Differentiable Systems

Systems that are "differentiable":

• Can have performance or quality attributed to specific components, so that those components can be improved
• Components have literal measures of quality so that progress in their quality is measurable
• You can infer impact from one component onto others

OLD! "Kernel" Discussion

What's a kernel?

• General: fundamental, irreducible core
• Operating systems: core program that mediates access to hardware
• Machine learning: a mapping from the domain space to an easily separable space
• Linear algebra: the set of vectors that a matrix maps to zero

There is something tempting in this - to characterize a kernel as a mapping between domains or problem spaces. This is explicit in ML, but abstracted (or embedded in the domain) for software. In software, kernels mediate access to shared resources, and map the real constraints and interfaces of the hardware into a simpler interface and interaction model for applications and services.

Zooming out a little, it is satisfying to imagine a complete application through this lens. For example, let's take Amazon retail: the incredible amounts of code that make it up are mappings of fractal-complex business situations and needs into interfaces that enable specific capabilities. At the highest level, this is turning the "purchase click" into a box on your doorstep. Breaking this down, its the sub components of the problem: checking that the item is still in stock, charging the card, routing delivery, etc.

Individually this might not be too exciting. This is already explicit in ML, and a small hop from the "abstraction" concept already fundamental in software. I think the utility might be in the unification or synthesis - that we can consider different things (like

• Tension between general "fundamental core" definition and ML "useful mapping" definition?
• The simpler your subspace, the simpler your kernel can be
  • Example: library code vs application code
• What does "kernel of truth" mean? More similar to the math "maps to zero" definition? Neurons that fire together?