide networks during stochastic gradient descent, and a derivation of their finite-width dynamics. We prove the conjecture for deep networks with polynomial activation functions, greatly extending the validity of these results. Finally, we point out a difference in the asymptotic behavior of networks with analytic (and non-linear) activation functions and those with piecewise-linear activations such as ReLU.

Why does the low dimensionality of representations, typically dapprox 1000, not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of data points? To answer this question, we study maximal-margin embeddings in the following retrieval model, classically studied in communication complexity [PS86] and more recently in embedding-based retrieval [WBNL26]. Let Ain {0,1}^{Ntimes n} be a matrix indicating whether each of N queries is relevant to each of n documents. We are interested in the largest margin m>0, denoted by m^{rd}(d, A), for which there exist unit norm embeddings of the queries and documents {U_j}_{j = 1}^N, {V_i}_{i = 1}^n with the following property. langle U_j, V_irangle ge m whenever A_{ji} = 1 and langle U_j, V_irangle le -m otherwise. A large margin is a key proxy for representation quality: it controls both robustness to perturbations and compositional generalization across queries. Our main theorem establishes that the best possible margin without a restriction on the dimension, m^{rd}(+infty, A), can be nearly achieved in dimension d = O(m^{rd}(+infty, A)^{-2}log n) which improves a theorem of [BDES02]. Together with a matching lower bound in Theorem 1.5, we conclude that when Ain {0,1}^{n{k}times n} is the matrix containing all possible k-sparse rows once, dimension d = O(klog (n/k)) is necessary and sufficient for the maximal possible margin m^{rd}(+infty, A) = Θ(k^{-1/2}) in this setting. This fully resolves the setup of [WBNL26]. We also give several constructions for large margins when d = o(klog (n/k)). Finally, we empirically test the InfoNCE and sigmoid losses for producing large margin embeddings and demonstrate a clear advantage of the sigmoid loss.

Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of parameters to train, but in practice they do not. Here we employ results from replica mean field theory to compute the generalisation gap of machine learning models with quenched features, in the teacher-student scenario and for regression problems with quadratic loss function. Notably, this framework includes the case of DNNs where the last layer is optimised given a specific realisation of the remaining weights. We show how these results -- combined with ideas from statistical learning theory -- provide a stringent asymptotic upper bound on the generalisation gap of fully trained DNN as a function of the size of the dataset P. In particular, in the limit of large P and N_{out} (where N_out is the size of the last layer) and N_out ll P, the generalisation gap approaches zero faster than 2 N_out/P, for any choice of both architecture and teacher function. Notably, this result greatly improves existing bounds from statistical learning theory. We test our predictions on a broad range of architectures, from toy fully-connected neural networks with few hidden layers to state-of-the-art deep convolutional neural networks.

Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al. 2023) modified the Neural Network Gaussian Process (NNGP) limit of Bayesian neural networks so that representation learning is retained. Furthermore, they found that applying this modified limit to a deep Gaussian process gives a practical learning algorithm which they dubbed the deep kernel machine (DKM). However, they only considered the simplest possible setting: regression in small, fully connected networks with e.g. 10 input features. Here, we introduce convolutional deep kernel machines. This required us to develop a novel inter-domain inducing point approximation, as well as introducing and experimentally assessing a number of techniques not previously seen in DKMs, including analogues to batch normalisation, different likelihoods, and different types of top-layer. The resulting model trains in roughly 77 GPU hours, achieving around 99% test accuracy on MNIST, 72% on CIFAR-100, and 92.7% on CIFAR-10, which is SOTA for kernel methods.

Singular limits for the following indirect signalling chemotaxis system align* \left\{ array{lllllll} \partial_t n = \Delta n - \nabla \cdot (n \nabla c ) & in \Omega\times(0,\infty) , \varepsilon \partial_t c = \Delta c - c + w & in \Omega\times(0,\infty), \varepsilon \partial_t w = \tau \Delta w - w + n & in \Omega\times (0,\infty), \partial_\nu n = \partial_\nu c = \partial_\nu w = 0, &on \partial\Omega\times (0,\infty) %(n,c,w)_{t=0} = (n_0,c_0,w_0) & on \Omega, array \right. align* are investigated. More precisely, we study parabolic-elliptic simplification, or PES, varepsilonto 0^+ with fixed tau>0 up to the critical dimension N=4, and indirect-direct simplification, or IDS, (varepsilon,tau)to (0^+,0^+) up to the critical dimension N=2. These are relevant in biological situations where the signalling process is on a much faster time scale compared to the species diffusion and all interactions. Showing singular limits in critical dimensions is challenging. To deal with the PES, we carefully combine the entropy function, an Adam-type inequality, the regularisation of slow evolution, and an energy equation method to obtain strong convergence in representative spaces. For the IDS, a bootstrap argument concerning the L^p-energy function is devised, which allows us to obtain suitable uniform bounds for the singular limits. Moreover, in both scenarios, we also present the convergence rates, where the effect of the initial layer and the convergence to the critical manifold are also revealed.

