OpenRaiser/Intern-Atlas huggingface dataset:
ProSub: Probabilistic Open-Set Semi-Supervised Learning with Subspace-Based Out-of-Distribution Detection
Venue: arXiv cs.LG 2026
Year: 2026

In open-set semi-supervised learning (OSSL), we consider unlabeled datasets that may contain unknown classes. Existing OSSL methods often use the softmax confidence for classifying data as in-distribution (ID) or out-of-distribution (OOD). Additionally, many works for OSSL rely on ad-hoc thresholds for ID/OOD classification, without considering the statistics of the problem. We propose a new score for ID/OOD classification based on angles in feature space between data and an ID subspace. Moreover, we propose an approach to estimate the conditional distributions of scores given ID or OOD data, enabling probabilistic predictions of data being ID or OOD. These components are put together in a framework for OSSL, termed ProSub, that is experimentally shown to reach SOTA performance on several benchmark problems. Our code is available at https://github.com/walline/prosub.
Harmonizing Safety and Speed: A Human-Algorithm Approach to Enhance the FDA's Medical Device Clearance Policy
Venue: arXiv cs.LG 2026
Year: 2026

The United States Food and Drug Administration's (FDA's) 510(k) pathway allows manufacturers to gain medical device approval by demonstrating substantial equivalence to a legally marketed device. However, the inherent ambiguity of this regulatory procedure has been associated with high recall among many devices cleared through this pathway, raising significant safety concerns. In this paper, we develop a combined human-algorithm approach to assist the FDA in improving its 510(k) medical device clearance process by reducing recall risk and regulatory workload. We first develop machine learning methods to estimate the risk of recall of 510(k) medical devices based on the information available at the time of submission. We then propose a data-driven clearance policy that recommends acceptance, rejection, or deferral to FDA's committees for in-depth evaluation. We conduct an empirical study using a unique dataset of over 31,000 submissions that we assembled based on data sources from the FDA and Centers for Medicare and Medicaid Service (CMS). Compared to the FDA's current practice, which has a recall rate of 10.3% and a normalized workload measure of 100%, a conservative evaluation of our policy shows a 32.9% improvement in the recall rate and a 40.5% reduction in the workload. Our analyses further suggest annual cost savings of approximately $1.7 billion for the healthcare system driven by avoided replacement costs, which is equivalent to 1.1% of the entire United States annual medical device expenditure. Our findings highlight the value of a holistic and data-driven approach to improve the FDA's current 510(k) pathway.
GraphFM: A generalist graph transformer that learns transferable representations across diverse domains
Venue: arXiv cs.LG 2026
Year: 2026

Graph neural networks (GNNs) are often trained on individual datasets, requiring specialized models and significant hyperparameter tuning due to the unique structures and features of each dataset. This approach limits the scalability and generalizability of GNNs, as models must be tailored for each specific graph type. To address these challenges, we introduce GraphFM, a scalable multi-graph pretraining approach designed for learning across diverse graph datasets. GraphFM uses a Perceiver-based encoder with learned latent tokens to compress domain-specific features into a shared latent space, enabling generalization across graph domains. We propose new techniques for scaling up graph training on datasets of different sizes, allowing us to train GraphFM on 152 distinct graph datasets, containing a total of 7.4 million nodes and 189 million edges. This allows us to study the effect of scale on pretraining across domains such as molecules, citation networks, and product graphs, and show that training on diverse datasets improves performance over single-source pretraining. Additionally, pretraining with a mixture of synthetic and real graphs enhances adaptability and stability, leading to competitive performance with state-of-the-art models across various node classification tasks. This approach reduces the burden of dataset-specific training and provides a single generalist model capable of performing across multiple diverse graph structures and tasks. Code is available at https://github.com/nerdslab/GraphFM.
Unified-EGformer: Exposure Guided Lightweight Transformer for Mixed-Exposure Image Enhancement
Venue: arXiv cs.CV 2026
Year: 2026

