These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads us to the framework of well-posedness and first considerations regarding reconstruction and inversion approaches. The second chapter then first deals with classical regularization theory of inverse problems in Hilbert spaces. After introducing the pseudo-inverse, we review the concept of convergent regularization. Within this chapter we then proceed to ask the question of how to realize practical reconstruction algorithms. Here, we mainly focus on Tikhonov and sparsity promoting regularization in finite dimensional spaces. In the third chapter, we dive into modern deep-learning methods, which allow solving inverse problems in a data-dependent approach. The intersection between inverse problems and machine learning is a rapidly growing field and our exposition here restricts itself to a very limited selection of topics. Among them are learned regularization, fully-learned Bayesian estimation, post-processing strategies and plug-n-play methods.

This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to assess how well LLMs understand, structure, and solve optimization problems across domains. The analysis is guided by critical review questions focusing on learning approaches, dataset designs, evaluation metrics, and prompting strategies. Our systematic evidence is complemented by targeted experiments designed to evaluate the performance of state-of-the-art LLMs in automatically generating optimization models for problems in computer networks. Using a newly constructed dataset, we apply three prompting strategies: Act-as-expert, chain-of-thought, and self-consistency, and evaluate the obtained outputs based on optimality gap, token-level F1 score, and compilation accuracy. Results show promising progress in LLMs' ability to parse natural language and represent symbolic formulations, but also reveal key limitations in accuracy, scalability, and interpretability. These empirical gaps motivate several future research directions, including structured datasets, domain-specific fine-tuning, hybrid neuro-symbolic approaches, modular multi-agent architectures, and dynamic retrieval via chain-of-RAGs. This paper contributes a structured roadmap for advancing LLM capabilities in mathematical programming.

Modern Code Review (MCR) is a standard practice in software engineering, yet it demands substantial time and resource investments. Recent research has increasingly explored automating core review tasks using machine learning (ML) and deep learning (DL). As a result, there is substantial variability in task definitions, datasets, and evaluation procedures. This study provides the first comprehensive analysis of MCR automation research, aiming to characterize the field's evolution, formalize learning tasks, highlight methodological challenges, and offer actionable recommendations to guide future research. Focusing on the primary code review tasks, we systematically surveyed 691 publications and identified 24 relevant studies published between May 2015 and April 2024. Each study was analyzed in terms of tasks, models, metrics, baselines, results, validity concerns, and artifact availability. In particular, our analysis reveals significant potential for standardization, including 48 task metric combinations, 22 of which were unique to their original paper, and limited dataset reuse. We highlight challenges and derive concrete recommendations for examples such as the temporal bias threat, which are rarely addressed so far. Our work contributes to a clearer overview of the field, supports the framing of new research, helps to avoid pitfalls, and promotes greater standardization in evaluation practices.

Aspect-based sentiment analysis enhances sentiment detection by associating it with specific aspects, offering deeper insights than traditional sentiment analysis. This study introduces a manually annotated dataset of 10,814 multilingual customer reviews covering brick-and-mortar retail stores, labeled with eight aspect categories and their sentiment. Using this dataset, the performance of GPT-4 and LLaMA-3 in aspect based sentiment analysis is evaluated to establish a baseline for the newly introduced data. The results show both models achieving over 85% accuracy, while GPT-4 outperforms LLaMA-3 overall with regard to all relevant metrics.

Recent advances in the intrinsic reasoning capabilities of large language models (LLMs) have given rise to LLM-based agent systems that exhibit near-human performance on a variety of automated tasks. However, although these systems share similarities in terms of their use of LLMs, different reasoning frameworks of the agent system steer and organize the reasoning process in different ways. In this survey, we propose a systematic taxonomy that decomposes agentic reasoning frameworks and analyze how these frameworks dominate framework-level reasoning by comparing their applications across different scenarios. Specifically, we propose an unified formal language to further classify agentic reasoning systems into single-agent methods, tool-based methods, and multi-agent methods. After that, we provide a comprehensive review of their key application scenarios in scientific discovery, healthcare, software engineering, social simulation, and economics. We also analyze the characteristic features of each framework and summarize different evaluation strategies. Our survey aims to provide the research community with a panoramic view to facilitate understanding of the strengths, suitable scenarios, and evaluation practices of different agentic reasoning frameworks.

