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Decoding neural activity into human-interpretable representations is a key research direction in brain-computer interfaces (BCIs) and computational neuroscience. Recent progress in machine learning and generative AI has driven growing interest in transforming non-invasive Electroencephalography (EEG) signals into images, text, and audio. This survey consolidates and analyzes developments across EEG-to-image synthesis, EEG-to-text generation, and EEG-to-audio reconstruction. We conducted a structured literature search across major databases (2017-2025), extracting key information on datasets, generative architectures (GANs, VAEs, transformers, diffusion models), EEG feature-encoding techniques, evaluation metrics, and the major challenges shaping current work in this area. Our review finds that EEG-to-image models predominantly employ encoder-decoder architectures built on GANs, VAEs, or diffusion models; EEG-to-text approaches increasingly leverage transformer-based language models for open-vocabulary decoding; and EEG-to-audio methods commonly map EEG signals to mel-spectrograms that are subsequently rendered into audio using neural vocoders. Despite promising advances, the field remains constrained by small and heterogeneous datasets, limited cross-subject generalization, and the absence of standardized benchmarks. By consolidating methodological trends and available datasets, this survey provides a foundational reference for advancing EEG-based generative AI and supporting reproducible research. We further highlight open-source datasets and baseline implementations to facilitate systematic benchmarking and accelerate progress in EEG-driven neural decoding.

Large Multimodal Models (LMMs) exhibit shortfalls when interpreting images and, by some measures, have poorer spatial cognition than young children or animals. Despite this, they attain high scores on many popular visual benchmarks, with headroom rapidly eroded by model progress. This creates a need for difficult benchmarks that remain relevant for longer. We introduce ZeroBench - a lightweight visual reasoning benchmark curated using adversarial filtering to be "impossible" for frontier LMMs at its original release, with initial SotA scores of 0% pass@1 and pass^5. We track progress on ZeroBench over the subsequent year, observing SotA reaching 6% pass^5 and 19% pass@5, indicating the potential longevity of the benchmark. We evaluate 46 LMMs on ZeroBench, compare performance to a human baseline, analyse strengths and weaknesses, chart a year of progress in visual capabilities, and publicly release ZeroBench at https://zerobench.github.io.

To overcome the black-box nature of predictive AI and the hallucination risks of generative models, retrieval-based models offer an interpretable, evidence-based paradigm for pathology clinical workflow. However, real-world clinical queries are inherently interleaved (e.g., pathology images and text). Current dual-encoders suffer from an \textbf{Architectural Mismatch}, lacking the mechanism to fuse such composed queries. To address this, we formalize the task of Pathology Composed Retrieval (PCR). While Multimodal Large Language Models (MLLMs) offer deep-fusion capabilities, directly applying them exposes a \textbf{Task Mismatch} and a \textbf{Domain Mismatch}. To resolve these challenges, we propose HOMIE, a model-agnostic adaptation framework that transforms any generative MLLM into a specialized pathology retrieval expert. Evaluated on our newly introduced PCR Benchmark, a lightweight 2B-parameter HOMIE variant substantially outperforms existing paradigms, surpassing specialized 7B pathology MLLMs and dual-encoders by large margins on composed retrieval, while maintaining strong performance on traditional simple retrieval. The project page is available at https://qfchou.github.io/HOMIE_page/.

Natural-language instructions rarely specify every detail required for embodied action. An agent asked to ``prepare an apple,'' for example, must still determine whether to wash or cut it, where to place it, and in what order to perform these actions. Such decisions often reflect user-specific preferences that are demonstrated through behavior but never explicitly stated. We study whether embodied agents can infer these latent preferences from a small number of prior demonstrations and apply them when planning in new situations. To support systematic evaluation, we introduce Preference-based Planning (PbP), a benchmark containing 5,000 evaluation groups and 290 preferences organized into three levels: atomic action parameters, strategic interaction and placement policies, and temporal ordering constraints. We further propose Inferring the Unspoken (InTU), a two-stage framework that first verbalizes the preference inferred from multimodal behavioral demonstrations and then generates an action plan conditioned on that explicit representation. Experiments with video-language and language models reveal a substantial preference-acquisition gap: models plan effectively when given the ground-truth preference, but their performance degrades sharply when the same preference must be inferred from behavior. Explicit verbalization consistently improves alignment over direct end-to-end planning, particularly for strong multimodal models, and provides greater robustness when preferences must transfer across visually distinct scenes. These results identify visual-to-semantic preference acquisition, rather than preference-conditioned planning alone, as a central bottleneck in personalized embodied intelligence. They also demonstrate that language can serve as an interpretable and transferable intermediate representation between observed behavior and personalized action.

