13 posts found
For continuous stationary positive-definite kernels, Bochner’s theorem turns kernel design into a choice of spectral measure. We derive random Fourier features, connect positional rotations to frequency, and explain where the bridge to attention and spectral transformers needs extra assumptions.
A practical guide to Fourier transforms, spectral bias, and choosing a useful representation: why audio and images need different spectral tools, how Fourier features change learning, and where FFT mixing helps or loses information.
A practitioner-level synthesis of twelve weeks of tutorials through one lens — spectral bias, Fourier features, FFT-based token mixing, Bochner's theorem, and neural operators — showing that positional encodings, kernels, state-space models and diffusion schedules are the same idea in different clothes.
A practical framework for building self-play curricula without mistaking reward hacking, forgetting, or correlated self-grading for genuine capability gains.
A hands-on guide to mixed strategies, regret, exploitability, and the measurements that distinguish equilibrium from a merely stable-looking neural policy.
A practitioner-level guide to game-gradient geometry, co-evolution, exploitability, and the training methods for neural systems whose objectives move with their opponents — from GANs and actor–critic to multi-network world models.
A practitioner's tour of how an agent turns a doubtful model into a decision: model-predictive control and why replanning every step is the robustness, CEM and random shooting as the planners world-model papers actually run, planning through a posterior instead of a point estimate, and expected free energy with the sign convention stated the right way round.
Calibrated confidence is a permission slip — this week we spend it. From PILCO's 17.5 seconds of robot experience to V-JEPA 2 planning zero-shot on a Franka arm, we trace how uncertainty becomes action. Then we look at the 2026 result that breaks the arc's own thesis: a world model can be locally well-calibrated and globally, confidently wrong.
A beginner-friendly tour of neuro-symbolic AI: why neural networks perceive brilliantly but can't guarantee anything, why symbolic engines reason perfectly but can't see, and how the field is finally joining the two — with calibrated confidence as the glue at the seam.
Neural networks perceive fluently but hallucinate confidently; symbolic engines reason reliably but shatter on noisy inputs. This week we join the two — and argue the hinge that makes the join work is the calibrated uncertainty we built last week. From Tensor Logic's single equation to confidence-gated inference, here is how AI reasons about what it sees.
3D Gaussian Splatting gives us a single best-fit scene — but no sense of where that geometry is trustworthy. This week we turn point-estimate splats into distributions over geometry, connecting Bayesian rendering, Fisher information, and diffusion priors back to last week's GP framework.
Why AI systems that express calibrated uncertainty are safer and more useful — covering overconfident models, epistemic vs aleatoric uncertainty, and calibration metrics including ECE and reliability diagrams.
How scaled dot-product attention is secretly Nadaraya–Watson kernel regression — and what that reveals about the GP–Transformer duality, the Deep GP revival, and why uncertainty is the missing ingredient for world models.