We develop a general mathematical framework to analyze scaling regimes and derive explicit analytic solutions for gradient flow (GF) in large learning problems. Our key innovation is a formal power series expansion of the loss evolution, with coefficients encoded by diagrams akin to Feynman diagrams. We show that this expansion has a well-defined large-size limit that can be used to reveal different learning phases and, in some cases, to obtain explicit solutions of the nonlinear GF. We focus on learning Canonical Polyadic (CP) decompositions of high-order tensors, and show that this model has several distinct extreme lazy and rich GF regimes such as free evolution, NTK and under- and over-parameterized mean-field. We show that these regimes depend on the parameter scaling, tensor order, and symmetry of the model in a specific and subtle way. Moreover, we propose a general approach to summing the formal loss expansion by reducing it to a PDE; in a wide range of scenarios, it turns out to be first-order and solvable by the method of characteristics. We observe a very good agreement of our theoretical predictions with experimental results.

We classify four-dimensional N=1 supersymmetric gauge theories with a simple gauge group admitting a large N limit that flow to non-trivial superconformal fixed points in the infrared. We focus on the cases where the large N limit can be taken while keeping the flavor symmetry fixed so that the putative holographic dual has a fixed gauge group. We find that they can be classified into three types -- Type I, Type II, and Type III -- exhibiting universal behavior. Type I theories have a neq c in the large N limit and scale linearly in N; the gap of scaling dimensions among BPS operators behaves as 1/N. Type II theories have a=c in the large N limit, and satisfy a simeq c simeq 27{128} dim G, and Type III theories have a simeq c simeq 1{4} dim G. For Type II and Type III theories, the gap of scaling dimensions stays O(1) in the large N limit. We enumerate relevant and marginal operators of these theories and find that non-trivial conformal manifolds emerge upon relevant deformations. Moreover, we find that a modified version of the AdS Weak Gravity Conjecture, based on the supersymmetric Cardy formula, holds for all of these theories, even for finite N.

When training large-scale models, the performance typically scales with the number of parameters and the dataset size according to a slow power law. A fundamental theoretical and practical question is whether comparable performance can be achieved with significantly smaller models and substantially less data. In this work, we provide a positive and constructive answer. We prove that a generic permutation-invariant function of d objects can be asymptotically compressed into a function of polylog d objects with vanishing error, which is proved to be the optimal compression rate. This theorem yields two key implications: (Ia) a large neural network can be compressed to polylogarithmic width while preserving its learning dynamics; (Ib) a large dataset can be compressed to polylogarithmic size while leaving the loss landscape of the corresponding model unchanged. Implication (Ia) directly establishes a proof of the dynamical lottery ticket hypothesis, which states that any ordinary network can be strongly compressed such that the learning dynamics and result remain unchanged. (Ib) shows that a neural scaling law of the form Lsim d^{-α} can be boosted to an arbitrarily fast power law decay, and ultimately to exp(-α' sqrt[m]{d}).

A new approach to solving random matrix models directly in the large N limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large N loop equations are then used to generate values of higher-pt correlation functions based on this guess. Then one tests whether these higher-pt functions are consistent with positivity requirements, e.g., langle tr M^{2k} rangle ge 0. If not, the guessed values are systematically ruled out. In this way, one can constrain the correlation functions of random matrices to a tiny subregion which contains (and perhaps converges to) the true solution. This approach is tested on single and multi-matrix models and handily reproduces known solutions. It also produces strong results for multi-matrix models which are not believed to be solvable. A tantalizing possibility is that this method could be used to search for new critical points, or string worldsheet theories.

