The central idea of this paper is "A continually self-improving AI is one that, once created, can autonomously and continually improve itself better than its human creators can improve it." (P1) Continues acquiring knowledge into weights without forgetting (P2) Generates its own training signal - learning from it beats human-generated signals (P3) Can autonomously design … Continue reading Towards Continually Self-Improving AI by Zitong Yang Stanford Dissertation

If you follow textbook, you would have learned Lagrangian then Dirac Equation, but in real history, it was other way around. Paul Dirac Combine quantum mechanics with special relativity and Fix problems with the Klein–Gordon equation: Only afterward did physicists realized that this equation can come from a Lagrangian and proved it. Another interesting thing … Continue reading From Dirac to Langrangian

What is OpenClaw? It's a self-hosted personal AI assistant gateway - it not only runs on your own machine, but also connects Claude to any messaging platform (WhatsApp, Telegram, Slack, iMessage, Discord, etc.), and gives it tools (browser, canvas, memory, cron, sessions). Full Repo Hierarchy openclaw/├── src/ # Gateway source (82 dirs, 35 files)│ ├── … Continue reading Quick Study of OpenClaw Repo

Kaparthy's autoresearch is a scientific method encoded as agent instructions. The agent is a ML trainer/researcher running overnight experiments on a GPU - modifying train.py, running 5-minute training runs, logging results, keeping improvements, reverting failures. Both GSD and Autoresearch aims to have the agents to automatically get a complex coding task done, The elegance of … Continue reading Kaparthy’s Autoresearch Github

GSD(get the shit done) is an autonomous AI agent CLI that runs multi-phase software projects end-to-end. The tagline: "One command. Walk away. Come back to a built project." Its key innovation is Each task gets a fresh context window so the context doesn't degrade over a long run. It creates and maintains four files: state.md, … Continue reading Review of gsd-build/gsd-2

We hear perturbation in QFT a lot, but what is it? It's Perturbing the free (non-interacting) theory by turning on interactions. The Lagrangian density of two fields consist the free part and interaction part. The latter, full interacting theory is generally impossible to solve exactly. So Treat the interaction, i.e. the time evolution / amplitudes … Continue reading Perturbation in QFT

According to Born’s rule, the probability is obtained from the square of the wavefunction. More generally, this is written as the product of the complex conjugate of the wavefunction and the wavefunction itself, ψ∗ψor(𝜓ˉ𝜓)ψ ∗ ψ or( 𝜓 ˉ 𝜓 ) to ensure the probability density is real and non-negative. Now focus on the Dirac … Continue reading Need Dirac Adjoint to Describe 1/2 Spinor’s Lorentz Transformation

It's originally invented by Green to solve difficult PDE problems, let's reduce it to simple matrix form first Now let's solve a real, simple PDE problem: If we increase the number of grid points: The formula turns into Green's function A Green's function is literally the inverse of a differential operator, just like: A−1

In history, Dirac derived Dirac Equation by combining Quantum Mechanics and Special Relativity, led the equation, Later: Lagrangian is constructed to reproduce the equation In this post, Let’s derive the Dirac equation from the Dirac Lagrangian step-by-step using the Euler–Lagrange equation.

Noether's theorem states that For every continuous symmetry of the action, there is a corresponding conserved quantity. Continuous symmetry → a transformation that can be done smoothly, not discrete. Action → integral of the Lagrangian over time. SymmetryConserved quantityTime translation (Lagrangian doesn’t depend explicitly on time)EnergySpace translation (Lagrangian doesn’t depend on position)MomentumRotational symmetry (Lagrangian doesn’t … Continue reading Conservation of Charge