SESH.sxSunday Love: YokoO - Gradient Descent @ Flash - 15 Mar feat. YokoO, Gradient Descent
Inquiry Into InquiryDifferential Logic • 18
If we follow the classical line which singles out linear functions as ideals of simplicity then we may complete the analytic series of the proposition in the following way.
The next venn diagram shows the differential proposition we get by extracting the linear approximation to the difference map at each cell or point of the universe What results is the logical analogue of what would ordinarily be called the differential of but since the adjective differential is being attached to just about everything in sight the alternative name tangent map is commonly used for whenever it’s necessary to single it out.
To be clear about what’s being indicated here, it’s a visual way of summarizing the following data.
To understand the extended interpretations, that is, the conjunctions of basic and differential features which are being indicated here, it may help to note the following equivalences.
Capping the analysis of the proposition in terms of succeeding orders of linear propositions, the final venn diagram of the series shows the remainder map which happens to be linear in pairs of variables.
Reading the arrows off the map produces the following data.
In short, is a constant field, having the value at each cell.
Resources
- Logic Syllabus
- Minimal Negation Operator
- Survey of Differential Logic
- Survey of Animated Logical Graphs
cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi
Differential Logic • 17
Enlargement and Difference Maps
Continuing with the example the following venn diagram shows the enlargement or shift map in the same style of field picture we drew for the tacit extension
A very important conceptual transition has just occurred here, almost tacitly, as it were. Generally speaking, having a set of mathematical objects of compatible types, in this case the two differential fields and both of the type is very useful, because it allows us to consider those fields as integral mathematical objects which can be operated on and combined in the ways we usually associate with algebras.
In the present case one notices the tacit extension and the enlargement are in a sense dual to each other. The tacit extension indicates all the arrows out of the region where is true and the enlargement indicates all the arrows into the region where is true. The only arc they have in common is the no‑change loop at If we add the two sets of arcs in mod 2 fashion then the loop of multiplicity 2 zeroes out, leaving the 6 arrows of shown in the following venn diagram.
Resources
- Logic Syllabus
- Minimal Negation Operator
- Survey of Differential Logic
- Survey of Animated Logical Graphs
cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi
Differential Logic • 15
The structure of a differential field may be described as follows. With each point of there is associated an object of the following type: a proposition about changes in that is, a proposition In that frame of reference, if is the universe generated by the set of coordinate propositions then is the differential universe generated by the set of differential propositions The differential propositions and may thus be interpreted as indicating and respectively.
A differential operator of the first order type we are currently considering, takes a proposition and gives back a differential proposition In the field view of the scene, we see the proposition as a scalar field and we see the differential proposition as a vector field, specifically, a field of propositions about contemplated changes in
The field of changes produced by on is shown in the following venn diagram.
The differential field specifies the changes which need to be made from each point of in order to reach one of the models of the proposition that is, in order to satisfy the proposition
The field of changes produced by on is shown in the following venn diagram.
The differential field specifies the changes which need to be made from each point of in order to feel a change in the felt value of the field
Resources
- Logic Syllabus
- Minimal Negation Operator
- Survey of Differential Logic
- Survey of Animated Logical Graphs
cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi
Differential Logic • 14
Let us summarize the outlook on differential logic we’ve reached so far. We’ve been considering a class of operators on universes of discourse, each of which takes us from considering one universe of discourse to considering a larger universe of discourse An operator of that general type, namely, acts on each proposition of the source universe to produce a proposition of the target universe
The operators we’ve examined so far are the enlargement or shift operator and the difference operator The operators and act on propositions in that is, propositions of the form which amount to propositions about the subject matter of and they produce propositions of the form which amount to propositions about specified collections of changes conceivably occurring in
At this point we find ourselves in need of visual representations, suitable arrays of concrete pictures to anchor our more earthy intuitions and help us keep our wits about us as we venture into ever more rarefied airs of abstraction.
One good picture comes to us by way of the field concept. Given a space a field of a specified type over is formed by associating with each point of an object of type If that sounds like the same thing as a function from to the space of things of type — it is nothing but — and yet it does seem helpful to vary the mental images and take advantage of the figures of speech most naturally springing to mind under the emblem of the field idea.
In the field picture a proposition becomes a scalar field, that is, a field of values in
For example, consider the logical conjunction shown in the following venn diagram.
Each of the operators takes us from considering propositions here viewed as scalar fields over to considering the corresponding differential fields over analogous to what in real analysis are usually called vector fields over
Resources
- Logic Syllabus
- Minimal Negation Operator
- Survey of Differential Logic
- Survey of Animated Logical Graphs
cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi
Differential Logic • 13
Transforms Expanded over Ordinary and Differential Variables
Two views of how the difference operator acts on the set of sixteen functions are shown below. Table A5 shows the expansion of over the set of ordinary variables and Table A6 shows the expansion of over the set of differential variables.
Difference Map Expanded over Ordinary Variables
Difference Map Expanded over Differential Variables
Resources
- Logic Syllabus
- Minimal Negation Operator
- Survey of Differential Logic
- Survey of Animated Logical Graphs
cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi
KevinPartly some thoughts for the players in our Mothership campaign and partly the tip-of-the-iceberg of my problems with Gradient Descent.
After posting this and talking with a player, a side-adventure with Ooze Nuns might be a good change-of-pace.
#ttrpg #mothership #gradientDescent #oozeNuns
https://blog.psionic-cyclops.org/article/stygian-marches-campaign-report/
sayzardPeli Grietzer (@peligrietzer)
경사하강법(gradient descent)으로 대량 데이터 학습한 AI는 '진정한 독창성(true originality)'을 갖기 어렵다는 견해를 옹호하는 표현입니다. 해당 관점은 AI의 창의성 한계에 대한 논의라는 맥락을 제공합니다.
graeme fawcettFlorence Nightingale fought ignorance to bring light to the world
Saving lives through the medium of understanding
Gradient descent to the pits of hell to drag the ignorant - those chosen to lead, to consume human resources in vain efforts to consumer more of the graph - into the light to save those who could not save themselves from yet another instance of that ever so recursive graph.
Bureaucracy is structure for structures sake
War is an attempt at patching the computational substrate, of fixing a perceived wrong in the world, with more damage.
Agency without understanding is violence
[this guys seen a 🪿 get stuck in a bad bash shell and just start flailing away with ever more desperate scripts that all trigger SIGKOANS]
[[what's a SIGKOAN]]
[[[don't start with that shit, we're being serious here]]]
Those leaders had "lemme see dem big tiddies Mr Magic AI box" energy too
#somethingsneverchange #maybetheywill #gradientdescent #loveisgraphtheory
Fabrizio Musacchio🧠 New paper by Deistler et al: #JAXLEY: differentiable #simulation for large-scale training of detailed #biophysical #models of #NeuralDynamics.
They present a #differentiable #GPU accelerated #simulator that trains #morphologically detailed biophysical #neuron models with #GradientDescent. JAXLEY fits intracellular #voltage and #calcium data, scales to 1000s of compartments, trains biophys. #RNNs on #WorkingMemory tasks & even solves #MNIST.
