The theory of training deep networks has become a central question of modern machine learning and has inspired many practical advancements. In particular, the gradient descent (GD) optimization algorithm has been extensively studied in recent years. A key assumption about GD has appeared in several recent works: the \emph{GD map is non-singular} -- it preserves sets of measure zero under preimages. Crucially, this assumption has been used to prove that GD avoids saddle points and maxima, and to establish the existence of a computable quantity that determines the convergence to global minima (both for GD and stochastic GD). However, the current literature either assumes the non-singularity of the GD map or imposes restrictive assumptions, such as Lipschitz smoothness of the loss (for example, Lipschitzness does not hold for deep ReLU networks with the cross-entropy loss) and restricts the analysis to GD with small step-sizes. In this paper, we investigate the neural network map as a function on the space of weights and biases. We also prove, for the first time, the non-singularity of the gradient descent (GD) map on the loss landscape of realistic neural network architectures (with fully connected, convolutional, or softmax attention layers) and piecewise analytic activations (which includes sigmoid, ReLU, leaky ReLU, etc.) for almost all step-sizes. Our work significantly extends the existing results on the convergence of GD and SGD by guaranteeing that they apply to practical neural network settings and has the potential to unlock further exploration of learning dynamics.

Multimodal large language models (MLLMs) have shown impressive capabilities in vision-language tasks such as reasoning segmentation, where models generate segmentation masks based on textual queries. While prior work has primarily focused on perturbing image inputs, semantically equivalent textual paraphrases-crucial in real-world applications where users express the same intent in varied ways-remain underexplored. To address this gap, we introduce a novel adversarial paraphrasing task: generating grammatically correct paraphrases that preserve the original query meaning while degrading segmentation performance. To evaluate the quality of adversarial paraphrases, we develop a comprehensive automatic evaluation protocol validated with human studies. Furthermore, we introduce SPARTA-a black-box, sentence-level optimization method that operates in the low-dimensional semantic latent space of a text autoencoder, guided by reinforcement learning. SPARTA achieves significantly higher success rates, outperforming prior methods by up to 2x on both the ReasonSeg and LLMSeg-40k datasets. We use SPARTA and competitive baselines to assess the robustness of advanced reasoning segmentation models. We reveal that they remain vulnerable to adversarial paraphrasing-even under strict semantic and grammatical constraints. All code and data will be released publicly upon acceptance.

Since real-world legal experiments are often costly or infeasible, simulating legal societies with Artificial Intelligence (AI) systems provides an effective alternative for verifying and developing legal theory, as well as supporting legal administration. Large Language Models (LLMs), with their world knowledge and role-playing capabilities, are strong candidates to serve as the foundation for legal society simulation. However, the application of LLMs to simulate legal systems remains underexplored. In this work, we introduce Law in Silico, an LLM-based agent framework for simulating legal scenarios with individual decision-making and institutional mechanisms of legislation, adjudication, and enforcement. Our experiments, which compare simulated crime rates with real-world data, demonstrate that LLM-based agents can largely reproduce macro-level crime trends and provide insights that align with real-world observations. At the same time, micro-level simulations reveal that a well-functioning, transparent, and adaptive legal system offers better protection of the rights of vulnerable individuals.

Large language models are increasingly used for Islamic guidance, but risk misquoting texts, misapplying jurisprudence, or producing culturally inconsistent responses. We pilot an evaluation of GPT-4o, Ansari AI, and Fanar on prompts from authentic Islamic blogs. Our dual-agent framework uses a quantitative agent for citation verification and six-dimensional scoring (e.g., Structure, Islamic Consistency, Citations) and a qualitative agent for five-dimensional side-by-side comparison (e.g., Tone, Depth, Originality). GPT-4o scored highest in Islamic Accuracy (3.93) and Citation (3.38), Ansari AI followed (3.68, 3.32), and Fanar lagged (2.76, 1.82). Despite relatively strong performance, models still fall short in reliably producing accurate Islamic content and citations -- a paramount requirement in faith-sensitive writing. GPT-4o had the highest mean quantitative score (3.90/5), while Ansari AI led qualitative pairwise wins (116/200). Fanar, though trailing, introduces innovations for Islamic and Arabic contexts. This study underscores the need for community-driven benchmarks centering Muslim perspectives, offering an early step toward more reliable AI in Islamic knowledge and other high-stakes domains such as medicine, law, and journalism.

Evaluating reasoning ability in Large Language Models (LLMs) is important for advancing artificial intelligence, as it transcends mere linguistic task performance. It involves understanding whether these models truly understand information, perform inferences, and are able to draw conclusions in a logical and valid way. This study compare logical and abstract reasoning skills of several LLMs - including GPT, Claude, DeepSeek, Gemini, Grok, Llama, Mistral, Perplexity, and Sabi a - using a set of eight custom-designed reasoning questions. The LLM results are benchmarked against human performance on the same tasks, revealing significant differences and indicating areas where LLMs struggle with deduction.