Supervised dimensionality reduction maps labeled data into a low-dimensional feature space while preserving class separation. A common strategy is to learn features that maximize a measure of statistical dissimilarity between the class-conditional probability distributions. Information geometry, which is rooted in Riemannian geometry, provides an alternative framework for measuring class dissimilarity. It treats probability distributions as points in a statistical manifold and uses the Fisher information metric to define a geodesic distance--the Fisher-Rao distance--between distributions The Fisher-Rao distance is an appealing candidate for measuring class separation because the Fisher information metric is a local measure of discriminability, and because it allows a geometric interpretation. Here, we present Supervised Quadratic Feature Analysis (SQFA), a supervised dimensionality reduction method which learns linear features that maximize Fisher-Rao distances between class-conditional distributions, under Gaussian assumptions. In multiple real world datasets, we find that SQFA features support classification accuracy that is competitive with features that maximize more popular measures of dissimilarity, or that are learned by other state-of-the-art dimensionality reduction methods. Notably, the best classification accuracy is achieved by SQFA-H features, a variant of SQFA that maximizes the Hellinger distance, a rarely used objective for dimensionality reduction. These results demonstrate the potential of information geometry as a tool for supervised dimensionality reduction. We provide a Python implementation of SQFA at https://github.com/dherrera1911/sqfa.

Recent work has demonstrated the potential of large language models (LLMs) for program optimization, a key challenge in programming languages. We propose a blackbox adaptation method called Retrieval Augmented Search (RAS) that performs beam search over candidate optimizations; at each step, it retrieves in-context examples from a given training dataset of slow-fast program pairs to guide the LLM. Critically, we find that performing contextual retrieval based on an LLM-generated natural language description significantly outperforms retrieval based on the source code. We also propose AEGIS, a method for improving interpretability by decomposing training examples into ''atomic edits'' that are significantly more incremental in nature. We show that RAS performs up to 2.06$\times$ better than prior state-of-the-art blackbox adaptation strategies on optimizing C++ programs, and that AEGIS performs up to 1.37$\times$ better while making significantly smaller edits. We also show that using RAS improves the mean runtime percentile of Python programs by 10.27 compared to baselines.

Code-related benchmarks play a critical role in evaluating large language models (LLMs), yet their quality fundamentally shapes how the community interprets model capabilities. In the past few years, awareness of benchmark quality has grown. Yet, after a decade-scale (2014-2025) survey over 672 code benchmarks, we observed a lag between growing awareness and actual practice. For example, in 2025 alone, the number of benchmarks that ignore code coverage when providing test cases nearly matches the total count accumulated across the previous ten years. In response, we take a clear position: Code benchmarks must prioritize rigor in benchmark construction, reliability in evaluation, and reproducibility in release. To operationalize this position, we introduce a code benchmark guideline HOW2BENCH with 55 checklists. Finally, our further human study also exposed that the current issues not only stem from the significant effort required, but also from a lack of awareness regarding their importance.

We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean loss in the input layer, and under the assumption that the weights are, in a precise sense, adapted to the coordinate system distinguished by the activations. We show that gradient descent corresponds to a dynamical process in the input layer, whereby clusters of data are progressively reduced in complexity ("truncated") at an exponential rate that increases with the number of data points that have already been truncated. We provide a detailed discussion of several types of solutions to the gradient flow equations. A main motivation for this work is to shed light on the interpretability question in supervised learning.

