Daily Papers

Mathematical formulas are a fundamental and widely used component in various scientific fields, serving as a universal language for expressing complex concepts and relationships. While state-of-the-art transformer models excel in processing and understanding natural language, they encounter challenges with mathematical notation, which involves a complex structure and diverse representations. This study focuses on the development of specialized training datasets to enhance the encoding of mathematical content. We introduce Math Mutator (MAMUT), a framework capable of generating equivalent and falsified versions of a given mathematical formula in LaTeX notation, effectively capturing the mathematical variety in notation of the same concept. Based on MAMUT, we have generated four large mathematical datasets containing diverse notation, which can be used to train language models with enhanced mathematical embeddings.

Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not effective in creation of formulas for mathematical constants because each such formula must be correct for infinite digits of precision, with "near-true" formulas providing no insight toward the correct ones. Consequently, formula discovery lacks a clear distance metric needed to guide automated discovery in this realm. In this work, we propose a systematic methodology for categorization, characterization, and pattern identification of such formulas. The key to our methodology is introducing metrics based on the convergence dynamics of the formulas, rather than on the numerical value of the formula. These metrics enable the first automated clustering of mathematical formulas. We demonstrate this methodology on Polynomial Continued Fraction formulas, which are ubiquitous in their intrinsic connections to mathematical constants, and generalize many mathematical functions and structures. We test our methodology on a set of 1,768,900 such formulas, identifying many known formulas for mathematical constants, and discover previously unknown formulas for pi, ln(2), Gauss', and Lemniscate's constants. The uncovered patterns enable a direct generalization of individual formulas to infinite families, unveiling rich mathematical structures. This success paves the way towards a generative model that creates formulas fulfilling specified mathematical properties, accelerating the rate of discovery of useful formulas.

In this project, we train a vision encoder-decoder model to generate LaTeX code from images of mathematical formulas and text. Utilizing a diverse collection of image-to-LaTeX data, we build two models: a base model with a Swin Transformer encoder and a GPT-2 decoder, trained on machine-generated images, and a fine-tuned version enhanced with Low-Rank Adaptation (LoRA) trained on handwritten formulas. We then compare the BLEU performance of our specialized model on a handwritten test set with other similar models, such as Pix2Text, TexTeller, and Sumen. Through this project, we contribute open-source models for converting images to LaTeX and provide from-scratch code for building these models with distributed training and GPU optimizations.

Correctly parsing mathematical formulas from PDFs is critical for training large language models and building scientific knowledge bases from academic literature, yet existing benchmarks either exclude formulas entirely or lack semantically-aware evaluation metrics. We introduce a novel benchmarking framework centered on synthetically generated PDFs with precise LaTeX ground truth, enabling systematic control over layout, formulas, and content characteristics. A key methodological contribution is pioneering LLM-as-a-judge for semantic formula assessment, combined with a robust two-stage matching pipeline that handles parser output inconsistencies. Through human validation on 250 formula pairs (750 ratings from 30 evaluators), we demonstrate that LLM-based evaluation achieves substantially higher correlation with human judgment (Pearson r=0.78) compared to CDM (r=0.34) and text similarity (r~0). Evaluating 20+ contemporary PDF parsers (including specialized OCR models, vision-language models, and rule-based approaches) across 100 synthetic documents with 2,000+ formulas reveals significant performance disparities. Our findings provide crucial insights for practitioners selecting parsers for downstream applications and establish a robust, scalable methodology that enables reproducible evaluation of PDF formula extraction quality. Code and benchmark data: https://github.com/phorn1/pdf-parse-bench

Building on recent advances in image generation, we present a fully data-driven approach to rendering markup into images. The approach is based on diffusion models, which parameterize the distribution of data using a sequence of denoising operations on top of a Gaussian noise distribution. We view the diffusion denoising process as a sequential decision making process, and show that it exhibits compounding errors similar to exposure bias issues in imitation learning problems. To mitigate these issues, we adapt the scheduled sampling algorithm to diffusion training. We conduct experiments on four markup datasets: mathematical formulas (LaTeX), table layouts (HTML), sheet music (LilyPond), and molecular images (SMILES). These experiments each verify the effectiveness of the diffusion process and the use of scheduled sampling to fix generation issues. These results also show that the markup-to-image task presents a useful controlled compositional setting for diagnosing and analyzing generative image models.

Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A grand challenge lies in the arduous search for parsimonious and generalizable mathematical formulas, in an infinite search space, while intending to fit the training data. Existing algorithms have faced a critical bottleneck of accuracy and efficiency over a decade when handling problems of complexity, which essentially hinders the pace of applying symbolic regression for scientific exploration across interdisciplinary domains. To this end, we introduce a parallelized tree search (PTS) model to efficiently distill generic mathematical expressions from limited data. Through a series of extensive experiments, we demonstrate the superior accuracy and efficiency of PTS for equation discovery, which greatly outperforms the state-of-the-art baseline models on over 80 synthetic and experimental datasets (e.g., lifting its performance by up to 99% accuracy improvement and one-order of magnitude speed up). PTS represents a key advance in accurate and efficient data-driven discovery of symbolic, interpretable models (e.g., underlying physical laws) and marks a pivotal transition towards scalable symbolic learning.

Formula recognition is an important task in document intelligence. It involves converting mathematical expressions from document images into structured symbolic formats that computers can easily work with. LaTeX is the most common format used for this purpose. In this work, we present PP-FormulaNet, a state-of-the-art formula recognition model that excels in both accuracy and efficiency. To meet the diverse needs of applications, we have developed two specialized models: PP-FormulaNet-L, tailored for high-accuracy scenarios, and PP-FormulaNet-S, optimized for high-efficiency contexts. Our extensive evaluations reveal that PP-FormulaNet-L attains accuracy levels that surpass those of prominent models such as UniMERNet by a significant 6%. Conversely, PP-FormulaNet-S operates at speeds that are over 16 times faster. These advancements facilitate seamless integration of PP-FormulaNet into a broad spectrum of document processing environments that involve intricate mathematical formulas. Furthermore, we introduce a Formula Mining System, which is capable of extracting a vast amount of high-quality formula data. This system further enhances the robustness and applicability of our formula recognition model. Code and models are publicly available at PaddleOCR(https://github.com/PaddlePaddle/PaddleOCR) and PaddleX(https://github.com/PaddlePaddle/PaddleX).

Understanding complex scientific and mathematical concepts, particularly those presented in dense research papers, poses a significant challenge for learners. Dynamic visualizations can greatly enhance comprehension, but creating them manually is time-consuming and requires specialized knowledge and skills. We introduce manimator, an open-source system that leverages Large Language Models to transform research papers and natural language prompts into explanatory animations using the Manim engine. Manimator employs a pipeline where an LLM interprets the input text or research paper PDF to generate a structured scene description outlining key concepts, mathematical formulas, and visual elements and another LLM translates this description into executable Manim Python code. We discuss its potential as an educational tool for rapidly creating engaging visual explanations for complex STEM topics, democratizing the creation of high-quality educational content.

