How Random are the Digits of π? State of the Art & Free Book on the Topic
Over the last 10 years, I spent a lot of time analyzing the digits of the classic math constants such as π, e, log 2, √2 and so on. Not testing them for randomness but trying to formally prove that they are undistinguishable from random bit streams. And trying to identify which constants are the […]
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Checking for Randomness: Replacing Test Batteries with a Single Test
In cybersecurity applications where replicability is critical, or when building pseudo-random number generators, it is typical to perform a large number of various tests to check if a sequence of bits is random enough for practical purposes. This is also true in scientific research, to assess whether or not the digits of π or other […]
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New Book: No-Blackbox, Secure, Efficient AI and xLLM Solutions
Large language models and modern AI is often presented as technology that needs deep neural networks (DNNs) with billions of Blackbox parameters, expensive and time consuming training, along with GPU farms, yet prone to hallucinations. This book presents alternatives that rely on explainable AI, featuring new algorithms based on radically different technology with trustworthy, auditable, […]
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How to Build and Optimize High-Performance Deep Neural Networks from Scratch
With explainable AI, intuitive parameters easy to fine-tune, versatile, robust, fast to train, without any library other than Numpy. In short, you have full control over all components, allowing for deep customization, and much fewer parameters than in standard architectures. Introduction I explore deep neural networks (DNNs) starting from the foundations, introducing a new type […]
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Watermarking and Forensics for AI Models, Data, and Deep Neural Networks
In my previous paper posted here, I explained how I built a new class of non-standard deep neural networks, with various case studies based on synthetic data and open-source code, covering problems such as noise filtering, high-dimensional curve fitting, and predictive analytics. One of the models featured a promising universal function able to represent any […]
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How Synthetic Primes Reveal the Quantum States in the Riemann Hypothesis
This research paper showcases spectacular discoveries across multiple disciplines. The main question — yet unanswered — is how the mathematical engineering behind the scenes could be applied to modern AI, deep neural networks (DNNs) and LLMs in particular, to dramatically accelerate the convergence of some slow algorithms. Most notoriously, the laborious and expensive training attached […]
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10 Tips to Boost Performance of your AI Models
These model enhancements techniques apply to deep neural networks (DNNs) used in AI. The focus is on the core engine that powers all DNNs: gradient descent, layering and loss function. Reparameterization — Typically, in DNNs, many different parameter sets lead to the same optimum: loss minimization. DNN models are non-identifiable. This redundancy is a strength that […]
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A New Type of Non-Standard High Performance DNN with Remarkable Stability
I explore deep neural networks (DNNs) starting from the foundations, introducing a new type of architecture, as much different from machine learning than it is from traditional AI. The original adaptive loss function introduced here for the first time, leads to spectacular performance improvements via a mechanism called equalization. To accurately approximate any response, rather […]
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New Book: 0 and 1 – From Elemental Math to Quantum AI
The book is available on our E-store, here. It all started with the number 1. This e-book offers a trip deep into the most elusive and fascinating multi-century old conjecture in number theory: are the binary digits of the fundamental math constants evenly distributed? No one even knows if the proportions of ‘0’ and ‘1’ […]
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Doing Better with Less: LLM 2.0 for Enterprise
Standard LLMs are trained to predict the next tokens or missing tokens. It requires deep neural networks (DNN) with billions or even trillions of tokens, as highlighted by Jensen Huang, CEO of Nvidia, in his keynote talk at the GTC conference earlier this year. Yet, 10 trillion tokens cover all possible string combinations; the vast […]
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