Despite recent strides made by AI in image processing, the issue of mixed exposure, pivotal in many real-world scenarios like surveillance and photography, remains inadequately addressed. Traditional image enhancement techniques and current transformer models are limited with primary focus on either overexposure or underexposure. To bridge this gap, we introduce the Unified-Exposure Guided Transformer (Unified-EGformer). Our proposed solution is built upon advanced transformer architectures, equipped with local pixel-level refinement and global refinement blocks for color correction and image-wide adjustments. We employ a guided attention mechanism to precisely identify exposure-compromised regions, ensuring its adaptability across various real-world conditions. U-EGformer, with a lightweight design featuring a memory footprint (peak memory) of only $\sim$1134 MB (0.1 Million parameters) and an inference time of 95 ms (9.61x faster than the average), is a viable choice for real-time applications such as surveillance and autonomous navigation. Additionally, our model is highly generalizable, requiring minimal fine-tuning to handle multiple tasks and datasets with a single architecture.
When Can Transformers Count to n?
Venue: arXiv cs.CL 2026
Year: 2026

Large language models based on the transformer architecture can solve highly complex tasks, yet their fundamental limitations on simple algorithmic problems remain poorly understood. In this work, we focus on basic counting tasks and investigate how the difficulty of these tasks scales with the transformer embedding dimension, the context length, and the vocabulary size. We reveal a sharp theoretical phase transition governed by the relationship between the embedding dimension and the vocabulary size. When the dimension is at least as large as the vocabulary, transformers can perfectly maintain token counts. However, when the vocabulary exceeds the embedding dimension, the interference between non-orthogonal token representations forces the network weights to scale polynomially. This renders the exact counting algorithm numerically unstable and practically unlearnable. We empirically validate this bottleneck by training transformers from scratch, demonstrating a strict performance drop at the theoretical threshold and catastrophic out of distribution failure when scaling the vocabulary or context length. Furthermore, we show that state-of-the-art pretrained models suffer from similar failure cases. Our work reveals a critical blind spot absent from the current literature regarding the connection among these three parameters, proving that vocabulary size fundamentally dictates the difficulty of counting tasks.
Parallel Split Learning with Global Sampling
Venue: arXiv cs.LG 2026
Year: 2026

Parallel split learning (PSL) suffers from two intertwined issues: the effective batch size grows with the number of clients, and data that is not identically and independently distributed (non-IID) skews global batches. We present parallel split learning with global sampling (GPSL), a server-driven scheme that fixes the global batch size while computing per-client batch-size schedules using pooled-level proportions. The actual samples are drawn locally without replacement by each selected client. This eliminates per-class rounding, decouples the effective batch from the client count, and makes each global batch distributionally equivalent to centralized uniform sampling without replacement. Consequently, we obtain finite-population deviation guarantees via Serfling's inequality, yielding a zero rounding bias compared to local sampling schemes. GPSL is a drop-in replacement for PSL with negligible overhead and scales to large client populations. In extensive experiments on CIFAR-10/100 and ResNet-18/34 under non-IID splits, GPSL stabilizes optimization and achieves centralized-like accuracy, while fixed local batching trails by up to 60%. Furthermore, GPSL shortens training time by avoiding inflation of training steps induced by data-depletion. These findings suggest GPSL is a promising and scalable approach for learning in resource-constrained environments.
Mathematical theory of deep learning
Venue: arXiv cs.LG 2026
Year: 2026

This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural network theory. Serving as a guide for students and researchers in mathematics and related fields, the book aims to equip readers with foundational knowledge on the topic. It prioritizes simplicity over generality, and presents rigorous yet accessible results to help build an understanding of the essential mathematical concepts underpinning deep learning.
Fairness Definitions in Language Models Explained
Venue: arXiv cs.CL 2026
Year: 2026