As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK parametrization). However, we show that the standard and NTK parametrizations of a neural network do not admit infinite-width limits that can learn features, which is crucial for pretraining and transfer learning such as with BERT. We propose simple modifications to the standard parametrization to allow for feature learning in the limit. Using the *Tensor Programs* technique, we derive explicit formulas for such limits. On Word2Vec and few-shot learning on Omniglot via MAML, two canonical tasks that rely crucially on feature learning, we compute these limits exactly. We find that they outperform both NTK baselines and finite-width networks, with the latter approaching the infinite-width feature learning performance as width increases. More generally, we classify a natural space of neural network parametrizations that generalizes standard, NTK, and Mean Field parametrizations. We show 1) any parametrization in this space either admits feature learning or has an infinite-width training dynamics given by kernel gradient descent, but not both; 2) any such infinite-width limit can be computed using the Tensor Programs technique. Code for our experiments can be found at github.com/edwardjhu/TP4.

We study the fine-grained uniform convergence behavior of halfspaces beyond worst-case VC bounds. For inhomogeneous halfspaces in R^d with dge 2, we show that standard first-order VC bounds are essentially tight: even consistent hypotheses can incur population error Θ(dln(n/d)/n), and in the agnostic setting the deviation scales as τln(1/τ) at true error τ. In contrast, homogeneous halfspaces in R^2 exhibit a markedly different behavior. In the realizable case, every hypothesis consistent with the sample has error O(1/n). In the agnostic case, we prove a bandwise, log-free deviation bound on each dyadic risk band via a critical-wedge localization argument. Unioning over bands incurs only a lnln n overhead, and we establish a matching lower bound showing this overhead is unavoidable. Together, these results give a fine-grained and nearly complete picture of uniform convergence for halfspaces, revealing sharp dimensional and structural thresholds.

A burgeoning line of research leverages deep neural networks to approximate the solutions to high dimensional PDEs, opening lines of theoretical inquiry focused on explaining how it is that these models appear to evade the curse of dimensionality. However, most prior theoretical analyses have been limited to linear PDEs. In this work, we take a step towards studying the representational power of neural networks for approximating solutions to nonlinear PDEs. We focus on a class of PDEs known as nonlinear elliptic variational PDEs, whose solutions minimize an Euler-Lagrange energy functional E(u) = int_Omega L(x, u(x), nabla u(x)) - f(x) u(x)dx. We show that if composing a function with Barron norm b with partial derivatives of L produces a function of Barron norm at most B_L b^p, the solution to the PDE can be epsilon-approximated in the L^2 sense by a function with Barron norm Oleft(left(dB_Lright)^{max{p log(1/ epsilon), p^{log(1/epsilon)}}}right). By a classical result due to Barron [1993], this correspondingly bounds the size of a 2-layer neural network needed to approximate the solution. Treating p, epsilon, B_L as constants, this quantity is polynomial in dimension, thus showing neural networks can evade the curse of dimensionality. Our proof technique involves neurally simulating (preconditioned) gradient in an appropriate Hilbert space, which converges exponentially fast to the solution of the PDE, and such that we can bound the increase of the Barron norm at each iterate. Our results subsume and substantially generalize analogous prior results for linear elliptic PDEs over a unit hypercube.

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain poorly understood, as universality is traditionally studied for models accepting inputs of a fixed size, defined on a compact subset of their domain. In sharp contrast, any-dimensional models can be viewed as sequences of functions defined on growing-sized inputs, and it is not clear in which sense they can be universal. We develop a systematic approach to establish any-dimensional universality, by identifying any-dimensional functions with a unique function taking inputs in a suitable infinite-dimensional limit space containing inputs of all finite sizes as well as their limits. Using the symmetries of these inputs and relations between inputs of different sizes, we show that this limit space admits a natural topology with rich families of compact sets on which any-dimensional universality can be established. We illustrate our approach by showing that several existing architectures fail to be universal, and we propose simple modifications that restore universality.

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width w^*_{min}=max(d_x,d_y), where d_x and d_y are the dimensions of the input and output, respectively. Recently, cai2022achieve shows that a leaky-ReLU NN with this critical width can achieve UAP for L^p functions on a compact domain K, i.e., the UAP for L^p(K,R^{d_y}). This paper examines a uniform UAP for the function class C(K,R^{d_y}) and gives the exact minimum width of the leaky-ReLU NN as w_{min}=max(d_x+1,d_y)+1_{d_y=d_x+1}, which involves the effects of the output dimensions. To obtain this result, we propose a novel lift-flow-discretization approach that shows that the uniform UAP has a deep connection with topological theory.

