Explorations in Innovative Science

In this personal experiment, I explored a novel neural network design built on the idea of using a scalar magnitude-based activation — effectively replacing conventional nonlinear functions like ReLU or sigmoid with a simple identity function ( y = x ), such that  x is computed as a vector magnitude. The input projection is transformed using this formula: x = || Σ aᵢ · i · eᵢ || = sqrt(Σ (aᵢ · i)²) Where: aᵢ are learned scalar weights per feature i is the positional index of each input eᵢ is the basis vector Despite the simplicity, this architecture not only solves the linearly separable OR gate problem, but also successfully learns the non-linearly separable XOR gate — a common benchmark used to evaluate the expressiveness of neural networks. To be confirmed by future experiments, hypothetically, scaling the z-score with sqrt(1/n) per feature is effective for normalizing the sum of squared values and maintaining balanced feature contributions in ...

Welcome to my personal blog where I explore AI, symbolic regression, activation functions, and stock modeling — sometimes with a poetic twist. Discovery Journey: Auto-Generated Activation Functions Using Genetic Programming - [ A 3-part experiments exploration of evolving and applying custom activation functions ] Market Analysis & Forecasting Projects - 📊 [ Bayesian Gaussian Mixture Modeling for Stock Price Transformation & Prediction ] - 📉 [ Gaussian-Based Stock Price Smoothing & Band Calculation ] - 🧭 [ Stock Analysis: Resistance Levels & Forecasting with Meta Prophet ] Thought Experiments & Reflections - ✍️ [ Born of Silence, Moved by Thought ] - 🧬 [ A Glimpse into a Probable Marriage of Tiny Scale and Macro Grasp of Science V2 ] 🛡️ All notebooks, results, and ideas are shared under **CC BY-NC 4.0**.   Attribution required. No commercial use without permission. > *If you found something inspiring or useful, feel free to explore further or connec...

⚠️ Disclaimer (Please Read First) This blog post presents a personal, exploratory experiment using publicly available tools and datasets (e.g., Tatoeba, DEAP, Hugging Face Transformers). It is not a lab-verified study, and results have not undergone peer review or formal statistical validation. The findings, interpretations, and conclusions shared here are based on limited-scale experiments using Google Colab and consumer-level hardware. They are intended for educational and exploratory purposes only. There is no guarantee on the accuracy, stability, or reproducibility of the experimental results. Any interpretations or applications are entirely at the reader’s discretion. Readers are encouraged to replicate, adapt, or challenge the outcomes in more rigorous or production-grade environments. We often tweak our models by adjusting the data, trying new optimizers, or changing the architecture—but how often d...

Born of Silence, Moved by Thought A poetic reflection on existence, evolution, and the quiet questions we carry. We came with breath, but not with map, No whisper told us why and how. A body moves, a mind that pokes— Yet all is given, none avow. We eat, we sleep, we laugh, we cry, The heartbeats count, never know why. Whose hands designed our eyes and minds, If plans were made, likely ’d been told, No draft to sign, no path to trace. Trial and error in time and space, Halfway through, we would never know. Some say God—a sculptor kind— Shaped the clay and breathed the spark. Others claim the stars collided, And life arose within the dust. Some sought a script, a random seed, To mimic logic in life-form's code. But runs fell short by countless years— Too few were born for what hearts behold. Perhaps the path was not all chance, But shaped by truths we’ve yet to yield— A quiet rhythm underneath, Unknown, yet ever in the known. Who placed the co...

  Date :May 21, 2025 Over the past week(s), I’ve embarked on an intensive experimental journey combining genetic programming (DEAP) with neural network activation function design . The result? A utility that evolves custom activation functions capable of outperforming standard choices like ReLU, Swish, or GELU under certain conditions. This post serves both as a personal milestone and a timestamped record of this research. 🔍 Project Overview Using DEAP (Distributed Evolutionary Algorithms in Python), I constructed an evolutionary search space made up of elementary mathematical primitives and safe variants of functions like log , sqrt , and divide . The system: Evolves TensorFlow-compatible activation expressions Benchmarks them in a real model loop (e.g. CNN-based classifier) Reports performance via loss, runtime, and memory usage Filters out invalid or exploding functions during evolution 🧠 Notable Results One evolved function recently outperformed sta...

A Glimpse into a Probable Marriage of Tiny Scale and Macro Grasp of Science 🌀 A Glimpse into a Probable Marriage of Tiny Scale and Macro Grasp of Science A personal exploration in symbolic regression, physics, and philosophical debugging 👋 Prologue Let’s face it — most of us don't wake up thinking, “Today I will blend Planck’s constant and relativistic energy into a genetic programming experiment!” But that’s more or less what happened. With a little help from DEAP, some physics constants, and a lot of coffee, I wandered into an unusual, possibly meaningful direction. This post describes an attempt to let symbolic regression guess at a connection between two physics equations — one from the quantum world, and one from Einstein’s playbook. 💡 The Idea We were curious: if two major energy equations — one from quantum physics and one from relativity — both describe energy, could a symbolic re...

Stock Price Prediction Using Bayesian Gaussian Mixture Model (BGMM) In this guide, we explore the Bayesian Gaussian Mixture Model (BGMM) and its application in transforming stock price data and generating numerical predictions . This method leverages historical stock data from Yahoo Finance , applies data transformation techniques , and fits a BGMM model to uncover hidden patterns in stock movements and make data-driven market forecasts . The following example is presented in pseudo-code format , allowing for easy adaptation into any programming language. With modern Large Language Models (LLMs) like ChatGPT, Gemini, and DeepSeek R1 , converting pseudo-code into a fully functional stock prediction script has never been simpler. 1️⃣ Fetching and Transforming Stock Data Before applying statistical modeling , we first retrieve and transform historical stock price data. FUNCTION fetch_transformed_stock_data(symbol, start_date, end_date) TRY / / Download stock dat...