Automatic analysis of the enormous sets of images is a critical task in life sciences. This faces many challenges such as: algorithms are highly parameterized, significant human input is intertwined, and lacking a standard meta-visualization approach. This paper proposes an alternative iterative approach for optimizing input parameters, saving time by minimizing the user involvement, and allowing for understanding the workflow of algorithms and discovering new ones. The main focus is on developing an interactive visualization technique that enables users to analyze the relationships between sampled input parameters and corresponding output. This technique is implemented as a prototype called Veni Vidi Vici, or "I came, I saw, I conquered." This strategy is inspired by the mathematical formulas of numbering computable functions and is developed atop ImageJ, a scientific image processing program. A case study is presented to investigate the proposed framework. Finally, the paper explores some potential future issues in the application of the proposed approach in parameter space analysis in visualization.

Large Language Models (LLMs) struggle with reliably generating highly structured outputs, such as program code, mathematical formulas, or well-formed markup. Constrained decoding approaches mitigate this problem by greedily restricting what tokens an LLM can output at each step to guarantee that the output matches a given constraint. Specifically, in grammar-constrained decoding (GCD), the LLM's output must follow a given grammar. In this paper, we demonstrate that GCD techniques (and in general constrained decoding techniques) can distort the LLM's distribution, leading to outputs that are grammatical but appear with likelihoods that are not proportional to the ones given by the LLM, and so ultimately are low-quality. We call the problem of aligning sampling with a grammar constraint, grammar-aligned decoding (GAD), and propose adaptive sampling with approximate expected futures (ASAp), a decoding algorithm that guarantees the output to be grammatical while provably producing outputs that match the conditional probability of the LLM's distribution conditioned on the given grammar constraint. Our algorithm uses prior sample outputs to soundly overapproximate the future grammaticality of different output prefixes. Our evaluation on code generation and structured NLP tasks shows how ASAp often produces outputs with higher likelihood (according to the LLM's distribution) than existing GCD techniques, while still enforcing the desired grammatical constraints.

Effective communication, specifically through documentation, is the beating heart of collaboration among contributors in software development. Recent advancements in language models (LMs) have enabled the introduction of a new type of actor in that ecosystem: LM-powered assistants capable of code generation, optimization, and maintenance. Our study investigates the efficacy of small language models (SLMs) for generating high-quality docstrings by assessing accuracy, conciseness, and clarity, benchmarking performance quantitatively through mathematical formulas and qualitatively through human evaluation using Likert scale. Further, we introduce DocuMint, as a large-scale supervised fine-tuning dataset with 100,000 samples. In quantitative experiments, Llama 3 8B achieved the best performance across all metrics, with conciseness and clarity scores of 0.605 and 64.88, respectively. However, under human evaluation, CodeGemma 7B achieved the highest overall score with an average of 8.3 out of 10 across all metrics. Fine-tuning the CodeGemma 2B model using the DocuMint dataset led to significant improvements in performance across all metrics, with gains of up to 22.5% in conciseness. The fine-tuned model and the dataset can be found in HuggingFace and the code can be found in the repository.

Formulas involving fundamental mathematical constants had a great impact on various fields of science and mathematics, for example aiding in proofs of irrationality of constants. However, the discovery of such formulas has historically remained scarce, often perceived as an act of mathematical genius by great mathematicians such as Ramanujan, Euler, and Gauss. Recent efforts to automate the discovery of formulas for mathematical constants, such as the Ramanujan Machine project, relied on exhaustive search. Despite several successful discoveries, exhaustive search remains limited by the space of options that can be covered and by the need for vast amounts of computational resources. Here we propose a fundamentally different method to search for conjectures on mathematical constants: through analysis of integer sequences. We introduce the Enumerated Signed-continued-fraction Massey Approve (ESMA) algorithm, which builds on the Berlekamp-Massey algorithm to identify patterns in integer sequences that represent mathematical constants. The ESMA algorithm found various known formulas for e, e^2, tan(1), and ratios of values of Bessel functions. The algorithm further discovered a large number of new conjectures for these constants, some providing simpler representations and some providing faster numerical convergence than the corresponding simple continued fractions. Along with the algorithm, we present mathematical tools for manipulating continued fractions. These connections enable us to characterize what space of constants can be found by ESMA and quantify its algorithmic advantage in certain scenarios. Altogether, this work continues in the development of augmenting mathematical intuition by computer algorithms, to help reveal mathematical structures and accelerate mathematical research.

Large Audio-Language Models (LALMs) have unclocked audio dialogue capabilities, where audio dialogues are a direct exchange of spoken language between LALMs and humans. Recent advances, such as GPT-4o, have enabled LALMs in back-and-forth audio dialogues with humans. This progression not only underscores the potential of LALMs but also broadens their applicability across a wide range of practical scenarios supported by audio dialogues. However, given these advancements, a comprehensive benchmark to evaluate the performance of LALMs in the open-ended audio dialogue understanding remains absent currently. To address this gap, we propose an Audio Dialogue Understanding Benchmark (ADU-Bench), which consists of 4 benchmark datasets. They assess the open-ended audio dialogue ability for LALMs in 3 general scenarios, 12 skills, 9 multilingual languages, and 4 categories of ambiguity handling. Notably, we firstly propose the evaluation of ambiguity handling in audio dialogues that expresses different intentions beyond the same literal meaning of sentences, e.g., "Really!?" with different intonations. In summary, ADU-Bench includes over 20,000 open-ended audio dialogues for the assessment of LALMs. Through extensive experiments conducted on 13 LALMs, our analysis reveals that there is still considerable room for improvement in the audio dialogue understanding abilities of existing LALMs. In particular, they struggle with mathematical symbols and formulas, understanding human behavior such as roleplay, comprehending multiple languages, and handling audio dialogue ambiguities from different phonetic elements, such as intonations, pause positions, and homophones.

Without writing a single line of code by a human, an example Monte Carlo simulation based application for stochastic dependence modeling with copulas is developed using a state-of-the-art large language model (LLM) fine-tuned for conversations. This includes interaction with ChatGPT in natural language and using mathematical formalism, which, under careful supervision by a human-expert, led to producing a working code in MATLAB, Python and R for sampling from a given copula model, evaluation of the model's density, performing maximum likelihood estimation, optimizing the code for parallel computing for CPUs as well as for GPUs, and visualization of the computed results. In contrast to other emerging studies that assess the accuracy of LLMs like ChatGPT on tasks from a selected area, this work rather investigates ways how to achieve a successful solution of a standard statistical task in a collaboration of a human-expert and artificial intelligence (AI). Particularly, through careful prompt engineering, we separate successful solutions generated by ChatGPT from unsuccessful ones, resulting in a comprehensive list of related pros and cons. It is demonstrated that if the typical pitfalls are avoided, we can substantially benefit from collaborating with an AI partner. For example, we show that if ChatGPT is not able to provide a correct solution due to a lack of or incorrect knowledge, the human-expert can feed it with the correct knowledge, e.g., in the form of mathematical theorems and formulas, and make it to apply the gained knowledge in order to provide a solution that is correct. Such ability presents an attractive opportunity to achieve a programmed solution even for users with rather limited knowledge of programming techniques.

