Kazem Meidani’s Post

Why Large Language Models (LLMs) fail on most (not all) of the mathematical problems 1. LLM training data focuses on language, not formal mathematics. 2. Math equations require precise syntax and tokenization .LLMs might misinterpret or struggle with this process. 3. Math involves abstract symbols and operations. LLMs might not fully comprehend the symbolic meaning, leading to errors. 4. LLMs can perform simple arithmetic, not designed for complex calculations 5. Mis understanding of context Most models, including the new Llama 3.1, fail to answer questions like ‘Which number is bigger, 9.11 or 9.9?’ One of the workarounds would be to use agentic workflows and include mathematical tools to address the user’s math problem _______ If you like my posts please follow me

🌟 14 Essential Algorithms Every Programmer Should Know 🌟 As a programmer, understanding key algorithms is crucial for solving complex problems efficiently. Here are 14 algorithms that form the backbone of computational thinking: Sorting Algorithms: e.g., Bubble Sort, Quick Sort, Merge Sort. Searching Algorithms: e.g., Binary Search, Linear Search. Graph Algorithms: e.g., Breadth-First Search (BFS), Depth-First Search (DFS). Dynamic Programming: Optimal substructure and overlapping subproblems. Greedy Algorithms: e.g., Dijkstra's algorithm, Prim's algorithm. String Algorithms: e.g., Knuth-Morris-Pratt (KMP) algorithm, Rabin-Karp algorithm. Tree Algorithms: e.g., Binary Tree traversal (inorder, preorder, postorder). Divide and Conquer: e.g., Binary Search, Merge Sort. Backtracking: e.g., N-Queens problem, Sudoku solver. Mathematical Algorithms: e.g., Euclidean algorithm (GCD), Sieve of Eratosthenes. Bit Manipulation: e.g., Bitwise operations, XOR properties. Sorting Network: e.g., Bitonic sort, Batcher's odd-even merge. Parallel Algorithms: e.g., Parallel merge sort, Parallel prefix sum. Randomized Algorithms: e.g., QuickSelect, Monte Carlo algorithms. Mastering these algorithms not only enhances problem-solving skills but also lays a strong foundation for algorithmic thinking in software development. Which algorithms have been most impactful in your programming journey? #Algorithms #Programming #SoftwareDevelopment #ProblemSolving #ComputerScience #ContinuousLearning

Interesting paper: Programmable Variational Inference Paper link on Hugging Face: https://lnkd.in/gRnQ2WQC #paper #bookmark

🔥 𝟐 𝐍𝐞𝐰 𝐄𝐩𝐢𝐬𝐨𝐝𝐞𝐬 𝐨𝐟 𝐃𝐚𝐭𝐚 𝐒𝐜𝐢𝐞𝐧𝐜𝐞 𝐃𝐞𝐜𝐨𝐝𝐞𝐝 🔥 with #legendary Daniel A. and Nir Regev 📚 🧠 𝐀 𝐥𝐞𝐠𝐞𝐧𝐝𝐚𝐫𝐲 𝐩𝐚𝐩𝐞𝐫 𝐨𝐟 𝐂𝐥𝐚𝐮𝐝𝐞 𝐒𝐡𝐚𝐧𝐧𝐨𝐧 "𝐀 𝐦𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐚𝐥 𝐭𝐡𝐞𝐨𝐫𝐲 𝐨𝐟 𝐜𝐨𝐦𝐦𝐮𝐧𝐢𝐜𝐚𝐭𝐢𝐨𝐧" 📚 🧠 , Part 1 and 2 ✍ The paper fundamentally reshapes how we understand communication. ✍ It introduces a formal framework for analyzing communication systems, addressing the transmission of information with and without noise. ✍ Key concepts include the definition of information entropy, the logarithmic measure of information, and the capacity of communication channels. ✍ Shannon demonstrates that information can be efficiently encoded and decoded to maximize the transmission rate while minimizing errors introduced by noise. ✍ This work is pivotal today as it underpins digital communication technologies, from data compression to error correction in modern telecommunication systems. This is the second part out of 3, as the paper is quite long! 🛁 𝐘𝐨𝐮𝐭𝐮𝐛𝐞: https://lnkd.in/dhE5gy8D, https://lnkd.in/dnUHM2ur 🖖 𝐒𝐩𝐨𝐭𝐢𝐟𝐲: https://lnkd.in/d4uD8-a2, https://lnkd.in/d4uD8-a2 🍎 𝐀𝐩𝐩𝐥𝐞 𝐏𝐨𝐝𝐜𝐚𝐬𝐭𝐬: https://lnkd.in/ddDWT5Bk, Data Science Decoded - A Mathematical Theory of Communication (1948), Shannon, C. E. Part - 1.mp3 ✍ Full breakdown of the paper with math and python code is at our website: https://lnkd.in/dfVZuNKy You're cordially invited to watch 👁 , listen 👂 and comment ✍ #datasciencedecoded #mathematics #datascience #machinelearning

