Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between accuracy and complexity. In this paper, we introduce DiffuSR, a pre-training framework for symbolic regression built upon a continuous-state diffusion language model. DiffuSR employs a trainable embedding layer within the diffusion process to map discrete mathematical symbols into a continuous latent space, modeling equation distributions effectively. Through iterative denoising, DiffuSR converts an initial noisy sequence into a symbolic equation, guided by numerical data injected via a cross-attention mechanism. We also design an effective inference strategy to enhance the accuracy of the diffusion-based equation generator, which injects logit priors into genetic programming. Experimental results on standard symbolic regression benchmarks demonstrate that Dif-fuSR achieves competitive performance with state-of-the-art autoregressive methods and generates more interpretable and diverse mathematical expressions.

Mathematical word problems (MWPs) involve the task of converting textual descriptions into mathematical equations. This poses a significant challenge in natural language processing, particularly for low-resource languages such as Bengali. This paper addresses this challenge by developing an innovative approach to solving Bengali MWPs using transformer-based models, including Basic Transformer, mT5, BanglaT5, and mBART50. To support this effort, the "PatiGonit" dataset was introduced, containing 10,000 Bengali math problems, and these models were fine-tuned to translate the word problems into equations accurately. The evaluation revealed that the mT5 model achieved the highest accuracy of 97.30%, demonstrating the effectiveness of transformer models in this domain. This research marks a significant step forward in Bengali natural language processing, offering valuable methodologies and resources for educational AI tools. By improving math education, it also supports the development of advanced problem-solving skills for Bengali-speaking students.

Recent advances in natural language processing (NLP), particularly with the emergence of large language models (LLMs), have significantly enhanced the field of textual analysis. However, while these developments have yielded substantial progress in analyzing textual data, applying analysis to mathematical equations and their relationships within texts has produced mixed results. In this paper, we take the initial steps toward understanding the dependency relationships between mathematical expressions in STEM articles. Our dataset, sourced from a random sampling of the arXiv corpus, contains an analysis of 107 published STEM manuscripts whose inter-equation dependency relationships have been hand-labeled, resulting in a new object we refer to as a derivation graph that summarizes the mathematical content of the manuscript. We exhaustively evaluate analytical and NLP-based models to assess their capability to identify and extract the derivation relationships for each article and compare the results with the ground truth. Our comprehensive testing finds that both analytical and NLP models (including LLMs) achieve $\sim$40-50% F1 scores for extracting derivation graphs from articles, revealing that the recent advances in NLP have not made significant inroads in comprehending mathematical texts compared to simpler analytic models. While current approaches offer a solid foundation for extracting mathematical information, further research is necessary to improve accuracy and depth in this area.

Have you ever spotted someone in a crowd that you thought was a friend, only to discover it was simply someone who looks remarkably similar? Many of us have seen so-called doppelgängers of loved ones, family members and even ourselves. Now, a study has revealed that these doppelgängers don't just look alike – they also likely have very similar DNA, and even share personality traits. Researchers from the Josep Carreras Leukaemia Research Institute in Barcelona have revealed that strong facial similarity is associated with shared genetic variants. 'These results will have future implications in forensic medicine - reconstructing the criminal's face from DNA - and in genetic diagnosis - the photo of the patient's face will already give you clues as to which genome he or she has,' said Dr Manel Esteller, senior author of the study.

From Amy Adams and Isla Fisher to Liam Neeson and Ralph Fiennes, many celebrities are regularly mistaken for one another, despite being unrelated. Now, a study has revealed that these famous faces don't just look alike – they also likely have very similar DNA. Researchers from the Josep Carreras Leukaemia Research Institute in Barcelona have revealed that strong facial similarity is associated with shared genetic variants. 'These results will have future implications in forensic medicine - reconstructing the criminal's face from DNA - and in genetic diagnosis - the photo of the patient's face will already give you clues as to which genome he or she has,' said Dr Manel Esteller, senior author of the study. In 2015, researchers revealed that the chance of finding your doppelganger is one in a trillion. Teghan Lucas, a student at the University of Adelaide, conducted the study using a large database of face and body measurements from almost 4,000 individuals, combined with mathematical equations.

On a summer Monday evening in 1833, Ada Byron and her mother Anne Isabella "Annabella" Byron went to the home of English mathematician Charles Babbage. Twelve days earlier, when the younger Byron met Babbage at a high society soiree, she had been taken with his description of a machine he was building. The hand-cranked apparatus of bronze and steel used stacks of cogs, hammer-like metal arms, and thousands of numbered wheels to automatically solve mathematical equations. But the Difference Engine, as Babbage called it, was incomplete. He had finished a small prototype that stood about two-and-a-half feet tall.

"A fundamental problem in artificial intelligence is that nobody really knows what intelligence is." That's the opening sentence of "Universal Intelligence: A Definition of Machine Intelligence" (link) authored by Shane Legg and Marcus Hutter. If those names sound familiar, they are. Legg is a co-founder of DeepMind and Hutter is a senior scientist at DeepMind - two very well accomplished individuals with a long track record researching artificial general intelligence. While both have done exemplary work in this field, this paper, in my opinion, is poor.

Many of us have read about the Bias and Variance at various places in the AI literature but still many people struggle to explain it with respect to mathematical equation. People always comment about bias-variance whenever they build a model in order to figure out whether the model can be used or not in the real world and how good its performance will be. In this article, we will focus on the mathematical equation depicting Bias-Variance and try to understand different parts of this equation from a mathematical perspective. We will be using above assumptions in the equation below. As the main focus of this article is to understand the bias-variance equation from mathematical perspective, we will directly look at the equation without going into the derivation behind it(Please check the references, if you want to understand the derivation).

There are different modules to realize different functions in deep learning. Expertise in deep learning involves designing architectures to complete particular tasks. It reduces a complex function into a graph of functional modules (possibly dynamic), the functions of which are finalized by learning. Recurrent Neural Network (RNN)is one type of architecture that we can use to deal with sequences of data. We learned that a signal can be either 1D, 2D or 3D depending on the domain. The domain is defined by what you are mapping from and what you are mapping to.

Explaining Traditional Engineering Models It is a well-known fact that models of physical phenomena that are generated through mathematical equations can be explained. This is one of the main reasons behind the expectation of engineers and scientists that any potential model of the physical phenomena should be explainable. Explainability of the traditional models of physical phenomena is achieved through the solutions of the mathematical equations that are used to build the models. Explanations of such models are achieved through analytical solutions (for reasonably simple mathematical equations) or numerical solutions (for complex mathematical equations) of the mathematical equations. Solutions of the mathematical equations provide the opportunities to get answers to almost any question that might be asked from the model of the physical phenomena. Solutions of the mathematical equations are used to explain why and how certain results are generated by the model. It allows examination and explanation of the influence and effect of all the involved parameters (variables) on one another and on the model's results (output parameters).