Understanding sentences that contain mathematical expressions in text form poses significant challenges. To address this, the importance of converting these expressions into formula images has been highlighted. For instance, the expression ``x equals minus b plus or minus the square root of b squared minus four a c, all over two a'' is more readily comprehensible when displayed as an image x = -b pm sqrt{b^2 - 4ac}{2a}. To develop a text-to-image conversion system, we can break down the process into text-to-LaTeX and LaTeX-to-image conversions, with the latter being managed with by existing various LaTeX engines. However, the former approach has been notably hindered by the severe scarcity of text-to-LaTeX paired data, presenting a significant challenge in the field.In this context, we introduce MathBridge, the first extensive dataset for translating mathematical spoken English into LaTeX, which aims to establish a robust baseline for future research in text-to-LaTeX translation. MathBridge comprises approximately 23 million LaTeX formulas paired with corresponding spoken English expressions. Through comprehensive evaluations, including fine-tuning and testing with data, we discovered that MathBridge significantly enhances pre-trained language models' capabilities for text-to-LaTeX translation. Specifically, for the T5-large model, the sacreBLEU score increased from 4.77 to 46.8, demonstrating substantial enhancement. Our findings indicate the necessity for a new metric specifically for text-to-LaTeX conversion evaluation.

This paper presents the UniMER dataset to provide the first study on Mathematical Expression Recognition (MER) towards complex real-world scenarios. The UniMER dataset consists of a large-scale training set UniMER-1M offering an unprecedented scale and diversity with one million training instances and a meticulously designed test set UniMER-Test that reflects a diverse range of formula distributions prevalent in real-world scenarios. Therefore, the UniMER dataset enables the training of a robust and high-accuracy MER model and comprehensive evaluation of model performance. Moreover, we introduce the Universal Mathematical Expression Recognition Network (UniMERNet), an innovative framework designed to enhance MER in practical scenarios. UniMERNet incorporates a Length-Aware Module to process formulas of varied lengths efficiently, thereby enabling the model to handle complex mathematical expressions with greater accuracy. In addition, UniMERNet employs our UniMER-1M data and image augmentation techniques to improve the model's robustness under different noise conditions. Our extensive experiments demonstrate that UniMERNet outperforms existing MER models, setting a new benchmark in various scenarios and ensuring superior recognition quality in real-world applications. The dataset and model are available at https://github.com/opendatalab/UniMERNet.

In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and algorithms become more powerful, an intriguing possibility arises - the interplay between human intuition and computer algorithms can lead to discoveries of novel mathematical concepts that would otherwise remain elusive. To realize this perspective, we have developed a massively parallel computer algorithm that discovers an unprecedented number of continued fraction formulas for fundamental mathematical constants. The sheer number of formulas discovered by the algorithm unveils a novel mathematical structure that we call the conservative matrix field. Such matrix fields (1) unify thousands of existing formulas, (2) generate infinitely many new formulas, and most importantly, (3) lead to unexpected relations between different mathematical constants, including multiple integer values of the Riemann zeta function. Conservative matrix fields also enable new mathematical proofs of irrationality. In particular, we can use them to generalize the celebrated proof by Ap\'ery for the irrationality of zeta(3). Utilizing thousands of personal computers worldwide, our computer-supported research strategy demonstrates the power of experimental mathematics, highlighting the prospects of large-scale computational approaches to tackle longstanding open problems and discover unexpected connections across diverse fields of science.

Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve the understanding of complex number combination reasoning. In this work, we propose TRIGO, an ATP benchmark that not only requires a model to reduce a trigonometric expression with step-by-step proofs but also evaluates a generative LM's reasoning ability on formulas and its capability to manipulate, group, and factor number terms. We gather trigonometric expressions and their reduced forms from the web, annotate the simplification process manually, and translate it into the Lean formal language system. We then automatically generate additional examples from the annotated samples to expand the dataset. Furthermore, we develop an automatic generator based on Lean-Gym to create dataset splits of varying difficulties and distributions in order to thoroughly analyze the model's generalization ability. Our extensive experiments show our proposed TRIGO poses a new challenge for advanced generative LM's including GPT-4 which is pre-trained on a considerable amount of open-source formal theorem-proving language data, and provide a new tool to study the generative LM's ability on both formal and mathematical reasoning.

Recently, most handwritten mathematical expression recognition (HMER) methods adopt the encoder-decoder networks, which directly predict the markup sequences from formula images with the attention mechanism. However, such methods may fail to accurately read formulas with complicated structure or generate long markup sequences, as the attention results are often inaccurate due to the large variance of writing styles or spatial layouts. To alleviate this problem, we propose an unconventional network for HMER named Counting-Aware Network (CAN), which jointly optimizes two tasks: HMER and symbol counting. Specifically, we design a weakly-supervised counting module that can predict the number of each symbol class without the symbol-level position annotations, and then plug it into a typical attention-based encoder-decoder model for HMER. Experiments on the benchmark datasets for HMER validate that both joint optimization and counting results are beneficial for correcting the prediction errors of encoder-decoder models, and CAN consistently outperforms the state-of-the-art methods. In particular, compared with an encoder-decoder model for HMER, the extra time cost caused by the proposed counting module is marginal. The source code is available at https://github.com/LBH1024/CAN.

We propose Monte Carlo Permutation Search (MCPS), a general-purpose Monte Carlo Tree Search (MCTS) algorithm that improves upon the GRAVE algorithm. MCPS is relevant when deep reinforcement learning is not an option, or when the computing power available before play is not substantial, such as in General Game Playing, for example. The principle of MCPS is to include in the exploration term of a node the statistics on all the playouts that contain all the moves on the path from the root to the node. We extensively test MCPS on a variety of games: board games, wargame, investment game, video game and multi-player games. MCPS has better results than GRAVE in all the two-player games. It has equivalent results for multi-player games because these games are inherently balanced even when players have different strengths. We also show that using abstract codes for moves instead of exact codes can be beneficial to both MCPS and GRAVE, as they improve the permutation statistics and the AMAF statistics. We also provide a mathematical derivation of the formulas used for weighting the three sources of statistics. These formulas are an improvement on the GRAVE formula since they no longer use the bias hyperparameter of GRAVE. Moreover, MCPS is not sensitive to the ref hyperparameter.

With the development of data-centric AI, the focus has shifted from model-driven approaches to improving data quality. Academic literature, as one of the crucial types, is predominantly stored in PDF formats and needs to be parsed into texts before further processing. However, parsing diverse structured texts in academic literature remains challenging due to the lack of datasets that cover various text structures. In this paper, we introduce AceParse, the first comprehensive dataset designed to support the parsing of a wide range of structured texts, including formulas, tables, lists, algorithms, and sentences with embedded mathematical expressions. Based on AceParse, we fine-tuned a multimodal model, named AceParser, which accurately parses various structured texts within academic literature. This model outperforms the previous state-of-the-art by 4.1% in terms of F1 score and by 5% in Jaccard Similarity, demonstrating the potential of multimodal models in academic literature parsing. Our dataset is available at https://github.com/JHW5981/AceParse.

In this paper, we give an in-depth analysis on the mathematical problem formulations and the probabilistic optimization explorations for some of the key components in Transformer model [33] in the field of generative AI. We explore and discuss some potential further enhancement for current state of the art methods for some key underlying technologies of generative AI models from algorithmic and probabilistic optimization perspective. In particular, we present an optimal solution for sub-word encoding (SWE) based on similar initial settings as that of byte-pair encoding (BPE) algorithm in [9] with similar objectives as that of WordPiece approach in [28, 31] to maximize the likelihood of the training data. We also present cross entropy optimization method to optimize hyperparameters for word2vec model [17]. In addition, we propose a factored combination of rotary positional encoding (RoPE) [32] and attention with linear biases (ALiBi) [23] with a harmonic series. We also present a probabilistic FlashAttention [6, 7] (PrFlashAttention) method with a probability distribution over block distances in the matrix to decide which block is likely to participate in a given round of attention computation while maintaining the lower triangle shape of the tensor for autoregressive language models by re-shaping the tensors. Finally, we present staircase adaptive quantization (SAQ) of key-value (KV) cache for multi-query attention (MQA) based on the framework presented in [16] to have gradual quantization degradation while achieving reasonable model quality and cost savings.