A Visual Understanding of Decision Trees and Gradient Boosting "Gradient boosting is an example of ensemble learning. Ensemble learning is a machine learning approach that improves the predictive performance by combining the predictions from multiple models. Boosting is an ensemble learning method that combines multiple weak learning models sequentially to improve the predictive performance. Gradient boosting can be used for both classification and regression problems. Since it is based on the concept of boosting, it creates a strong learner by combining several weak learners sequentially. Theoretically, gradient boosting can use any weak models, however, the decision trees are the most common choice due to their ability to capture complex interactions and non-linear relationships. " By Reza Bagheri at Towards Data Science Link https://lnkd.in/dFhh2u7y

💡 "Mathematics behind Machine Learning" 💡 Here's all what I have learnt on the Day5📝: #Day5 of Machine Learning In my latest blog, we dive into the world of implicit functions and mastering their differentiation🧑🔬 While explicit functions are more straightforward, implicit functions (where the variable appears on both sides) are far more common in real-world applications. Some key highlights from the post: ✨ Understand the difference between explicit and implicit functions with clear examples. ✨ Step-by-step guide to finding derivatives of implicit functions, both analytically and computationally. ✨ Detailed walk-through of 3 examples, applying the product rule, chain rule, and algebraic manipulation. . 🤔 What's Next? Next, we discuss about higher order derivatives and solve some interesting use case using mathematics and python as well. 🚀 Let's keep pushing the boundaries of technology together! #ImplicitFunctions #Derivatives #CalculusRules #ProductRule #ChainRule #MachineLearning

This dataset contains highly curated and synthetically created prompt/response pairs specifically designed to teach LLM models three general concepts: - The PFAF function to replace standard word vectorization. - Higher Order Logic and how to generally employ it. - First Order Predicate Calculus and how to generally define and use it. These concepts are taught to the model specifically to increase their generalizability. Across the board. It is essentially a set of tools and functions for logical generalizability. The equation to me is quite simple, either LLM models are stochastic parrots, or they truly are able to dissect and understand patterns between words. If it is the latter, then these three tools are specifically targeted towards teaching the LLM model how to improve those skills. If it is the former, this dataset should not improve the outputs of a model fine tuned on the dataset in any generalizably measurable way. I have trained a Phi-2 model on the dataset. I can do so again easily. I cannot upload the fine tuned model to HuggingFace without quantizing it first because it would cost money to do those things. When I quantize the Phi-2 model, it is like hitting it with a giant nerf bat. I can also fine tune a Llama 7B model on the dataset if anyone is interested. I didn't tell anyone at all about the first and second datasets, and they both have a good amount of downloads. So, someone out there is interested in this dataset. Link to dataset on HuggingFace: https://lnkd.in/gEK8jWYb Link to video I made showing outputs of Phi-2 model fine tuned on my dataset: https://lnkd.in/gUmcybKi

The #book SAR Image Analysis—A Computational Statistics Approach: With #RCode, Data, and Applications stands out as an exceptional resource dedicated to statistical methodologies to extract information from synthetic aperture #radar (#SAR) imagery, all within a computational framework using R programming language. The book covers a wide range of topics in 183 pages and seven chapters, including a detailed overview of SAR data acquisition and its strong connection with specific concepts of non-Gaussian statistical models due to the physical properties of the scene. Its primary objective is to consolidate a comprehensive repository about well-established and state-of-the-art parametric models utilized in SAR image processing. It also addresses the critical task of parameter estimation, which is essential for extracting valuable information from the data. Moreover, all of the R codes and datasets are available at https://lnkd.in/gEJMp9md, allowing readers to directly apply the concepts discussed and see their practical implications, making the learning experience more engaging as it bridges the gap between theory and practice.

https://lnkd.in/gWST_H4P ReProver: code-generation LLM for lean, to mathematicall and automatically proof theorems using Turing-complete compiler (lean language) with wide-extended, human dedicated theorems (mathlib). LLM x building math from scratch and we are trying to surpass it

Gradient Descent on Multiple Variables Introduction: As we delve deeper into machine learning, understanding optimization techniques becomes crucial. Gradient descent, a fundamental algorithm, undergoes a slight modification when applied to multiple variables. Let's explore why and how. Key Concepts: Gradient Descent Overview: Gradient descent is a method to minimize a function iteratively. In multiple variable scenarios, the algorithm simultaneously updates coefficients for each feature, moving towards the optimal values. Partial Derivatives: The gradient in multiple variables involves partial derivatives. The update rule for each parameter (θ) becomes: θⱼ := θⱼ - α * (∂/∂θⱼ)J(θ₀, θ₁, ..., θₙ), where α is the learning rate. Convergence Checks: Monitoring the convergence of gradient descent involves calculating the cost function and observing its decrease over iterations. This ensures the algorithm is progressing towards an optimal solution. Code Implementation: python def gradient_descent_multi(X, y, theta, alpha, iterations): m = len(y) for _ in range(iterations): gradients = (1 / m) * np.dot(X.T, (np.dot(X, theta) - y)) theta = theta - alpha * gradients return theta Practical Insight: In real-world scenarios, such as predicting house prices based on multiple features, gradient descent on multiple variables enables fine-tuning of coefficients, optimizing predictions. Stay tuned for upcoming posts on feature scaling and the art of choosing the right learning rate. sahil yadav & Shubham Bansal #MachineLearning #EfficiencyInML #Vectorization #DataScience #NumPyMagic #OptimizedCode #LinearAlgebra #CodingEfficiency #PythonProgramming #TechInnovation