Language Models (LMs) have demonstrated exceptional performance across various Natural Language Processing (NLP) tasks. Despite these advancements, LMs can inherit and amplify societal biases related to sensitive attributes such as gender and race, limiting their adoption in real-world applications. Therefore, fairness has been extensively explored in LMs, leading to the proposal of various fairness notions. However, the lack of clear agreement on which fairness definition to apply in specific contexts and the complexity of understanding the distinctions between these definitions can create confusion and impede further progress. To this end, this paper proposes a systematic survey that clarifies the definitions of fairness as they apply to LMs. Specifically, we begin with a brief introduction to LMs and fairness in LMs, followed by a comprehensive, up-to-date overview of existing fairness notions in LMs and the introduction of a novel taxonomy that categorizes these concepts based on their transformer architecture: encoder-only, decoder-only, and encoder-decoder LMs. We further illustrate each definition through experiments, showcasing their practical implications and outcomes. Finally, we discuss current research challenges and open questions, aiming to foster innovative ideas and advance the field. The repository is publicly available online at https://github.com/vanbanTruong/Fairness-in-Large-Language-Models/tree/main/definitions.
Right Now, Wrong Then: Non-Stationary Direct Preference Optimization under Preference Drift
Venue: arXiv cs.LG 2026
Year: 2026

Current Large Language Model (LLM) preference optimization algorithms do not account for temporal preference drift, which can lead to severe misalignment. To address this limitation, we propose Non-Stationary Direct Preference Optimisation (NS-DPO) that models time-dependent reward functions with a Dynamic Bradley-Terry model. NS-DPO proposes a computationally efficient solution by introducing only a single discount parameter in the loss function, which is used for exponential weighting that proportionally focuses learning on more time-relevant datapoints. We theoretically analyze the convergence of NS-DPO in a general setting where the exact nature of the preference drift is not known, providing upper bounds on the estimation error and regret caused by non-stationary preferences. Finally, we demonstrate the effectiveness of NS-DPO for fine-tuning LLMs under drifting preferences. Using scenarios where various levels of preference drift is introduced, with popular LLM reward models and datasets, we show that NS-DPO fine-tuned LLMs remain robust under non-stationarity, significantly outperforming baseline algorithms that ignore temporal preference changes, without sacrificing performance in stationary cases.
Towards the Terminator Economy: Assessing Job Exposure to AI through LLMs
Venue: arXiv cs.CY 2026
Year: 2026

AI and related technologies are reshaping jobs and tasks, either by automating or augmenting human skills in the workplace. Many researchers have been working on estimating if and to what extent jobs and tasks are exposed to the risk of being automatized by AI-related technologies. Our work tackles this issue through a data-driven approach by: (i) developing a reproducible framework that uses cutting-edge open-source large language models to assess the current capabilities of AI and robotics in performing job-related tasks; (ii) formalizing and computing a measure of AI exposure by occupation, the Task Exposure to AI (TEAI) index, and a measure of Task Replacement by AI (TRAI), both validated through a human user evaluation and compared with the state of the art. Our results show that the TEAI index is positively correlated with cognitive, problem-solving and management skills, while it is negatively correlated with social skills. Applying the index to the US, we obtain that about one-third of US employment is highly exposed to AI, primarily in high-skill jobs requiring a graduate or postgraduate level of education. We also find that AI exposure is positively associated with both employment and wage growth in 2003-2023, suggesting that AI has an overall positive effect on productivity. Considering specifically the TRAI index, we find that even in high-skill occupations, AI exhibits high variability in task substitution, suggesting that AI and humans complement each other within the same occupation, while the allocation of tasks within occupations is likely to change. All results, models, and code are freely available online to allow the community to reproduce our results, compare outcomes, and use our work as a benchmark to monitor AI's progress over time.
Shapley Value Computation in Ontology-Mediated Query Answering
Venue: arXiv cs.AI 2026
Year: 2026