Improving the reliability and completeness of colonoscopic inspection is critical for reducing missed lesions and improving colorectal cancer prevention. Reliable scene understanding is essential for navigation, reconstruction, and assessment of inspection completeness. Anatomical structures such as mucosal folds provide stable geometric cues for endoscope localization, while surgical instruments introduce dynamic occlusions that complicate visual interpretation. However, existing gastrointestinal endoscopy datasets largely focus on disease detection or artifact segmentation, leaving a gap in precise annotations of structural landmarks and instruments. We introduce SegCol, a dataset and benchmark for semantic segmentation of colon fold edges and surgical instruments derived from the EndoMapper dataset. SegCol provides manually annotated pixel-level masks for three instrument classes and thin fold-edge structures across temporally consistent image sequences. It forms the basis of the SegCol Challenge, organized as part of the EndoVis Challenge at MICCAI 2024, evaluating both supervised segmentation and annotation-efficient active learning. We further study segmentation metrics, including Dice, ODS/OIS, AP, and CLDice, under structural perturbations and different object geometries, and analyze participating methods, architectural choices, and active learning strategies. Our findings show that metric behavior strongly depends on target structure, highlighting the need for carefully selected evaluation protocols in endoscopic segmentation. Details are available at https://www.synapse.org/Synapse:syn54124209/wiki/626563, and code at https://github.com/surgical-vision/segcol_challenge.

The rapid development of large language models (LLMs) has transformed many industries, including healthcare. In practice, hospitals and patients increasingly seek LLM-based systems capable of interpreting personal health records and providing healthcare guidance. However, existing approaches mainly rely on general medical knowledge and often fail to account for individual variability, limiting their ability to provide personalized guidance. To address this, we propose personalized prompt learning (PPL), a framework that learns individualized prompts to guide LLMs in generating personalized healthcare recommendations. PPL constructs initial personalized prompts by leveraging both self-informed patient information and peer-informed signals derived from clinically similar cases. These prompts are then refined using reinforcement learning (RL) to better align the generated responses with physician recommendations written for each patient. PPL operates with hard prompts, enabling seamless integration with proprietary LLMs without modifying the underlying models. We evaluate PPL on real-world obstetrics and gynecology data. The results show that our approach produces more personalized healthcare guidance and wins 97 out of 100 comparisons in expert evaluation, demonstrating its potential for broader healthcare applications. Our code is publicly available at https://github.com/CGCL-codes/PPL.

Consumers' engagement with stories is shaped by their expectations about what will happen next, yet modeling these forward-looking beliefs over unstructured narrative content has remained challenging. We develop a framework that uses large language models to approximate consumers' story expectations. Our method generates multiple imagined story continuations from a pre-trained LLM and extracts interpretable, theory-motivated features from these continuations, such as emotion and narrative path features. We propose two complementary validation procedures suited to different data availability: a survey-based approach that compares LLM-derived expectations to human-reported beliefs, and a rational-expectations approach that compares them to actual story outcomes. Applying the framework to both survey data collected in a controlled lab setting and observational data from an online reading platform, we find that LLM-derived expectations correlate with human-reported beliefs as well as actual story continuations along all features studied. In both settings, forward-looking expectations are associated with reader engagement above and beyond features of the content already consumed. Our framework provides a scalable method for modeling consumer beliefs about narrative content, with implications for content creation, platform strategy, and the study of narrative media.

Driven by practical demands in land resource monitoring and national defense security, this paper introduces the Remote Sensing Copy-Move Question Answering (RSCMQA) task. Unlike traditional Remote Sensing Visual Question Answering (RSVQA), RSCMQA focuses on interpreting complex tampering scenarios and inferring relationships between objects. We present a suite of global RSCMQA datasets, comprising images from 29 different regions across 14 countries. Specifically, we propose five distinct datasets, including the basic dataset RS-CMQA, the category-balanced dataset RS-CMQA-B, the high-authenticity dataset Real-RSCM, the extended dataset RS-TQA, and the extended category-balanced dataset RS-TQA-B. These datasets fill a critical gap in the field while ensuring comprehensiveness, balance, and challenging scenarios. Furthermore, we introduce a region-discrimination-guided multimodal copy-move forgery perception framework (CMFPF), which enhances the accuracy of answering questions about tampered images by leveraging prompts about the differences and connections between the source and tampered regions. Extensive experiments demonstrate that our method establishes a stronger benchmark for RSCMQA compared to general VQA and RSVQA models. Our datasets and code are publicly available at https://github.com/shenyedepisa/RSCMQA.