Optimization modeling enables critical decisions across industries but remains difficult to automate: informal language must be mapped to precise mathematical formulations and executable solver code. Prior LLM approaches either rely on brittle prompting or costly retraining with limited generalization. We present AlphaOPT, a self-improving experience library that enables an LLM to learn from limited demonstrations (even answers alone, without gold-standard programs) and solver feedback - without annotated reasoning traces or parameter updates. AlphaOPT operates in a continual two-phase cycle: (i) a Library Learning phase that reflects on failed attempts, extracting solver-verified, structured insights as {taxonomy, condition, explanation, example}; and (ii) a Library Evolution phase that diagnoses retrieval misalignments and refines the applicability conditions of stored insights, improving transfer across tasks. This design (1) learns efficiently from limited demonstrations without curated rationales, (2) expands continually without costly retraining by updating the library rather than model weights, and (3) makes knowledge explicit and interpretable for human inspection and intervention. Experiments show that AlphaOPT steadily improves with more data (65% to 72% from 100 to 300 training items) and surpasses the strongest baseline by 7.7% on the out-of-distribution OptiBench dataset when trained only on answers. Code and data are available at: https://github.com/Minw913/AlphaOPT.

We introduce a unified mathematical and probabilistic framework for understanding and comparing diverse AI agent strategies. We bridge the gap between high-level agent design concepts, such as ReAct, multi-agent systems, and control flows, and a rigorous mathematical formulation. Our approach frames agentic processes as a chain of probabilities, enabling a detailed analysis of how different strategies manipulate these probabilities to achieve desired outcomes. Our framework provides a common language for discussing the trade-offs inherent in various agent architectures. One of our many key contributions is the introduction of the "Degrees of Freedom" concept, which intuitively differentiates the optimizable levers available for each approach, thereby guiding the selection of appropriate strategies for specific tasks. This work aims to enhance the clarity and precision in designing and evaluating AI agents, offering insights into maximizing the probability of successful actions within complex agentic systems.

Reasoning language models (RLMs), also known as Large Reasoning Models (LRMs), such as OpenAI's o1 and o3, DeepSeek-V3, and Alibaba's QwQ, have redefined AI's problem-solving capabilities by extending large language models (LLMs) with advanced reasoning mechanisms. Yet, their high costs, proprietary nature, and complex architectures - uniquely combining Reinforcement Learning (RL), search heuristics, and LLMs - present accessibility and scalability challenges. To address these, we propose a comprehensive blueprint that organizes RLM components into a modular framework, based on a survey and analysis of all RLM works. This blueprint incorporates diverse reasoning structures (chains, trees, graphs, and nested forms), reasoning strategies (e.g., Monte Carlo Tree Search, Beam Search), RL concepts (policy, value models and others), and supervision schemes (Output-Based and Process-Based Supervision). We also provide detailed mathematical formulations and algorithmic specifications to simplify RLM implementation. By showing how schemes like LLaMA-Berry, QwQ, Journey Learning, and Graph of Thoughts fit as special cases, we demonstrate the blueprint's versatility and unifying potential. To illustrate its utility, we introduce x1, a modular implementation for rapid RLM prototyping and experimentation. Using x1 and a literature review, we provide key insights, such as multi-phase training for policy and value models, and the importance of familiar training distributions. Finally, we outline how RLMs can integrate with a broader LLM ecosystem, including tools and databases. Our work demystifies RLM construction, democratizes advanced reasoning capabilities, and fosters innovation, aiming to mitigate the gap between "rich AI" and "poor AI" by lowering barriers to RLM development and experimentation.

We present Generalized LoRA (GLoRA), an advanced approach for universal parameter-efficient fine-tuning tasks. Enhancing Low-Rank Adaptation (LoRA), GLoRA employs a generalized prompt module to optimize pre-trained model weights and adjust intermediate activations, providing more flexibility and capability across diverse tasks and datasets. Moreover, GLoRA facilitates efficient parameter adaptation by employing a scalable, modular, layer-wise structure search that learns individual adapter of each layer. Originating from a unified mathematical formulation, GLoRA exhibits strong transfer learning, few-shot learning and domain generalization abilities, as it adjusts to new tasks through additional dimensions on weights and activations. Comprehensive experiments demonstrate that GLoRA outperforms all previous methods in natural, specialized, and structured benchmarks, achieving superior accuracy with fewer parameters and computations on various datasets. Furthermore, our structural re-parameterization design ensures that GLoRA incurs no extra inference cost, rendering it a practical solution for resource-limited applications. Code is available at: https://github.com/Arnav0400/ViT-Slim/tree/master/GLoRA.

This research presents a framework for quantitative risk management in volatile markets, specifically focusing on expectile-based methodologies applied to the FTSE 100 index. Traditional risk measures such as Value-at-Risk (VaR) have demonstrated significant limitations during periods of market stress, as evidenced during the 2008 financial crisis and subsequent volatile periods. This study develops an advanced expectile-based framework that addresses the shortcomings of conventional quantile-based approaches by providing greater sensitivity to tail losses and improved stability in extreme market conditions. The research employs a dataset spanning two decades of FTSE 100 returns, incorporating periods of high volatility, market crashes, and recovery phases. Our methodology introduces novel mathematical formulations for expectile regression models, enhanced threshold determination techniques using time series analysis, and robust backtesting procedures. The empirical results demonstrate that expectile-based Value-at-Risk (EVaR) consistently outperforms traditional VaR measures across various confidence levels and market conditions. The framework exhibits superior performance during volatile periods, with reduced model risk and enhanced predictive accuracy. Furthermore, the study establishes practical implementation guidelines for financial institutions and provides evidence-based recommendations for regulatory compliance and portfolio management. The findings contribute significantly to the literature on financial risk management and offer practical tools for practitioners dealing with volatile market environments.

This paper introduces a novel framework for detecting and segmenting critical road assets on Thai highways using an advanced Refined Generalized Focal Loss (REG) formulation. Integrated into state-of-the-art vision-based detection and segmentation models, the proposed method effectively addresses class imbalance and the challenges of localizing small, underrepresented road elements, including pavilions, pedestrian bridges, information signs, single-arm poles, bus stops, warning signs, and concrete guardrails. To improve both detection and segmentation accuracy, a multi-task learning strategy is adopted, optimizing REG across multiple tasks. REG is further enhanced by incorporating a spatial-contextual adjustment term, which accounts for the spatial distribution of road assets, and a probabilistic refinement that captures prediction uncertainty in complex environments, such as varying lighting conditions and cluttered backgrounds. Our rigorous mathematical formulation demonstrates that REG minimizes localization and classification errors by applying adaptive weighting to hard-to-detect instances while down-weighting easier examples. Experimental results show a substantial performance improvement, achieving a mAP50 of 80.34 and an F1-score of 77.87, significantly outperforming conventional methods. This research underscores the capability of advanced loss function refinements to enhance the robustness and accuracy of road asset detection and segmentation, thereby contributing to improved road safety and infrastructure management. For an in-depth discussion of the mathematical background and related methods, please refer to previous work available at https://github.com/kaopanboonyuen/REG.

