“I wanted to review the definitions of specific operations, so I summarized them.”

“はじめに ディープラーニングの実装をしているとベクトル微分とかを頻繁に目にしますが、具体的な演算の定義を改めて確認したいなと思い、まとめてみました。”

“なるほど、これは パターソン復号法における「エラー値の計算」で微分が現れる理由 を、関数論・有限体上の留数 の観点から説明するという話ですね。”

“I'm looking for resources to study the following: -statistics and probability -calculus (for applications like optimization, gradients, and understanding models) ... I don't want to study the entire math courses, just what is necessary for AI/ML.”

“The paper derives an exact identity for overdamped Langevin dynamics that equates the total EP rate to the mutual-information rate.”

“The resulting formulation is based on a 4D Hodge-Laplacian operator with a spatiotemporal diffusion tensor and convection field, augmented by a small temporal perturbation to ensure nondegeneracy.”

“DeepSeek-V3 has the best performance in all three categories... All three LLMs exhibited notably weak performance in Geometry.”

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“Schrödinger AI demonstrates: (a) emergent semantic manifolds that reflect human-conceived class relations without explicit supervision; (b) dynamic reasoning that adapts to changing environments, including maze navigation with real-time potential-field perturbations; and (c) exact operator generalization on modular arithmetic tasks, where the system learns group actions and composes them across sequences far beyond training length.”

“The paper likely provides a detailed mathematical treatment of the intersection of cylinders.”

“Python is a must. Around 70–80% of AI ML job postings expect solid Python skills, so there is no way around it.”

“The conformable derivative is not a fractional operator but a useful computational tool for systems with power-law time scaling, equivalent to classical differentiation under a nonlinear time reparametrization.”

“An application to a system of $(k,ρ)$-fractional Hilfer integral equations via a measure of noncompactness.”

“Based on the prompt, there is no subordinate information to quote from.”

“”

“The paper investigates the nth-Level Prabhakar Type Fractional Derivative.”

“The context refers to a boundary value problem involving the Prabhakar fractional derivative.”

“TensoriaCalc is a user-friendly tensor calculus package for the Wolfram Language.”

“The study focuses on fractional-order modeling for nonlinear soft actuators via Particle Swarm Optimization.”

“”

“Think of it like this: Physics found its language in calculus. Circuit design found its language in Boolean logic. Pedro argues that AI has been missing its language - until now.”

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“To make safe and effective use of artificial intelligence, we need to understand its profound capabilities and limitations, the clues to which lie in the math that makes machine learning possible.”

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“”

“The article's presence on Hacker News suggests it was considered informative to a technical audience.”

“The article likely discusses the mathematical principles that form the foundation of deep learning algorithms.”

“”

“The article is sourced from Hacker News.”

“The source is Hacker News.”

“The article likely discusses matrix calculus.”

“The article's key fact cannot be determined without the content.”

“”

“Backpropagation is the key algorithm that makes training deep models computationally tractable.”