Let D(N) denote the largest cardinality of a subset of {1,ldots,N} containing no nonzero square difference. While a construction certifying D(N)geq (1-o(1))N^{1/2} is almost trivial, Erdős conjectured that this bound is sharp up to polylogarithmic factors. This was disproved by Sárközy and later again by Ruzsa, who found an elegant construction showing that D(N)geq ccdot N^{0.733077dots}, with an absolute constant c>0. His approach was subsequently refined, leading to the previously best known lower bound with exponent 0.7334117dots due to Beigel-Gasarch and, independently, Lewko. However, in the original paper Ruzsa observed that 3/4 seems to be the natural barrier of his approach. In this paper we develop a new construction leading to the lower bound \[ \liminf_{N\to\infty}\log D(N){\log N} \geq α_*:= 0.7527964558\ldots; \] thus crossing the natural exponent-3/4 barrier of Ruzsa's method. The value 0.7527964558ldots arises from a simple optimisation problem and appears to be the limit of the new approach.

The second part of Hilbert's 16th problem is one of the most fundamental open problems in the qualitative theory of ordinary differential equations and dynamical systems. A central unresolved question is whether the Hilbert number H(d) is finite for arbitrary polynomial degree d. (A very recent manuscript from OpenAI asserts the finiteness of H(d); see the remark at the end of this paper.) In the absence of a general upper bound theory, most existing work constructs explicit perturbed polynomial systems to obtain improved lower bounds for H(d), while rigorous upper bound estimates remain largely unavailable. This paper focuses on improving the quantitative lower bound for polynomial systems through a systematic Hierarchical Melnikov Realization framework. We construct perturbed dynamics based on an anisotropic Chebyshev Hamiltonian, where hierarchically selected perturbation coefficients generate simple zeros of the first-order Melnikov function simultaneously across multiple disjoint period annuli. Two distinct 3-adic filtrations supply the necessary logarithmic correction factors, and a Borel--Gauss analysis establishes the required local rank condition under sufficiently strong anisotropy. As the main result of this work, we prove that H(d)=Ωbigl(d^2ln^2 dbigr), which improves the previously known lower bound by a factor of ln d. The full construction of limit cycles and the resulting dynamical bounds are formally certified using Lean 4 formal verification.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

This paper is the second in the series Commutative Scaling of Width and Depth (WD) about commutativity of infinite width and depth limits in deep neural networks. Our aim is to understand the behaviour of neural functions (functions that depend on a neural network model) as width and depth go to infinity (in some sense), and eventually identify settings under which commutativity holds, i.e. the neural function tends to the same limit no matter how width and depth limits are taken. In this paper, we formally introduce and define the commutativity framework, and discuss its implications on neural network design and scaling. We study commutativity for the neural covariance kernel which reflects how network layers separate data. Our findings extend previous results established in [55] by showing that taking the width and depth to infinity in a deep neural network with skip connections, when branches are suitably scaled to avoid exploding behaviour, result in the same covariance structure no matter how that limit is taken. This has a number of theoretical and practical implications that we discuss in the paper. The proof techniques in this paper are novel and rely on tools that are more accessible to readers who are not familiar with stochastic calculus (used in the proofs of WD(I))).

We study the robustness of stochastic mirror descent (SMD) under heavy-tailed noise, focusing on whether the method retains its convergence guarantees when run with infinite-variance stochastic gradient input. To address this question in a principled manner, we begin by introducing a continuous-time model of SMD as a stochastic differential equation (SDE) driven by a centered Lévy noise process with finite p-th order moments, 1 < p leq 2. This scheme -- which we call the Lévy mirror flow (LMF) -- arises naturally as the scaling limit of SMD in the presence of heavy-tailed noise. In particular, when p < 2 -- the heavy noise regime -- the trajectories of LMF generically exhibit jump discontinuities of arbitrary magnitude which, if frequent enough, lead to infinite variance. Nonetheless, despite this highly singular behavior, we show that LMF attains ε-optimality within O(ε^{-p/(p-1)}) time in the convex case, and within tilde O(ε^{-1/(p-1)}) time for (relatively) strongly convex objectives. These guarantees provide a transparent characterization of the impact of frequent long jumps on the convergence of the process, and percolate to a series of matching discrete-time guarantees for several variants of SMD under heavy-tailed noise.

This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a refinement of mean-square analysis in Li et al. (2019), and this refined framework automates the analysis of a large class of sampling algorithms based on discretizations of contractive SDEs. Using this framework, we establish an O(d/epsilon) mixing time bound for LMC, without warm start, under the common log-smooth and log-strongly-convex conditions, plus a growth condition on the 3rd-order derivative of the potential of target measures. This bound improves the best previously known O(d/epsilon) result and is optimal (in terms of order) in both dimension d and accuracy tolerance epsilon for target measures satisfying the aforementioned assumptions. Our theoretical analysis is further validated by numerical experiments.

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.