We introduce the Discrete Min-Max Violation (DMMV) as a general optimization problem which seeks an assignment of discrete values to variables that minimizes the largest constraint violation. This context-free mathematical formulation is applicable to a wide range of use cases that have worst-case performance requirements. After defining the DMMV problem mathematically, we explore its properties to establish a foundational understanding. To tackle DMMV instance sizes of practical relevance, we develop a GPU-accelerated heuristic that takes advantage of the mathematical properties of DMMV for speeding up the solution process. We demonstrate the versatile applicability of our heuristic by solving three optimization problems as use cases: (1) post-training quantization of language models, (2) discrete tomography, and (3) Finite Impulse Response (FIR) filter design. In quantization without outlier separation, our heuristic achieves 14% improvement on average over existing methods. In discrete tomography, it reduces reconstruction error by 16% under uniform noise and accelerates computations by a factor of 6 on GPU. For FIR filter design, it nearly achieves 50% ripple reduction compared to using the commercial integer optimization solver, Gurobi. Our comparative results point to the benefits of studying DMMV as a context-free optimization problem and the advantages that our proposed heuristic offers on three distinct problems. Our GPU-accelerated heuristic will be made open-source to further stimulate research on DMMV and its other applications. The code is available at https://anonymous.4open.science/r/AMVM-5F3E/

This paper studies the theoretical framework of the alignment process of generative models with Reinforcement Learning from Human Feedback (RLHF). We consider a standard mathematical formulation, the reverse-KL regularized contextual bandit for RLHF. Despite its widespread practical application, a rigorous theoretical analysis of this formulation remains open. We investigate its behavior in three distinct settings -- offline, online, and hybrid -- and propose efficient algorithms with finite-sample theoretical guarantees. Moving towards practical applications, our framework, with a robust approximation of the information-theoretical policy improvement oracle, naturally gives rise to several novel RLHF algorithms. This includes an iterative version of the Direct Preference Optimization (DPO) algorithm for online settings, and a multi-step rejection sampling strategy for offline scenarios. Our empirical evaluations on real-world alignment experiment of large language model demonstrate that these proposed methods significantly surpass existing strong baselines, such as DPO and Rejection Sampling Optimization (RSO), showcasing the connections between solid theoretical foundations and their powerful practical implementations.

Self-improvement is a mechanism in Large Language Model (LLM) pre-training, post-training and test-time inference. We explore a framework where the model verifies its own outputs, filters or reweights data based on this verification, and distills the filtered data. Despite several empirical successes, a fundamental understanding is still lacking. In this work, we initiate a comprehensive, modular and controlled study on LLM self-improvement. We provide a mathematical formulation for self-improvement, which is largely governed by a quantity which we formalize as the generation-verification gap. Through experiments with various model families and tasks, we discover a scaling phenomenon of self-improvement -- a variant of the generation-verification gap scales monotonically with the model pre-training flops. We also examine when self-improvement is possible, an iterative self-improvement procedure, and ways to improve its performance. Our findings not only advance understanding of LLM self-improvement with practical implications, but also open numerous avenues for future research into its capabilities and boundaries.

State-of-the-art natural language processing models have been shown to achieve remarkable performance in 'closed-world' settings where all the labels in the evaluation set are known at training time. However, in real-world settings, 'novel' instances that do not belong to any known class are often observed. This renders the ability to deal with novelties crucial. To initiate a systematic research in this important area of 'dealing with novelties', we introduce 'NoveltyTask', a multi-stage task to evaluate a system's performance on pipelined novelty 'detection' and 'accommodation' tasks. We provide mathematical formulation of NoveltyTask and instantiate it with the authorship attribution task that pertains to identifying the correct author of a given text. We use Amazon reviews corpus and compile a large dataset (consisting of 250k instances across 200 authors/labels) for NoveltyTask. We conduct comprehensive experiments and explore several baseline methods for the task. Our results show that the methods achieve considerably low performance making the task challenging and leaving sufficient room for improvement. Finally, we believe our work will encourage research in this underexplored area of dealing with novelties, an important step en route to developing robust systems.

Large language models (LLMs) have had a profound impact on numerous aspects of daily life including natural language processing, content generation, research methodologies and so on. However, one crucial issue concerning the inference results of large language models is security and privacy. In many scenarios, the results generated by LLMs could possibly leak many confidential or copyright information. A recent beautiful and breakthrough work [Vyas, Kakade and Barak 2023] focus on such privacy issue of the LLMs from theoretical perspective. It is well-known that computing the attention matrix is one of the major task during the LLMs computation. Thus, how to give a provable privately guarantees of computing the attention matrix is an important research direction. Previous work [Alman and Song 2023, Brand, Song and Zhou 2023] have proposed provable tight result for fast computation of attention without considering privacy concerns. One natural mathematical formulation to quantity the privacy in theoretical computer science graduate school textbook is differential privacy. Inspired by [Vyas, Kakade and Barak 2023], in this work, we provide a provable result for showing how to differentially private approximate the attention matrix. From technique perspective, our result replies on a pioneering work in the area of differential privacy by [Alabi, Kothari, Tankala, Venkat and Zhang 2022].

Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language descriptions (NL). This data scarcity also contributes to the generalization difficulties experienced by learning-based methods. To address these challenges, we propose a scalable framework for synthesizing a high-quality dataset, named OptMATH. Starting from curated seed data with mathematical formulations (MF), this framework automatically generates problem data (PD) with controllable complexity. Then, a back-translation step is employed to obtain NL. To verify the correspondence between the NL and the PD, a forward modeling step followed by rejection sampling is used. The accepted pairs constitute the training part of OptMATH. Then a collection of rejected pairs is identified and further filtered. This collection serves as a new benchmark for optimization modeling, containing difficult instances whose lengths are much longer than these of NL4OPT and MAMO. Through extensive experiments, we demonstrate that models of various sizes (0.5B-32B parameters) trained on OptMATH achieve superior results on multiple modeling benchmarks, thereby validating the effectiveness and scalability of our approach. Our dataset is publicly available at https://github.com/AuroraLHL/OptMATH.

The rapid development of diffusion models (DMs) has significantly advanced image and video applications, making "what you want is what you see" a reality. Among these, video editing has gained substantial attention and seen a swift rise in research activity, necessitating a comprehensive and systematic review of the existing literature. This paper reviews diffusion model-based video editing techniques, including theoretical foundations and practical applications. We begin by overviewing the mathematical formulation and image domain's key methods. Subsequently, we categorize video editing approaches by the inherent connections of their core technologies, depicting evolutionary trajectory. This paper also dives into novel applications, including point-based editing and pose-guided human video editing. Additionally, we present a comprehensive comparison using our newly introduced V2VBench. Building on the progress achieved to date, the paper concludes with ongoing challenges and potential directions for future research.

Variational AutoEncoders (VAEs) are powerful generative models that merge elements from statistics and information theory with the flexibility offered by deep neural networks to efficiently solve the generation problem for high dimensional data. The key insight of VAEs is to learn the latent distribution of data in such a way that new meaningful samples can be generated from it. This approach led to tremendous research and variations in the architectural design of VAEs, nourishing the recent field of research known as unsupervised representation learning. In this article, we provide a comparative evaluation of some of the most successful, recent variations of VAEs. We particularly focus the analysis on the energetic efficiency of the different models, in the spirit of the so called Green AI, aiming both to reduce the carbon footprint and the financial cost of generative techniques. For each architecture we provide its mathematical formulation, the ideas underlying its design, a detailed model description, a running implementation and quantitative results.

