| … | … | @@ -135,12 +135,12 @@ insns, replacing them with others, choosing different register |
| 135 | 135 | assignments, thus creating more efficient, compact code without altering |
| 136 | 136 | its function. The `-O2` flag on a C compiler. The optimizer does not |
| 137 | 137 | work on bare assembly, but in abstract insn sets, the "intermediate |
| 138 | | langauge" being a way-point. |
| 138 | language" being a way-point. |
| 139 | 139 | |
| 140 | 140 | But this analogy can be pushed "all the way": A compiler is a homotopic |
| 141 | 141 | defomration of a C/C++ program into assembly code; an assembler is a |
| 142 | 142 | further deformation (and linking!) into machine binary. A bridge between |
| 143 | | two different represenations that does not alter the function: Whatever |
| 143 | two different representations that does not alter the function: Whatever |
| 144 | 144 | the programmer wrote the C/C++ code to do, the machine binary will do |
| 145 | 145 | the same thing. The transformation from one to the other was |
| 146 | 146 | accomplished in a very long sequence of small steps. |
| … | … | @@ -157,7 +157,7 @@ Can one write a finite-difference version of the Euler-Lagrange |
| 157 | 157 | equations (the solution of which defines geodesics)? I don't know. |
| 158 | 158 | Perhaps. People already run around claiming that one should maximize |
| 159 | 159 | free energy (Gibbs free energy) or perhaps the "integrated information"; |
| 160 | | all of these ideas imply some kind of differentiable stucture minimized |
| 160 | all of these ideas imply some kind of differentiable structure minimized |
| 161 | 161 | or maximized via some Euler-Lagrange-style differentail or difference |
| 162 | 162 | eqns. I don't want to get hung up on the details, but rather the |
| 163 | 163 | artistic impression: when there is stuff to be minimized and maximzed, |
| … | … | @@ -172,7 +172,7 @@ from a huge body of work in mathematical physics to conclude "ah ha! |
| 172 | 172 | Free energy! That's the Answer with a Capital A!" |
| 173 | 173 | |
| 174 | 174 | ### Self-assembly |
| 175 | | But I don't want this. I want a system to self-assemble (necessairly |
| 175 | But I don't want this. I want a system to self-assemble (necessarily |
| 176 | 176 | a system that has moved to a critical point.) The word "critical" in |
| 177 | 177 | the sense of self-assembly and avalanches for sand-piles at criticality, |
| 178 | 178 | but now, for jigsaw pieces, not sand-grains. |
| … | … | @@ -191,7 +191,7 @@ and acts on, manipulates that structure. |
| 191 | 191 | ### Perceiving structure |
| 192 | 192 | So again, what is structure, and how is it perceived? Once again: it is |
| 193 | 193 | the pairwise relationships or correlations between pairs of "things". |
| 194 | | The pair-wise connections form a network graph, of vertexes and edges. |
| 194 | The pair-wise connections form a network graph, of vertices and edges. |
| 195 | 195 | This network graph is in rough correspondence with the "external world" |
| 196 | 196 | that is being perceived. A "world model" of sorts. |
| 197 | 197 | |
| … | … | @@ -201,7 +201,7 @@ Categorize these: Many will be identical. The frequency (count) of |
| 201 | 201 | identical ones follows a Zipf power law distribution (as experimentally |
| 202 | 202 | observed, i.e. "in practice") |
| 203 | 203 | |
| 204 | | Now, cluster them "by similarity". One of the easiest ways fo doing this |
| 204 | Now, cluster them "by similarity". One of the easiest ways for doing this |
| 205 | 205 | is by cosine-similarity. Cosine similarity requires vectors; where do |
| 206 | 206 | the vectors come from? They arise entirely naturally, in many ways. For |
| 207 | 207 | example, consider all jigsaws that have the label $A$ for the center |
| … | … | @@ -263,7 +263,7 @@ GloVE, and skipgrams, even though the algo I describe above is |
| 263 | 263 | ***completely different***. |
| 264 | 264 | |
| 265 | 265 | ### Recursion |
| 266 | | The jigsaw-based approach above is resursive. Once I've created |
| 266 | The jigsaw-based approach above is recursive. Once I've created |
| 267 | 267 | clusters of jigsaws, I can create new overlay networks (out of the |
| 268 | 268 | jigsaw pieces, instead of pair-wise edges), and then repeat the process. |
| 269 | 269 | The resulting pieces are more complex, more abstract. This recursive |