Acute ischemic stroke (AIS) requires time-critical decision-making, where inaccurate interpretation of neuroimaging findings can lead to irreversible disability. Diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC) maps from magnetic resonance imaging (MRI) are central to detecting acute infarction, yet generating factually reliable radiology reports directly from 3D MRI remains challenging due to the difficulty of learning robust cross-modal alignments between volumetric images and clinical text. We propose paired image-domain retrieval and text-domain augmentation (PIRTA), a retrieval-augmented generation framework that improves report factuality by avoiding explicit image-text alignment. PIRTA retrieves clinically similar 3D DWI/ADC volumes using a pretrained 3D vision encoder and leverages their paired clinician-authored reports to ground large language model (LLM)-based report generation. Experiments on multi-institutional in-house data, a held-out external privacy-preserving cohort, and the public ISLES benchmark demonstrate that PIRTA achieves strong image-domain retrieval performance and consistently improves ischemic-territory accuracy, a clinically grounded surrogate for report factuality, compared to direct image-to-text baselines. These results indicate that retrieval-grounded generation provides a scalable and reliable paradigm for producing factually consistent radiology reports from complex 3D brain MRI. Source code is available at https://github.com/jhlee0619/PIRTA.

Large-scale pretraining of transformers has been central to the success of foundation models. However, the scale of those models limits our understanding of the mechanisms at play during optimization. In this work, we study the training dynamics of transformers in a controlled and interpretable setting. On the sparse modular addition task, we demonstrate that specialized attention circuits, called clustering heads, can be implemented during gradient descent to solve the problem. Our experiments show that such pathways naturally emerge during training. By monitoring the evolution of tokens via a visual sandbox, we uncover a two-stage learning and the occurrences of loss spikes due to the high curvature of normalization layers. Our findings provide several insights into patterns observed in more practical settings, such as the pretraining of large language models.

To effectively address potential harms from Artificial Intelligence (AI) systems, it is essential to identify and mitigate system-level hazards. Current analysis approaches focus on individual components of an AI system, like training data or models, in isolation, overlooking hazards from component interactions or how they are situated within a company's development process. To this end, we draw from the established field of system safety, which considers safety as an emergent property of the entire system. In this work, we translate System Theoretic Process Analysis (STPA) - a recognized system safety framework - for analyzing AI development and operation processes. We focus on systems that rely on machine learning algorithms and conduct STPA on three case studies involving linear regression, reinforcement learning, and transformer-based generative models. Our analysis explored how STPA's control and system-theoretic perspectives apply to AI systems and whether unique AI traits - such as model opacity, capability uncertainty, and output complexity - necessitate modifications to the framework. We find that the key concepts and steps of conducting an STPA apply to AI systems but require targeted adaptations to address AI-specific challenges that arise to differing degrees across three case studies. We present the Process-oriented Hazard Analysis for AI Systems (PHASE) as a guideline that adapts STPA concepts for AI. Applying and interpreting STPA using the PHASE guidelines enables four key affordances for analysts responsible for managing AI system harms: 1) detection of system-level hazards, including those from accumulation of disparate issues; 2) explicit acknowledgment of social factors contributing to algorithmic harms; 3) creation of traceable accountability chains between harms and those who can mitigate them; and 4) ongoing monitoring and mitigation of new hazards.

As trajectories sampled by policies used by reinforcement learning (RL) and generative flow networks (GFlowNets) grow longer, credit assignment and exploration become more challenging, and the long planning horizon hinders mode discovery and generalization. The challenge is particularly pronounced in entropy-seeking RL methods, such as generative flow networks, where the agent must learn to sample from a structured distribution and discover multiple high-reward states, each of which take many steps to reach. To tackle this challenge, we propose an approach to incorporate the discovery of action abstractions, or high-level actions, into the policy optimization process. Our approach involves iteratively extracting action subsequences commonly used across many high-reward trajectories and `chunking' them into a single action that is added to the action space. In empirical evaluation on synthetic and real-world environments, our approach demonstrates improved sample efficiency performance in discovering diverse high-reward objects, especially on harder exploration problems. We also observe that the abstracted high-order actions are interpretable, capturing the latent structure of the reward landscape of the action space. This work provides a cognitively motivated approach to action abstraction in RL and is the first demonstration of hierarchical planning in amortized sequential sampling.

Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference (PVI): a general inference framework that seeks and samples from an optimal posterior density such that the resulting posterior predictive distribution is as close to the true data generating process as possible, while this closeness is measured by multiple scoring rules. By optimizing the objective, the predictive variational inference is generally not the same as, or even attempting to approximate, the Bayesian posterior, even asymptotically. Rather, we interpret it as implicit hierarchical expansion. Further, the learned posterior uncertainty detects heterogeneity of parameters among the population, enabling automatic model diagnosis. This framework applies to both likelihood-exact and likelihood-free models. We demonstrate its application in real data examples.

Transformer-based Large Language Models (LLMs) traditionally rely on final-layer loss for finetuning and final-layer representations for predictions, potentially overlooking the predictive power embedded in late layers. Interpretability tools such as the logit lens show that late-layer representations already carry largely formed, task-relevant predictions; here we ask whether that observation can be turned into an actionable training signal. We find that focusing tuning effort on these layers can yield losses comparable to those of the final layer, with complementary test-time behaviour. Building on this, we introduce a tuning framework, Mixture-of-Depths Ensemble (MoDE), which treats the late layers as an ensemble that contributes to the final logits through learned routing weights. MoDE can be applied on top of any existing tuning method (e.g., LoRA) and, in our experiments, modestly improves reasoning performance at a small parameter overhead. We present MoDE as a mechanism study showing that late-layer logits can be made directly useful for tuning, and that they can substitute for substantially larger trainable modules with comparable performance.

In customer contact centers, human agents often struggle with long average handling times (AHT) due to the need to manually interpret queries and retrieve relevant knowledge base (KB) articles. While retrieval augmented generation (RAG) systems using large language models (LLMs) have been widely adopted in industry to assist with such tasks, RAG faces challenges in real-time conversations, such as inaccurate query formulation and redundant retrieval of frequently asked questions (FAQs). To address these limitations, we propose a decision support system that can look beyond RAG by first identifying customer questions in real time. If the query matches an FAQ, the system retrieves the answer directly from the FAQ database; otherwise, it generates answers via RAG. Our approach reduces reliance on manual queries, providing responses to agents within 2 seconds. Deployed in AI-powered human-agent assist solution at Minerva CQ, this system improves efficiency, reduces AHT, and lowers operational costs. We also introduce an automated LLM-agentic workflow to identify FAQs from historical transcripts when no predefined FAQs exist.

Despite being widely adopted as a canonical framework for learning robust models, adversarial training suffers from robust overfitting. Existing empirical and theoretical explorations fail to provide a satisfactory mechanistic interpretation of the phenomenon. By modeling adversarial training with momentum SGD as a discrete-time dynamical system, we propose a PAC-Bayesian analytical framework that proves time-resolved robust generalization bounds. Specifically, our framework tracks the closed-form evolution of the posterior mean and covariance under both stationary and non-stationary transient regimes, connecting the model's robust generalization performance to learning rate, local loss geometry, and mini-batch stochastic gradients. By estimating the key quantities associated with the bound, we illustrate the underlying mechanism of robust overfitting. Our framework also shows how adversarial weight perturbation reduces robust generalization gaps by suppressing dominant loss-curvature modes, while suggesting that excessive penalization can be sub-optimal for optimization.

Federated learning (FL) is a machine learning paradigm where clients with different behaviors and preferences can learn collaboratively without compromising data privacy. Typical FL methods often rely on fixed weighting for parameter aggregation, thereby neglecting the mutual influence among clients. In practice, clients with similar preferences or backgrounds may provide more useful knowledge to each other, which can be leveraged to improve local performance. However, how to quantify such cross-client influence and how to exploit it for personalized aggregation remain underexplored. To address this gap, we propose an influence-oriented Federated learning framework which quantitatively measures Client-level and Class-level Influence to realize adaptive parameter aggregation for each client (FedC^2I for short). Our core idea is to explicitly model the inter-client influence within an FL system via the well-crafted influence vector and influence matrix. Specifically, FedC^2I incorporate influence vectors to quantify client-level influence, enables clients to selectively acquire knowledge from others, and guides the aggregation of feature representation layers. Meanwhile, the influence matrix captures class-level influence in a more fine-grained manner to achieve personalized classifier aggregation. We evaluate the performance of FedC^2I against existing federated learning methods under non-IID settings, and the results demonstrate the superiority of our method in terms of effectiveness, robustness, and interpretability.