Formula-driven supervised learning (FDSL) is a pre-training method that relies on synthetic images generated from mathematical formulae such as fractals. Prior work on FDSL has shown that pre-training vision transformers on such synthetic datasets can yield competitive accuracy on a wide range of downstream tasks. These synthetic images are categorized according to the parameters in the mathematical formula that generate them. In the present work, we hypothesize that the process for generating different instances for the same category in FDSL, can be viewed as a form of data augmentation. We validate this hypothesis by replacing the instances with data augmentation, which means we only need a single image per category. Our experiments shows that this one-instance fractal database (OFDB) performs better than the original dataset where instances were explicitly generated. We further scale up OFDB to 21,000 categories and show that it matches, or even surpasses, the model pre-trained on ImageNet-21k in ImageNet-1k fine-tuning. The number of images in OFDB is 21k, whereas ImageNet-21k has 14M. This opens new possibilities for pre-training vision transformers with much smaller datasets.

Diffusion generative models have recently become a powerful technique for creating and modifying high-quality, coherent video content. This survey provides a comprehensive overview of the critical components of diffusion models for video generation, including their applications, architectural design, and temporal dynamics modeling. The paper begins by discussing the core principles and mathematical formulations, then explores various architectural choices and methods for maintaining temporal consistency. A taxonomy of applications is presented, categorizing models based on input modalities such as text prompts, images, videos, and audio signals. Advancements in text-to-video generation are discussed to illustrate the state-of-the-art capabilities and limitations of current approaches. Additionally, the survey summarizes recent developments in training and evaluation practices, including the use of diverse video and image datasets and the adoption of various evaluation metrics to assess model performance. The survey concludes with an examination of ongoing challenges, such as generating longer videos and managing computational costs, and offers insights into potential future directions for the field. By consolidating the latest research and developments, this survey aims to serve as a valuable resource for researchers and practitioners working with video diffusion models. Website: https://github.com/ndrwmlnk/Awesome-Video-Diffusion-Models

We propose Mish, a novel self-regularized non-monotonic activation function which can be mathematically defined as: f(x)=xtanh(softplus(x)). As activation functions play a crucial role in the performance and training dynamics in neural networks, we validated experimentally on several well-known benchmarks against the best combinations of architectures and activation functions. We also observe that data augmentation techniques have a favorable effect on benchmarks like ImageNet-1k and MS-COCO across multiple architectures. For example, Mish outperformed Leaky ReLU on YOLOv4 with a CSP-DarkNet-53 backbone on average precision (AP_{50}^{val}) by 2.1% in MS-COCO object detection and ReLU on ResNet-50 on ImageNet-1k in Top-1 accuracy by approx1% while keeping all other network parameters and hyperparameters constant. Furthermore, we explore the mathematical formulation of Mish in relation with the Swish family of functions and propose an intuitive understanding on how the first derivative behavior may be acting as a regularizer helping the optimization of deep neural networks. Code is publicly available at https://github.com/digantamisra98/Mish.

Implicit Personalization (IP) is a phenomenon of language models inferring a user's background from the implicit cues in the input prompts and tailoring the response based on this inference. While previous work has touched upon various instances of this problem, there lacks a unified framework to study this behavior. This work systematically studies IP through a rigorous mathematical formulation, a multi-perspective moral reasoning framework, and a set of case studies. Our theoretical foundation for IP relies on a structural causal model and introduces a novel method, indirect intervention, to estimate the causal effect of a mediator variable that cannot be directly intervened upon. Beyond the technical approach, we also introduce a set of moral reasoning principles based on three schools of moral philosophy to study when IP may or may not be ethically appropriate. Equipped with both mathematical and ethical insights, we present three diverse case studies illustrating the varied nature of the IP problem and offer recommendations for future research. Our code and data are at https://github.com/jiarui-liu/IP.

State-of-the-art neural algorithmic reasoners make use of message passing in graph neural networks (GNNs). But typical GNNs blur the distinction between the definition and invocation of the message function, forcing a node to send messages to its neighbours at every layer, synchronously. When applying GNNs to learn to execute dynamic programming algorithms, however, on most steps only a handful of the nodes would have meaningful updates to send. One, hence, runs the risk of inefficiencies by sending too much irrelevant data across the graph -- with many intermediate GNN steps having to learn identity functions. In this work, we explicitly separate the concepts of node state update and message function invocation. With this separation, we obtain a mathematical formulation that allows us to reason about asynchronous computation in both algorithms and neural networks.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a uniform physical grid suffer significant aliasing error and information loss. Moreover, signals can exist in different topological structures as, for example, points, lines, surfaces and volumes. It has been challenging to analyze signals with mixed topologies (for example, point cloud with surface mesh). To this end, we develop mathematical formulations for Non-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample nonuniform data signals of different topologies defined on a simplex mesh into the spectral domain with no spatial sampling error. The spectral transform is performed in the Euclidean space, which removes the translation ambiguity from works on the graph spectrum. Our representation has four distinct advantages: (1) the process causes no spatial sampling error during the initial sampling, (2) the generality of this approach provides a unified framework for using CNNs to analyze signals of mixed topologies, (3) it allows us to leverage state-of-the-art backbone CNN architectures for effective learning without having to design a particular architecture for a particular data structure in an ad-hoc fashion, and (4) the representation allows weighted meshes where each element has a different weight (i.e., texture) indicating local properties. We achieve results on par with the state-of-the-art for the 3D shape retrieval task, and a new state-of-the-art for the point cloud to surface reconstruction task.

Complex hierarchical structures composed of simple nanoscale building blocks form the basis of most biological materials. Here we demonstrate how analogies between seemingly different fields enable the understanding of general principles by which functional properties in hierarchical systems emerge, similar to an analogy learning process. Specifically, natural hierarchical materials like spider silk exhibit properties comparable to classical music in terms of their hierarchical structure and function. As a comparative tool here we apply hierarchical ontology logs (olog) that follow a rigorous mathematical formulation based on category theory to provide an insightful system representation by expressing knowledge in a conceptual map. We explain the process of analogy creation, draw connections at several levels of hierarchy and identify similar patterns that govern the structure of the hierarchical systems silk and music and discuss the impact of the derived analogy for nanotechnology.