The effectiveness of instruction-tuned Large Language Models (LLMs) is often limited in low-resource linguistic settings due to a lack of high-quality training data. We introduce LuxIT, a novel, monolingual instruction tuning dataset for Luxembourgish developed to mitigate this challenge. We synthesize the dataset from a corpus of native Luxembourgish texts, utilizing DeepSeek-R1-0528, chosen for its shown proficiency in Luxembourgish. Following generation, we apply a quality assurance process, employing an LLM-as-a-judge approach. To investigate the practical utility of the dataset, we fine-tune several smaller-scale LLMs on LuxIT. Subsequent benchmarking against their base models on Luxembourgish language proficiency examinations, however, yields mixed results, with performance varying significantly across different models. LuxIT represents a critical contribution to Luxembourgish natural language processing and offers a replicable monolingual methodology, though our findings highlight the need for further research to optimize its application.

The recent success of large language models (LLMs) has renewed interest in whether recommender systems can achieve similar scaling benefits. Conventional recommenders, dominated by massive embedding tables, tend to plateau as embedding dimensions grow. In contrast, the emerging generative paradigm replaces embeddings with compact Semantic ID (SID) sequences produced by autoregressive Transformers. Yet most industrial deployments remain proprietary, leaving two fundamental questions open: (1) Do the expected scaling laws hold on public benchmarks? (2) What is the minimal post-training recipe that enables competitive performance? We present MiniOneRec, to the best of our knowledge, the first fully open-source generative recommendation framework, which provides an end-to-end workflow spanning SID construction, supervised fine-tuning, and recommendation-oriented reinforcement learning. We generate SIDs via a Residual Quantized VAE and post-train Qwen backbones ranging from 0.5B to 7B parameters on the Amazon Review dataset. Our experiments reveal a consistent downward trend in both training and evaluation losses with increasing model size, validating the parameter efficiency of the generative approach. To further enhance performance, we propose a lightweight yet effective post-training pipeline that (1) enforces full-process SID alignment and (2) applies reinforcement learning with constrained decoding and hybrid rewards. Together, these techniques yield significant improvements in both ranking accuracy and candidate diversity.

Retrieval-Augmented Generation (RAG) struggles on long, structured financial filings where relevant evidence is sparse and cross-referenced. This paper presents a systematic investigation of advanced metadata-driven Retrieval-Augmented Generation (RAG) techniques, proposing and evaluating a novel, multi-stage RAG architecture that leverages LLM-generated metadata. We introduce a sophisticated indexing pipeline to create contextually rich document chunks and benchmark a spectrum of enhancements, including pre-retrieval filtering, post-retrieval reranking, and enriched embeddings, benchmarked on the FinanceBench dataset. Our results reveal that while a powerful reranker is essential for precision, the most significant performance gains come from embedding chunk metadata directly with text ("contextual chunks"). Our proposed optimal architecture combines LLM-driven pre-retrieval optimizations with these contextual embeddings to achieve superior performance. Additionally, we present a custom metadata reranker that offers a compelling, cost-effective alternative to commercial solutions, highlighting a practical trade-off between peak performance and operational efficiency. This study provides a blueprint for building robust, metadata-aware RAG systems for financial document analysis.

With the rapid development of LLM-based agents, there is a growing trend to incorporate agent-specific data into the pre-training stage of LLMs, aiming to better align LLMs with real-world autonomous task execution. However, current pre-training benchmarks primarily focus on isolated and static skills, e.g., common knowledge or mathematical/code reasoning, and fail to reflect model's agentic capabilities. On the other hand, agent benchmarks are typically designed for post-trained models, requiring multi-turn task execution abilities that base models struggle to support. Thus, there is a compelling need for a benchmark that can evaluate agentic potentials during pre-training and guide the model training more effectively. To address this gap, we propose APTBench, a framework that converts real-world agent tasks and successful trajectories into multiple-choice or text completion questions tailored for base models. It focuses on core agentic abilities, e.g., planning and action, and covers key agent scenarios, software engineering and deep research. Compared to existing general-purpose benchmarks, APTBench offers a more predictive signal of a model's downstream performance as an agent, while remaining significantly more lightweight and cost-effective than full-scale, end-to-end agent evaluations after post-training.

The integration of Large Language Models (LLMs) into real-time Web applications, such as AI-powered search and conversational agents, presents a fundamental Web infrastructure challenge: reconciling the demand for high-quality, complex reasoning with the stringent low-latency and high-throughput requirements of interactive services. Current LLM reasoning, hindered by computationally inefficient sequential generation and rigid reasoning strategies, creates a critical bottleneck for the Web services. Existing approaches typically optimize the LLM reasoning for either efficiency or quality but struggle to achieve both, and thus fail to meet the dual requirements of modern Web platforms. To overcome these limitations, we propose Orion, a novel and efficient reasoning framework that enables dependency-aware query decomposition and logic-parallel content expansion. Concretely, Orion decomposes a single query reasoning process into two synergistic phases: (1) \textit{key point generation}, which distills logically structured key points through retrieval-augmented few-shot prompting, and (2) \textit{content parallel expansion}, which concurrently elaborates on these points based on a dependency graph to ensure logical consistency. Furthermore, Orion introduces a pipeline scheduling mechanism that exploits the complementary computational characteristics of the two phases (generation imposes pressure on GPU computing and expansion stresses on GPU memory) across multiple queries, enabling cross-query parallelism and dramatically improving reasoning performance (\ie, efficiency and quality). Experiments on diverse benchmarks show that Orion not only delivers up to 4.33x higher token generation speed and 3.42x lower answer latency over the baselines but also improves reasoning quality by up to 18.75% through explicitly modeling inter-point dependencies.