Theory of Mind (ToM)-the ability to reason about the mental states of oneself and others-is a cornerstone of human social intelligence. As Large Language Models (LLMs) become increasingly integrated into daily life, understanding their ability to interpret and respond to human mental states is crucial for enabling effective interactions. In this paper, we review LLMs' ToM capabilities by analyzing both evaluation benchmarks and enhancement strategies. For evaluation, we focus on recently proposed and widely used story-based benchmarks. For enhancement, we provide an in-depth analysis of recent methods aimed at improving LLMs' ToM abilities. Furthermore, we outline promising directions for future research to further advance these capabilities and better adapt LLMs to more realistic and diverse scenarios. Our survey serves as a valuable resource for researchers interested in evaluating and advancing LLMs' ToM capabilities.

Automatic survey generation has emerged as a key task in scientific document processing. While large language models (LLMs) have shown promise in generating survey texts, the lack of standardized evaluation datasets critically hampers rigorous assessment of their performance against human-written surveys. In this work, we present SurveyGen, a large-scale dataset comprising over 4,200 human-written surveys across diverse scientific domains, along with 242,143 cited references and extensive quality-related metadata for both the surveys and the cited papers. Leveraging this resource, we build QUAL-SG, a novel quality-aware framework for survey generation that enhances the standard Retrieval-Augmented Generation (RAG) pipeline by incorporating quality-aware indicators into literature retrieval to assess and select higher-quality source papers. Using this dataset and framework, we systematically evaluate state-of-the-art LLMs under varying levels of human involvement - from fully automatic generation to human-guided writing. Experimental results and human evaluations show that while semi-automatic pipelines can achieve partially competitive outcomes, fully automatic survey generation still suffers from low citation quality and limited critical analysis.

Magnetic Resonance Imaging (MRI) is indispensable in clinical practice but remains constrained by fragmented, multi-stage workflows encompassing acquisition, reconstruction, segmentation, detection, diagnosis, and reporting. While deep learning has achieved progress in individual tasks, existing approaches are often anatomy- or application-specific and lack generalizability across diverse clinical settings. Moreover, current pipelines rarely integrate imaging data with complementary language information that radiologists rely on in routine practice. Here, we introduce OmniMRI, a unified vision-language foundation model designed to generalize across the entire MRI workflow. OmniMRI is trained on a large-scale, heterogeneous corpus curated from 60 public datasets, over 220,000 MRI volumes and 19 million MRI slices, incorporating image-only data, paired vision-text data, and instruction-response data. Its multi-stage training paradigm, comprising self-supervised vision pretraining, vision-language alignment, multimodal pretraining, and multi-task instruction tuning, progressively equips the model with transferable visual representations, cross-modal reasoning, and robust instruction-following capabilities. Qualitative results demonstrate OmniMRI's ability to perform diverse tasks within a single architecture, including MRI reconstruction, anatomical and pathological segmentation, abnormality detection, diagnostic suggestion, and radiology report generation. These findings highlight OmniMRI's potential to consolidate fragmented pipelines into a scalable, generalist framework, paving the way toward foundation models that unify imaging and clinical language for comprehensive, end-to-end MRI interpretation.

Classification in the context of multi-label data streams represents a challenge that has attracted significant attention due to its high real-world applicability. However, this task faces problems inherent to dynamic environments, such as the continuous arrival of data at high speed and volume, changes in the data distribution (concept drift), the emergence of new labels (concept evolution), and the latency in the arrival of ground truth labels. This systematic literature review presents an in-depth analysis of multi-label data stream classification proposals. We characterize the latest methods in the literature, providing a comprehensive overview, building a thorough hierarchy, and discussing how the proposals approach each problem. Furthermore, we discuss the adopted evaluation strategies and analyze the methods' asymptotic complexity and resource consumption. Finally, we identify the main gaps and offer recommendations for future research directions in the field.

Paraphrases are a vital tool to assist language understanding tasks such as question answering, style transfer, semantic parsing, and data augmentation tasks. Indic languages are complex in natural language processing (NLP) due to their rich morphological and syntactic variations, diverse scripts, and limited availability of annotated data. In this work, we present the L3Cube-MahaParaphrase Dataset, a high-quality paraphrase corpus for Marathi, a low resource Indic language, consisting of 8,000 sentence pairs, each annotated by human experts as either Paraphrase (P) or Non-paraphrase (NP). We also present the results of standard transformer-based BERT models on these datasets. The dataset and model are publicly shared at https://github.com/l3cube-pune/MarathiNLP