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

The Transformer architecture, underpinned by the Multi-Head Attention (MHA) mechanism, has become the de facto standard for state-of-the-art models in artificial intelligence. However, the quadratic computational complexity of MHA with respect to sequence length presents a significant barrier to scaling, particularly for applications involving long contexts. Prevailing solutions, such as Multi-Query Attention (MQA) and Grouped-Query Attention (GQA), have effectively addressed the memory bandwidth bottleneck that dominates autoregressive inference latency by sharing Key and Value projections. While highly successful, these methods do not reduce the fundamental number of floating-point operations (FLOPs) required for the attention score computation, which remains a critical bottleneck for training and full-sequence processing. This paper introduces Sparse Query Attention (SQA), a novel attention architecture that pursues an alternative and complementary optimization path. Instead of reducing Key/Value heads, SQA reduces the number of Query heads. This architectural modification directly decreases the computational complexity of the attention mechanism by a factor proportional to the reduction in query heads, thereby lowering the overall FLOPs. This work presents the theoretical foundation of SQA, its mathematical formulation, and a family of architectural variants. Empirical benchmarks on long sequences (32k-200k tokens) demonstrate that SQA can achieve significant throughput improvements of up to 3x in computation-bound scenarios such as model pre-training, fine-tuning, and encoder-based tasks, with only a minimal impact on model quality in preliminary smallscale experiments. SQA was discovered serendipitously during the development of the upcoming Reactive Transformer architecture, suggesting its potential as a powerful tool for building more efficient and scalable models

As large language models (LLMs) generate texts with increasing fluency and realism, there is a growing need to identify the source of texts to prevent the abuse of LLMs. Text watermarking techniques have proven reliable in distinguishing whether a text is generated by LLMs by injecting hidden patterns. However, we argue that existing LLM watermarking methods are encoding-inefficient and cannot flexibly meet the diverse information encoding needs (such as encoding model version, generation time, user id, etc.). In this work, we conduct the first systematic study on the topic of Codable Text Watermarking for LLMs (CTWL) that allows text watermarks to carry multi-bit customizable information. First of all, we study the taxonomy of LLM watermarking technologies and give a mathematical formulation for CTWL. Additionally, we provide a comprehensive evaluation system for CTWL: (1) watermarking success rate, (2) robustness against various corruptions, (3) coding rate of payload information, (4) encoding and decoding efficiency, (5) impacts on the quality of the generated text. To meet the requirements of these non-Pareto-improving metrics, we follow the most prominent vocabulary partition-based watermarking direction, and devise an advanced CTWL method named Balance-Marking. The core idea of our method is to use a proxy language model to split the vocabulary into probability-balanced parts, thereby effectively maintaining the quality of the watermarked text. Our code is available at https://github.com/lancopku/codable-watermarking-for-llm.

Deep Equilibrium Models (DEQs) and Neural Ordinary Differential Equations (Neural ODEs) are two branches of implicit models that have achieved remarkable success owing to their superior performance and low memory consumption. While both are implicit models, DEQs and Neural ODEs are derived from different mathematical formulations. Inspired by homotopy continuation, we establish a connection between these two models and illustrate that they are actually two sides of the same coin. Homotopy continuation is a classical method of solving nonlinear equations based on a corresponding ODE. Given this connection, we proposed a new implicit model called HomoODE that inherits the property of high accuracy from DEQs and the property of stability from Neural ODEs. Unlike DEQs, which explicitly solve an equilibrium-point-finding problem via Newton's methods in the forward pass, HomoODE solves the equilibrium-point-finding problem implicitly using a modified Neural ODE via homotopy continuation. Further, we developed an acceleration method for HomoODE with a shared learnable initial point. It is worth noting that our model also provides a better understanding of why Augmented Neural ODEs work as long as the augmented part is regarded as the equilibrium point to find. Comprehensive experiments with several image classification tasks demonstrate that HomoODE surpasses existing implicit models in terms of both accuracy and memory consumption.

Bird's eye view (BEV) representation is a new perception formulation for autonomous driving, which is based on spatial fusion. Further, temporal fusion is also introduced in BEV representation and gains great success. In this work, we propose a new method that unifies both spatial and temporal fusion and merges them into a unified mathematical formulation. The unified fusion could not only provide a new perspective on BEV fusion but also brings new capabilities. With the proposed unified spatial-temporal fusion, our method could support long-range fusion, which is hard to achieve in conventional BEV methods. Moreover, the BEV fusion in our work is temporal-adaptive and the weights of temporal fusion are learnable. In contrast, conventional methods mainly use fixed and equal weights for temporal fusion. Besides, the proposed unified fusion could avoid information lost in conventional BEV fusion methods and make full use of features. Extensive experiments and ablation studies on the NuScenes dataset show the effectiveness of the proposed method and our method gains the state-of-the-art performance in the map segmentation task.

Existing benchmarks fail to capture a crucial aspect of intelligence: physical reasoning, the integrated ability to combine domain knowledge, symbolic reasoning, and understanding of real-world constraints. To address this gap, we introduce PhyX: the first large-scale benchmark designed to assess models capacity for physics-grounded reasoning in visual scenarios. PhyX includes 3K meticulously curated multimodal questions spanning 6 reasoning types across 25 sub-domains and 6 core physics domains: thermodynamics, electromagnetism, mechanics, modern physics, optics, and wave\&acoustics. In our comprehensive evaluation, even state-of-the-art models struggle significantly with physical reasoning. GPT-4o, Claude3.7-Sonnet, and GPT-o4-mini achieve only 32.5\%, 42.2\%, and 45.8\% accuracy respectively-performance gaps exceeding 29\% compared to human experts. Our analysis exposes critical limitations in current models: over-reliance on memorized disciplinary knowledge, excessive dependence on mathematical formulations, and surface-level visual pattern matching rather than genuine physical understanding. We provide in-depth analysis through fine-grained statistics, detailed case studies, and multiple evaluation paradigms to thoroughly examine physical reasoning capabilities. To ensure reproducibility, we implement a compatible evaluation protocol based on widely-used toolkits such as VLMEvalKit, enabling one-click evaluation.

State Space Models (SSMs) have emerged as a promising alternative to the popular transformer-based models and have been increasingly gaining attention. Compared to transformers, SSMs excel at tasks with sequential data or longer contexts, demonstrating comparable performances with significant efficiency gains. In this survey, we provide a coherent and systematic overview for SSMs, including their theoretical motivations, mathematical formulations, comparison with existing model classes, and various applications. We divide the SSM series into three main sections, providing a detailed introduction to the original SSM, the structured SSM represented by S4, and the selective SSM typified by Mamba. We put an emphasis on technicality, and highlight the various key techniques introduced to address the effectiveness and efficiency of SSMs. We hope this manuscript serves as an introduction for researchers to explore the theoretical foundations of SSMs.

Recent advances in Large Vision-Language models (LVLM) have spurred significant progress in document parsing task. Compared to traditional pipeline-based methods, end-to-end paradigms have shown their excellence in converting PDF images into structured outputs through integrated Optical Character Recognition (OCR), table recognition, mathematical formula recognition and so on. However, the absence of explicit analytical stages for document layouts and reading orders limits the LVLM's capability in handling complex document types such as multi-column newspapers or posters. To address this limitation, we propose in this report Logics-Parsing: an end-to-end LVLM-based model augmented with reinforcement learning. Our model incorporates meticulously designed reward mechanisms to optimize complex layout analysis and reading order inference. In addition, we expand the model's versatility by incorporating diverse data types such as chemical formulas and handwritten Chinese characters into supervised fine-tuning. Finally, to enable rigorous evaluation of our approach, we introduce LogicsParsingBench, a curated set of 1,078 page-level PDF images spanning nine major categories and over twenty sub-categories, which will be released later. Comprehensive experiments conducted on LogicsParsingBench have validated the efficacy and State-of-the-art (SOTA) performance of our proposed model across diverse document analysis scenarios. Project Page: https://github.com/alibaba/Logics-Parsing

Ever since their conception, Transformers have taken over traditional sequence models in many tasks, such as NLP, image classification, and video/audio processing, for their fast training and superior performance. Much of the merit is attributable to positional encoding and multi-head attention. However, Transformers fall short in learning long-range dependencies mainly due to the quadratic complexity scaled with context length, in terms of both time and space. Consequently, over the past five years, a myriad of methods has been proposed to make Transformers more efficient. In this work, we first take a step back, study and compare existing solutions to long-sequence modeling in terms of their pure mathematical formulation. Specifically, we summarize them using a unified template, given their shared nature of token mixing. Through benchmarks, we then demonstrate that long context length does yield better performance, albeit application-dependent, and traditional Transformer models fall short in taking advantage of long-range dependencies. Next, inspired by emerging sparse models of huge capacity, we propose a machine learning system for handling million-scale dependencies. As a proof of concept, we evaluate the performance of one essential component of this system, namely, the distributed multi-head attention. We show that our algorithm can scale up attention computation by almost 40times using four GeForce RTX 4090 GPUs, compared to vanilla multi-head attention mechanism. We believe this study is an instrumental step towards modeling million-scale dependencies.

