12 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 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.
Highlights of AI News for July 13 - 19 2026
A beginner-friendly tour of Bayesian 3D reconstruction: why an ordinary 3D scan gives one confident answer everywhere, how turning geometry into a distribution produces honest confidence maps, and where the 'prior' that fills in unseen regions comes from.
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.
Highlights of AI News for July 6 - 12 2026
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.
A step-by-step introduction to Gaussian Processes — what they are, how kernel functions define them, how to do GP regression, and how Deep GPs extend them to multi-layer architectures.
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.