Big

lecture 2
introduction to
data types,
functions,
and barcode detection

hard memorising (no)
vs
understanding (yes)
pattern recognition as an example...

another key is "explanation in simple words only"
the Feynman Technique (check it out)

disclaimer: complex words are VERY important for communication

noodling time:
these ideas are numerically embedded in AI training technique as well... 🫣
aka "overfitting" and "regularisation"
we'll see

how we learn AI reflects in how AI learn (us)
breaking the fourth wall!🤯

avoid categorical thinking
things are more connected than they look like

this lecture we will go through more high-level abstract ideas as well as little low-level technical stuff
dots will be connected!
more applications starting next week😜

(human) intelligence:
- pattern recognition 🌌
- pattern generation 🦄
- task solving, story telling, emotions, etc.

artificial intelligence:
- nice tool to have 🔨 (engineering)
- for better understanding intelligence 🧬 (natural science)

representation:
- inevitable (our natural language falls short)
- powerful (good ones simplify recognition tasks)

representation:
- descriptive, "features"
- contextual, task-dependent
- perspective, always partial

numbers:
- strong representational power (for different data modalities)
- introducing the tool called math as our DAMAIN EXPANSION
- used with "protocol" (for consistent interpretation)

models:
- when using a model for the first time, ask about its input and output
- usually its input and output are numbers, then ask about the "protocol"

face recognition as an example:
- input: image (any size)
- output: bounding boxes and landmark locations (in numbers)

numerical/quantitative
- discrete (count)
- continuous (measure)
exceptions may apply

numerical
- Usually discrete values occurs as the result of counting something
- and continuous values occurs as the result of measuring something
but exceptions may apply
- 🌶️ can you think of an exception case where the data comes from measuring but is of discrete type?

categorical/qualitative
- ordinal (categories with an implied order)
- nominal (named category, no order implied)
exceptions may apply

lets appreciate this vinyl under microscope for 10 seconds
vid here

don't confuse data types with data categories/modalities
(data category/modality is looking from the perspective of "where do the data come from") more on this in the future
(data type is from "what are the characteristics of the numbers in the data" )

a function is a relationship between inputs where each input is related to exactly one output

but why this weird construct of "input, process, output"? where else can you find this pattern?

two perspectives of thinking:
mapping: captures relation between input and output (laser beams)
transformation: operation on the input (like folding a paper), transform it into the output and spit out the output ("dynamic" process)

these two are connected actually... avoid categorical thinking...
for fancy AI stuff (starting next week yay), i find the "transformation" perspective more helpful for understanding

input: x
function body: some maths operations on x
function output: f(x)
domain: the set of all possible inputs
f(x) = 2x (draw on whiteboard)

me "小" as a function:
🍎 -> 小 -> lecture
小(🍎) = lecture

you "lovelyStudents" as a function:
lecture -> lovelyStudents -> good sleep 💤
lovelyStudents(lecture)= good sleep 💤

we can chain functions together!
lovelyStudents(小(🍎))= good sleep 💤
recall models as a set of functions

good old face location detection model as f:
f(image) = bounding box
(expand into numeric representations on whiteboard)

notice the dimension of the output is different from the input
there has to be some parts inside the function that reduce (or expand) dimensions
we have a nice maths tool to manipulate dimensionality, more on this next week 😜

draw on whiteboard...are we familiar with this graphic representation of functions?

to use a function:
like a model, we feed in the input, get an output and do whatever

our first time touching upon tool making:
to make a function working, we want to "shape"/"tune" the function so that it captures the right transformation

I'll leave how to shape a function to next lecture (the "learning" process)
for now, let's look at what parts of function can be shaped (the affordance)

let's think graphically...
task: i have these points on whiteboard and i want to have a function go through each of these (weaving)

our skeleton are sort of fixed and serve as our scaffold,
to achieve different physical tasks,
we train our muscles (skeleton are untrainable ;( )

important things from this analogy are:
- some parts are fixed and untrainable
- other parts are trainable

scaffold of function(the fixed): its type
muscles of function(the shapeable/trainable/learnable): its parameters

parameters: all the parts in a function that are "shapeable" once the type is fixed

wait but why do we fix the type of function if there are better options???
it is not that we want to but we have to... (more on this later)
basically it is constrained by how learning process is currently interpreted and implemented in mathematics (hint: derivatives)

usually during model making, we have to choose the scaffold of function first and it will remain fixed.
we might also want to reshape our skeleton if we can 🥶

firstly, we define the funcion type, could be a combination of any type.
ways of combination could be adding, chaining, multiplying, etc.
recall model as a set of functions

in deep learning terms, these "shapeable" parameters comprise weights and biases

till now we only have used one type of function for weaving,
to increase the "expressiveness" of our selected function type,
we can go "overshoot" by including different functin types as one big function to be shaped,

expressiveness: it has potential to be shaped into different kinds of shapes

weights can be zero
overshoot big function can always be reduced to simple ones
deep learning is also based on the idea of starting with a (BIG) function that has great expressiveness

these notions will become clearer (dots being connected) in the future lecture

take home message:
- scaffold and muscle
- the task of weaving
- function types have different shapes
- overshoot using big function to increase expressiveness

- asymptotic (quite philosophical, it touches the notion of infinity)
- squash anything to be between 0 and 1 (remember probability?😉)
- symmetric (things can go wrong in many directions...)
- ignore negative(booo) numbers
- periodic (wooo, aperiodic signal can be represented by periodic stuff only)

🤯
underneath these functions of different personalities,
they all have the same "DNA" (polynomials)
they can all be represented just using polynomials and here is an example

In the artwork Pareidolia* facial detection is applied to grains of sand. A fully automated robot search engine examines the grains of sand in situ. When the machine finds a face in one of the grains, the portrait is recorded.

image refs:
https://impuria.com/blogs/impuria-ear-piercing-jewelry/least-to-most-painful-ear-piercings-a-comprehensive-ranking