The Shapley value was originally introduced in cooperative game theory as a wealth distribution mechanism. It has since found use in knowledge representation and databases for the purpose of assigning scores to formulas and database tuples based upon their contribution to obtaining a query result or inconsistency. The application of the Shapley value outside of its original setting relies upon defining a numeric wealth function that captures the phenomenon of interest. In the case of database queries, recent work has focused on the so-called drastic Shapley value, obtained by translating a Boolean query into a 0/1 function based upon whether the query is satisfied or not. The present paper explores the use of the drastic Shapley value in the context of ontology-mediated query answering (OMQA). We present a detailed complexity analysis of the drastic Shapley value computation (SVC$^{dr}$) problem in the OMQA setting. In particular, we establish a dichotomy result that shows that for every ontology-mediated query (T,q) composed of an ontology T formulated in the description logic $\mathcal{ELHI}_\bot$ and a connected constant-free homomorphism-closed query q the corresponding SVC$^{dr}$ problem is either tractable (in FP) or #P-hard. We further show how the #P-hardness side of the dichotomy can be strengthened to cover possibly disconnected queries with constants. Our results exploit recently discovered connections between SVC$^{dr}$ and probabilistic query evaluation and allow us to generalize existing results on probabilistic OMQA.
What Are Good Positional Encodings for Directed Graphs?
Venue: arXiv cs.LG 2026
Year: 2026

Positional encodings (PEs) are essential for building powerful and expressive graph neural networks and graph transformers, as they effectively capture the relative spatial relationships between nodes. Although extensive research has been devoted to PEs in undirected graphs, PEs for directed graphs remain relatively unexplored. This work seeks to address this gap. We first introduce the notion of Walk Profile, a generalization of walk-counting sequences for directed graphs. A walk profile encompasses numerous structural features crucial for directed graph-relevant applications, such as program analysis and circuit performance prediction. We identify the limitations of existing PE methods in representing walk profiles and propose a novel Multi-q Magnetic Laplacian PE, which extends the Magnetic Laplacian eigenvector-based PE by incorporating multiple potential factors. The new PE can provably express walk profiles. Furthermore, we generalize prior basis-invariant neural networks to enable the stable use of the new PE in the complex domain. Our numerical experiments validate the expressiveness of the proposed PEs and demonstrate their effectiveness in solving sorting network satisfiability and performing well on general circuit benchmarks. Our code is available at https://github.com/Graph-COM/Multi-q-Maglap.
Accelerating Large Language Model Inference with Self-Supervised Early Exits
Venue: arXiv cs.CL 2026
Year: 2026

This paper presents a modular approach to accelerate inference in large language models (LLMs) by adding early exit heads at intermediate transformer layers. Each head is trained in a self-supervised manner to mimic the main model's predictions, allowing computation to stop early when a calibrated confidence threshold is reached. We evaluate several confidence metrics and show that entropy provides the most reliable separation between correct and incorrect predictions. Experiments on the Pythia model suite (70M to 2.8B parameters) demonstrate that our method significantly reduces inference cost while maintaining accuracy across multiple benchmarks. We further adapt this approach to speculative decoding, introducing Dynamic Self-Speculative Decoding (DSSD), which achieves 1.66x higher token acceptance than manually-tuned LayerSkip baselines with minimal hyperparameter tuning.
Simpler Optimal Sorting from a Directed Acyclic Graph
Venue: arXiv cs.DS 2026
Year: 2026

Fredman proposed in 1976 the following algorithmic problem: Given are a ground set $X$, some partial order $P$ over $X$, and some comparison oracle $O_L$ that specifies a linear order $L$ over $X$ that extends $P$. A query to $O_L$ has as input distinct $x, x' \in X$ and outputs whether $x <_L x'$ or vice versa. If we denote by $e(P)$ the number of linear extensions of $P$, then $\log e(P)$ is a worst-case lower bound on the number of queries needed to output the sorted order of $X$. Fredman did not specify in what form the partial order is given. Haeupler, Hladík, Iacono, Rozhon, Tarjan, and Tětek ('24) propose to assume as input a directed acyclic graph, $G$, with $m$ edges and $n=|X|$ vertices. Denote by $P_G$ the partial order induced by $G$. Algorithmic performance is measured in running time and the number of queries used, where they use $Θ(m + n + \log e(P_G))$ time and $Θ(\log e(P_G))$ queries to output $X$ in its sorted order. Their algorithm is worst-case optimal in terms of running time and queries, both. Their algorithm combines topological sorting with heapsort. Their analysis relies upon sophisticated counting arguments using entropy, recursively defined sets defined over the run of their algorithm, and vertices in the graph that they identify as bottlenecks for sorting. In this paper, we do away with sophistication. We show that when the input is a directed acyclic graph then the problem admits a simple solution using $Θ(m + n + \log e(P_G))$ time and $Θ(\log e(P_G))$ queries. Especially our proofs are much simpler as we avoid the usage of advanced charging arguments and data structures, and instead rely upon two brief observations.
Intermittent Semi-Working Mask: A New Masking Paradigm for LLMs
Venue: arXiv cs.CL 2026
Year: 2026