Diffusion models have achieved remarkable performance in generative modeling, yet their theoretical foundations are often intricate, and the gap between mathematical formulations in papers and practical open-source implementations can be difficult to bridge. Existing tutorials primarily focus on deriving equations, offering limited guidance on how diffusion models actually operate in code. To address this, we present a concise implementation of approximately 300 lines that explains diffusion models from a code-execution perspective. Our minimal example preserves the essential components -- including forward diffusion, reverse sampling, the noise-prediction network, and the training loop -- while removing unnecessary engineering details. This technical report aims to provide researchers with a clear, implementation-first understanding of how diffusion models work in practice and how code and theory correspond. Our code and pre-trained models are available at: https://github.com/disanda/GM/tree/main/DDPM-DDIM-ClassifierFree.

Multi-robot coordination has traditionally relied on a mission-specific and expert-driven pipeline, where natural language mission descriptions are manually translated by domain experts into mathematical formulation, algorithm design, and executable code. This conventional process is labor-intensive, inaccessible to non-experts, and inflexible to changes in mission requirements. Here, we propose LAN2CB (Language to Collective Behavior), a novel framework that leverages large language models (LLMs) to streamline and generalize the multi-robot coordination pipeline. LAN2CB transforms natural language (NL) mission descriptions into executable Python code for multi-robot systems through two core modules: (1) Mission Analysis, which parses mission descriptions into behavior trees, and (2) Code Generation, which leverages the behavior tree and a structured knowledge base to generate robot control code. We further introduce a dataset of natural language mission descriptions to support development and benchmarking. Experiments in both simulation and real-world environments demonstrate that LAN2CB enables robust and flexible multi-robot coordination from natural language, significantly reducing manual engineering effort and supporting broad generalization across diverse mission types. Website: https://sites.google.com/view/lan-cb

Quantization effectively reduces the serving costs of Large Language Models (LLMs) by speeding up data movement through compressed parameters and enabling faster operations via integer arithmetic. However, activating integer arithmetic requires quantizing both weights and activations, which poses challenges due to the significant outliers in LLMs that increase quantization error. In this work, we investigate these outliers with an emphasis on their effect on layer-wise quantization error, then examine how smoothing and rotation transform the observed values. Our primary contributions include introducing a new metric to measure and visualize quantization difficulty based on channel magnitudes, as well as proposing a hybrid approach that applies channel-wise scaling before rotation, supported by a mathematical formulation of its benefits.

Large language models (LLMs) have exhibited their problem-solving abilities in mathematical reasoning. Solving realistic optimization (OPT) problems in application scenarios requires advanced and applied mathematics ability. However, current OPT benchmarks that merely solve linear programming are far from complex realistic situations. In this work, we propose OptiBench, a benchmark for End-to-end optimization problem-solving with human-readable inputs and outputs. OptiBench contains rich optimization problems, including linear and nonlinear programming with or without tabular data, which can comprehensively evaluate LLMs' solving ability. In our benchmark, LLMs are required to call a code solver to provide precise numerical answers. Furthermore, to alleviate the data scarcity for optimization problems, and to bridge the gap between open-source LLMs on a small scale (e.g., Llama-3-8b) and closed-source LLMs (e.g., GPT-4), we further propose a data synthesis method namely ReSocratic. Unlike general data synthesis methods that proceed from questions to answers, \ReSocratic first incrementally synthesizes formatted optimization demonstration with mathematical formulations step by step and then back-translates the generated demonstrations into questions. Based on this, we synthesize the ReSocratic-29k dataset. We further conduct supervised fine-tuning with ReSocratic-29k on multiple open-source models. Experimental results show that ReSocratic-29k significantly improves the performance of open-source models.

The Large Language Model Bias Index (LLMBI) is a pioneering approach designed to quantify and address biases inherent in large language models (LLMs), such as GPT-4. We recognise the increasing prevalence and impact of LLMs across diverse sectors. This research introduces a novel metric, LLMBI, to systematically measure and mitigate biases potentially skewing model responses. We formulated LLMBI using a composite scoring system incorporating multiple dimensions of bias, including but not limited to age, gender, and racial biases. To operationalise this metric, we engaged in a multi-step process involving collecting and annotating LLM responses, applying sophisticated Natural Language Processing (NLP) techniques for bias detection, and computing the LLMBI score through a specially crafted mathematical formula. The formula integrates weighted averages of various bias dimensions, a penalty for dataset diversity deficiencies, and a correction for sentiment biases. Our empirical analysis, conducted using responses from OpenAI's API, employs advanced sentiment analysis as a representative method for bias detection. The research reveals LLMs, whilst demonstrating impressive capabilities in text generation, exhibit varying degrees of bias across different dimensions. LLMBI provides a quantifiable measure to compare biases across models and over time, offering a vital tool for systems engineers, researchers and regulators in enhancing the fairness and reliability of LLMs. It highlights the potential of LLMs in mimicking unbiased human-like responses. Additionally, it underscores the necessity of continuously monitoring and recalibrating such models to align with evolving societal norms and ethical standards.

This paper presents a novel, fast and privacy preserving implementation of deep autoencoders. DAEF (Deep Autoencoder for Federated learning), unlike traditional neural networks, trains a deep autoencoder network in a non-iterative way, which drastically reduces its training time. Its training can be carried out in a distributed way (several partitions of the dataset in parallel) and incrementally (aggregation of partial models), and due to its mathematical formulation, the data that is exchanged does not endanger the privacy of the users. This makes DAEF a valid method for edge computing and federated learning scenarios. The method has been evaluated and compared to traditional (iterative) deep autoencoders using seven real anomaly detection datasets, and their performance have been shown to be similar despite DAEF's faster training.

Counterfactual explanations is one of the post-hoc methods used to provide explainability to machine learning models that have been attracting attention in recent years. Most examples in the literature, address the problem of generating post-hoc explanations for black-box machine learning models after the rejection of a loan application. In contrast, in this work, we investigate mathematical programming formulations for scorecard models, a type of interpretable model predominant within the banking industry for lending. The proposed mixed-integer programming formulations combine objective functions to ensure close, realistic and sparse counterfactuals using multi-objective optimization techniques for a binary, probability or continuous outcome. Moreover, we extend these formulations to generate multiple optimal counterfactuals simultaneously while guaranteeing diversity. Experiments on two real-world datasets confirm that the presented approach can generate optimal diverse counterfactuals addressing desired properties with assumable CPU times for practice use.