The growth rate of Av(1324) is the last unknown Stanley-Wilf limit of a length-four pattern. Since 2020 the best rigorous lower bound has been the 10.271012 of Bevan, Brignall, Elvey Price and Pantone; we raise it to 10.412263. Their construction lays 1324-avoiders along an infinite staircase of two-cell blocks alternating with single connecting cells, and forbids a 1324 by a local condition on how the points of a block interleave with the components of the cell beside it. Certain points of a block, its leaves, may be exempted from that condition. They exempt them on one axis only, and report that they could not count the possibilities when both are exempted. This paper exempts them on both axes and counts the result. The second relaxation is their own argument read in the other axis, and the Harris correlation inequality bounds the joint count below by the product of the two counts taken separately, at the cost of one factor of the component generating function.

We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem: LR+GD reduces to a batch version of the celebrated perceptron algorithm when the step size gamma to infty. Second, we observe that larger step sizes lead LR+GD to higher logistic losses when it tends to the perceptron algorithm, but larger step sizes also lead to faster convergence to a solution for the classification problem, meaning that logistic loss is an unreliable metric of the proximity to a solution. Surprisingly, high loss values can actually indicate faster convergence. Third, since the convergence rate in terms of loss function values of LR+GD is unreliable, we examine the iteration complexity required by LR+GD with large step sizes to solve the classification problem and prove that this complexity is suboptimal. To address this, we propose a new method, Normalized LR+GD - based on the connection between LR+GD and the perceptron algorithm - with much better theoretical guarantees.

When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well understood theoretically. Several previous works have attributed this success to the stochastic noise present in SGD. However, we show through a novel set of experiments that the stochastic noise is not sufficient to explain good non-convex training, and that instead the effect of a large learning rate itself is essential for obtaining best performance.We demonstrate the same effects also in the noise-less case, i.e. for full-batch GD. We formally prove that GD with large step size -- on certain non-convex function classes -- follows a different trajectory than GD with a small step size, which can lead to convergence to a global minimum instead of a local one. Our settings provide a framework for future analysis which allows comparing algorithms based on behaviors that can not be observed in the traditional settings.

We study the two-dimensional periodic resistive compressible magnetohydrodynamic equations with constant shear viscosity and magnetic diffusivity, bulk viscosity ρ^β, and pressure ρ^γ. For every β>1 and γ>1, we construct global finite-energy renormalized weak solutions from strictly positive bounded W^{1,q} densities, q>2, and arbitrary H^1 velocity and magnetic data. The construction combines approximation-independent finite density moments, generalized effective-flux identities, and a joint logarithmic renormalization of the density and its entropy defect. An augmented relative energy containing the β-power density potential yields weak--strong uniqueness against positive H^2 strong solutions for the same full pressure range. We also establish global strong existence for a large-background family when γ>max{5-2β,β+1}. Writing m=intρ_0, the density perturbation is bounded in the scaled norm m^{(γ-3)/2}|ρ_0-m|_{H^2}, while the fixed H^2 velocity and magnetic norms need not be small. For sufficiently large m, frequency-dependent acoustic dissipation, staged vorticity weights, and a separate initial-layer flux estimate close a simultaneous bootstrap. The admissible pressure exponents have infimum 7/3, with the endpoint excluded. For β>2 the relevant damping rate is the minimum of the viscous and pressure-relaxation rates; keeping both rates extends the argument without an upper restriction on β. The strong theorem has no upper restriction on γ under this scaled density hypothesis; for fixed additive density perturbations it applies in the stated lower range up to γ=3.

Motivated by the paradigm of reservoir computing, we consider randomly initialized controlled ResNets defined as Euler-discretizations of neural controlled differential equations (Neural CDEs), a unified architecture which enconpasses both RNNs and ResNets. We show that in the infinite-width-depth limit and under proper scaling, these architectures converge weakly to Gaussian processes indexed on some spaces of continuous paths and with kernels satisfying certain partial differential equations (PDEs) varying according to the choice of activation function, extending the results of Hayou (2022); Hayou & Yang (2023) to the controlled and homogeneous case. In the special, homogeneous, case where the activation is the identity, we show that the equation reduces to a linear PDE and the limiting kernel agrees with the signature kernel of Salvi et al. (2021a). We name this new family of limiting kernels neural signature kernels. Finally, we show that in the infinite-depth regime, finite-width controlled ResNets converge in distribution to Neural CDEs with random vector fields which, depending on whether the weights are shared across layers, are either time-independent and Gaussian or behave like a matrix-valued Brownian motion.