Large language models (LLMs) are increasingly being used as ad hoc therapists. While prior research has found that LLMs outperform human counselors in generating single-turn empathetic responses, fewer studies have compared their behaviors across multi-turn sessions. In this study, we compare the session-level behaviors of human peer counselors with those of an LLM, both trained on the same manual to deliver multi-turn, single-session Cognitive Behavioral Therapy (CBT). Our three-phase, mixed-methods study involved: (a) an 18-month ethnography of a peer support platform, where seven counselors iteratively refined CBT prompts through 110 self-counseling sessions and 60 weekly focus groups; (b) a novel session generation method that allows direct, controlled comparison of human and LLM counselors under matched conditions---client responses were drawn from publicly available human-led CBT sessions while counselor responses were generated by a CBT-prompted LLM; and (c) expert evaluations conducted by three licensed clinical psychologists. Through data triangulation, our results show a trade-off. Human peer counselors use relational techniques to interpret subtle cues, adapt CBT to users' values and cultural contexts, and use strategies such as small talk and contextually relevant self-disclosure to build rapport and guide the session, but often at the expense of session structure and therapeutic focus. LLM counselors, on the other hand, demonstrate greater methodological adherence to CBT techniques, but struggle to sustain turn-taking, frequently fail to distinguish between clinically important and trivial content, and are more prone to lecturing and imposing solutions. LLM counselors also tend to produce ``deceptive empathy'', excessively anthropomorphic responses that can inflate user expectations of genuine human care.

Workflows in drug-target interaction (DTI) assessment require integrating heterogeneous data from predictive models, curated resources, and observations from experimental literature. This evidence can be incomplete or conflicting. DrugAgent is a large language model (LLM)-based multi-agent system focused on DTI evidence integration that integrates outputs from machine learning, knowledge graph, and retrieval-augmented generation (RAG) agents. DrugAgent converts agent outputs into interpretable representations, then summarizes conflict across the evidence. We evaluated DrugAgent on kinase screening data of 900 pairs spanning 178 kinases and 42 inhibitors, and an androgen receptor antagonist screening benchmark. On the kinase dataset, LLM-as-a-Judge evaluation indicated outputs were faithful to input evidence in 98.8% of cases. Biological plausibility of returned summarization was high (scores 3-4 out of 5) across ground-truth classes: 79% of Weak activity labels cases (81% for Moderate/77% Strong); Strong cases received higher scores than Weak/Moderate. Label stability showed 98% agreement across runs. Results on the antagonist benchmark were consistent with the kinase dataset. Retrieved literature provided the greatest benefit when direct drug-target evidence was available, highlighting the importance of evidence availability for RAG-based integration. DrugAgent provides heterogeneous evidence-grounded DTI assessment, complementing standalone DTI prediction. We provide strategies to model agreement, conflict, and uncertainty in biomedical evidence integration. Code: https://github.com/sciluna/DrugAgent.

Cardiac arrhythmia, a condition characterized by irregular heartbeats, often serves as an early indication of various heart ailments. With the advent of deep learning, numerous innovative models have been introduced for diagnosing arrhythmias using Electrocardiogram (ECG) signals. However, recent studies solely focus on the performance of models, neglecting the interpretation of their results. This leads to a considerable lack of transparency, posing a significant risk in the actual diagnostic process. To solve this problem, this paper introduces MambaCapsule, a deep neural networks for ECG arrhythmias classification, which increases the explainability of the model while enhancing the accuracy.Our model utilizes Mamba for feature extraction and Capsule networks for prediction, providing not only a confidence score but also signal features. Akin to the processing mechanism of human brain, the model learns signal features and their relationship between them by reconstructing ECG signals in the predicted selection. The model evaluation was conducted on MIT-BIH and PTB dataset, following the AAMI standard. MambaCapsule has achieved a total accuracy of 99.54% and 99.59% on the test sets respectively. These results demonstrate the promising performance of under the standard test protocol.