Multi-turn dialogues and context-intensive tasks challenge Large Language Models (LLMs) to integrate long histories without sacrificing generation quality. Although prefix LLMs can better exploit historical context via bidirectional attention on prefix tokens, they are rarely used in practice because multi-turn training requires many duplicated triplets, and its bidirectional prefix prevents KV-cache reuse at inference time, driving up high cost and latency. To retain the contextual understanding of prefix mask while preserving the inference-time efficiency of causal mask, we introduce Intermittent Semi-working Mask (ISM), a masking scheme that injects sparse bidirectional attention into the causal backbone. ISM alternates bidirectional attention over query segments with unidirectional attention over answer segments, enabling the synthesis of in-context while preserving global causality. This design eliminates triplet expansion during training and maintains KV-cache reuse during inference, yielding latency comparable to standard causal LLMs. ISM is architecture-agnostic and parameter-free, adding only minimal latency. Across extensive evaluations, ISM outperforms causal baselines not only on multi-turn dialogue, but also on context-intensive tasks like mathematical reasoning.
Do Prevalent Bias Metrics Capture Allocational Harms from LLMs?
Venue: arXiv cs.CL 2026
Year: 2026

Allocational harms occur when resources or opportunities are unfairly withheld from specific groups. Many proposed bias measures ignore the discrepancy between predictions, which are what the proposed methods consider, and decisions that are made as a result of those predictions. Our work examines the reliability of current bias metrics in assessing allocational harms arising from predictions of large language models (LLMs). We evaluate their predictive validity and utility for model selection across ten LLMs and two allocation tasks. Our results reveal that commonly-used bias metrics based on average performance gap and distribution distance fail to reliably capture group disparities in allocation outcomes. Our work highlights the need to account for how model predictions are used in decisions, in particular in contexts where they are influenced by how limited resources are allocated.
Large Language Models for Secure Code Assessment: A Multi-Language Empirical Study
Venue: arXiv cs.SE 2026
Year: 2026

Most vulnerability detection studies focus on datasets of vulnerabilities in C/C++ code, offering limited language diversity. Thus, the effectiveness of deep learning methods, including large language models (LLMs), in detecting software vulnerabilities beyond these languages is still largely unexplored. In this paper, we evaluate the effectiveness of LLMs in detecting and classifying Common Weakness Enumerations (CWE) using different prompt and role strategies. Our experimental study targets six state-of-the-art pre-trained LLMs (GPT-3.5- Turbo, GPT-4 Turbo, GPT-4o, CodeLLama-7B, CodeLLama- 13B, and Gemini 1.5 Pro) and five programming languages: Python, C, C++, Java, and JavaScript. We compiled a multi-language vulnerability dataset from different sources, to ensure representativeness. Our results showed that GPT-4o achieves the highest vulnerability detection and CWE classification scores using a few-shot setting. Aside from the quantitative results of our study, we developed a library called CODEGUARDIAN integrated with VSCode which enables developers to perform LLM-assisted real-time vulnerability analysis in real-world security scenarios. We have evaluated CODEGUARDIAN with a user study involving 22 developers from the industry. Our study showed that, by using CODEGUARDIAN, developers are more accurate and faster at detecting vulnerabilities.