Fundamentals on Probably Aligned https://probablyaligned.ai/fundamentals/ Recent content in Fundamentals on Probably Aligned Hugo en-us Wed, 09 Apr 2025 00:00:00 +0000 Decision Theory: What an Agent Will Do and Why https://probablyaligned.ai/fundamentals/decision-theory-basics/ Wed, 09 Apr 2025 00:00:00 +0000 https://probablyaligned.ai/fundamentals/decision-theory-basics/ Expected utility, the VNM axioms, risk sensitivity, Newcomb's problem, and instrumental convergence — the decision theory that determines whether your AI is safe. Game Theory: Why Coordination on Safety Is So Hard https://probablyaligned.ai/fundamentals/game-theory-basics/ Wed, 26 Mar 2025 00:00:00 +0000 https://probablyaligned.ai/fundamentals/game-theory-basics/ Nash equilibria, dominant strategies, and mechanism design — building the game theory needed to understand why AI safety suffers from coordination failures, and what it would take to fix them. Why Sparsity, and How Do We Get It? https://probablyaligned.ai/fundamentals/sparsity/ Wed, 12 Mar 2025 00:00:00 +0000 https://probablyaligned.ai/fundamentals/sparsity/ Why sparse representations matter, how training encourages them, and why they're useful for safety. What Is RL, Why Is It So Hard, and How Does It Go Wrong? https://probablyaligned.ai/fundamentals/what-is-rl/ Wed, 26 Feb 2025 00:00:00 +0000 https://probablyaligned.ai/fundamentals/what-is-rl/ Where the neural nets are, what they do for us, why RL is fundamentally harder than supervised learning, and reward hacking vs. misalignment. Loss Functions, Decision Boundaries, Activation Spaces, and Why MSE https://probablyaligned.ai/fundamentals/loss-functions-and-spaces/ Wed, 12 Feb 2025 00:00:00 +0000 https://probablyaligned.ai/fundamentals/loss-functions-and-spaces/ Three views of what a model does, how they differ, which are data-dependent, why mini-batch works, and an intuition for MSE. Linear Algebra Proofs of Optimality for Gradient Descent https://probablyaligned.ai/fundamentals/linear-algebra-optimality/ Tue, 28 Jan 2025 00:00:00 +0000 https://probablyaligned.ai/fundamentals/linear-algebra-optimality/ When and why gradient descent provably finds the best solution — the linear algebra behind it. Gradient Descent, Backpropagation, and the Misconceptions That Tripped Me Up https://probablyaligned.ai/fundamentals/gradient-descent-and-backprop/ Wed, 15 Jan 2025 00:00:00 +0000 https://probablyaligned.ai/fundamentals/gradient-descent-and-backprop/ Building the intuition for why the gradient is steepest descent, what it actually lives in, and how it connects to training neural networks — including the wrong mental models I had to unlearn.