The rapid spread of false and misleading information on online platforms poses a growing societal challenge, overwhelming the capacity of manual fact-checking and increasing the demand for scalable, reliable automation. Recent advances in generative large language models (LLMs) have broadened the scope of automated fact-checking beyond accuracy-driven prediction. LLMs are now integral components of fact-checking pipelines, supporting tasks such as generating new data, performing and assisting with fact verification, and shaping how fact-checking systems are evaluated. This survey provides a comprehensive overview of the role of generative LLMs in automated fact-checking, based on a systematic review of 199 research papers. We introduce a unifying taxonomy that captures how generative LLMs are integrated into fact-checking workflows and analyze their use across core fact-checking tasks, dataset construction and augmentation strategies, task formulations, and evaluation practices. Additionally, we investigate the impact of generative LLMs in multilingual and low-resource settings in fact-checking, highlighting trends, limitations, and gaps in current research. By consolidating fragmented research efforts and identifying methodological patterns, limitations, and open challenges, this survey maps the current state of generative LLMs in automated fact-checking. It aims to support researchers in developing more reliable, interpretable, and inclusive fact-checking systems, while outlining promising directions for future research in this rapidly evolving field.

Navigation in the natural world is a feat of adaptive inference, where biological organisms maintain goal-directed behaviour despite noisy and incomplete sensory streams. Central to this ability is the Free Energy Principle (FEP), which posits that perception is a generative process where the brain minimises Variational Free Energy (VFE) to maintain accurate internal models of the world. While Deep Neural Networks (DNNs) have served as powerful analogues for biological brains, they typically lack the real-time plasticity required to handle abrupt sensory shifts. We introduce FEP-Nav, a biologically inspired framework for real-time perceptual adaptation in robust visual navigation. Motivated by the decomposition of VFE into prediction error and Bayesian surprise, FEP-Nav combines a Top-down Decoder, which provides an internal expectation of uncorrupted sensory input, with Adaptive Normalisation, which adjusts shifted feature distributions toward prior statistics. We interpret reconstruction and normalisation as approximate mechanisms for reducing the corresponding VFE-related terms during inference without gradient-based updates. Experiments across simulated and real-world visual corruptions show that FEP-Nav restores performance lost under visual corruption, outperforming non-adaptive baselines and strong adaptive methods. These results suggest that variational principles can provide a useful design perspective for robust autonomous behaviour under degraded sensory conditions.

In artificial-intelligence-aided signal processing, existing deep learning models often exhibit a black-box structure. Here, conceptually beyond spectral analysis, we demonstrate that topological methods not only effectively capture intrinsic and complex structural information but can also enhance neural networks. We provide a transparent methodology, TopCap, to capture topological features inherent in time series for basic machine learning. Compared to prior approaches, we obtain descriptors that probe finer information such as the vibration of a time series. Notably, in classifying voiced and voiceless consonants, TopCap achieves an accuracy consistently standing in comparison with neural network models. Moreover, by integrating TopCap features into those neural networks, our approach improves upon state-of-the-art methods in terms of robustness against noise, as well as accuracy, stability, convergence of loss function, and interpretability.

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To choose hyperparameters that control the sparsity level and amount of regularization, practitioners commonly use k-fold cross-validation. However, cross-validation substantially increases the computational cost of sparse regression as it requires solving many mixed-integer optimization problems (MIOs) for each hyperparameter combination. To address this computational burden, we derive computationally tractable relaxations of the k-fold cross-validation loss, facilitating hyperparameter selection while solving $50$--$80\%$ fewer MIOs in practice. Our computational results demonstrate, across eleven real-world UCI datasets, that exact MIO-based cross-validation can be competitive with mature software packages such as glmnet and L0Learn.

One of the primary reasons behind the success of neural networks has been the emergence of an array of new, highly-successful optimizers, perhaps most importantly the Adam optimizer. It is widely used for training neural networks, yet notoriously hard to interpret. Lacking a clear physical intuition, Adam is difficult to generalize to manifolds. Some attempts have been made to directly apply parts of the Adam algorithm to manifolds or to find an underlying structure, but a full generalization has remained elusive. In this work a new approach is presented that leverages the special structure of the manifolds which are relevant for optimization of neural networks, such as the Stiefel manifold, the symplectic Stiefel manifold and the Grassmann manifold: all of these are homogeneous spaces and as such admit a global tangent space representation. This is a common vector space, often called the Lie subspace, that makes the generalization of all steps in the Adam optimizer (as well as other optimizers) possible. It is thus possible to extend the Adam optimizer to manifolds without a projection step, something that was not possible before. The resulting algorithm is then applied to train transformers and a symplectic autoencoder for which orthogonality constraints are enforced up to machine precision and we conclusively demonstrate the advantage of the proposed optimizer over existing methods.