Create training episodes offline

[tkarab]

• [x] alter TaskGenerator so that there is a different function for generating task keys and different for gettting data based off of these keys
• [x] New generator class for generating data only, and saving them into csv (2 min for 640000 5way5shot tasks)
• [x] Mode in Data Generator for reading keys from csv and reshaping them
• [x] Time it
• [x] function for getting task keys from tubular csv read file
• [x] time both operations and check if creating episodes beforehand is quicker
• [x] create and save tasks with starting indices in them as well
• [x] remove TaskGeneratorKeysOnly
• [x] time and save examples of the process into OneNote
• [x] function for reading the csv and extracting tasks in TaskGenerator using either pandas or csv
• [x] #48

Create tasks with support set/query set data and not just keys

• [ ] array where there are Nxk + 1 data segments per line
• [ ] create an array of 64*10000 such entries
• [ ] add new data_intake mode to task generator
• [ ] change other functions if needed
• [ ] add shuffle function in task generator
• [ ] test if 10000 batches are enough and results are good

[tkarab]

To clarify the total number of possible tasks in our training set construction with 40 subjects, 49 gestures, 4 reps, and 5 categories of 5 samples for the support set:

1. Choosing 5 Gestures (Categories) from 49:

   • Number of ways to choose 5 gestures from 49: $\binom{49}{5} = \frac{49!}{5!(49-5)!} = 1906884$ Given that one of the categories will be chosen as the query category, this means that there are $\binom{N}{1} = 1$ possible query categories to be chosen for a given set of N categories of a task. This leaves us with $N\times\binom{g}{N}$ possible combinations of N chosen gestures and one query of those N. In our case $5\times\binom{49}{5} = 9534420$ combinations of tasks

2. Choosing 5 Samples per Category (for Support Set):

   • For each chosen gesture ( g ), there are 160 possible subject-rep (s, r) combinations: $40 \text{ (subjects)} \times 4 \text{ (reps)} = 160$

   • Number of ways to choose 5 samples from 160 for the support set: $\binom{160}{5} = \frac{160!}{5!(160-5)!} = 820384032$

3. Choosing 1 Query Sample from One of the Support Set Categories:

   • For the gesture category used for the query, we need to choose 6 samples from 160 (5 for support set and 1 for query): $\binom{160}{6} = \frac{160!}{6!(160-6)!} = 2.12\times10^{10}$

Total Possible Tasks

For each quintet of gestures, the possible configurations are:

• 4 categories each with $\binom{160}{5}$ combinations for the support set.
• 1 category with $\binom{160}{6}$ combinations (5 for the support set and 1 for the query).

Thus, for each quintet of gestures: $\binom{160}{5}^4 \times \binom{160}{6}$

Given $5\times\binom{49}{5}\$ possible quintets of gestures: $5\times\binom{49}{5} \times\binom{160}{5}^4 \times \binom{160}{6}$

Conclusion

The total number of possible tasks, given our constraints, is: $5\times\binom{49}{5} \times\binom{160}{5}^4 \times \binom{160}{6} = 9.15\times10^{52}$ total tasks for Experiment 1

If we account for segmentation of the images, given that each task is made up of $N \times k + 1$ images where each one is segmented into ~55 samples, that should give us $(total tasks)\times55^{N \times k+1} = 3.25\times10^{97}$ possible combinations of tasks

[tkarab]

General formula for number of possible task configurations for a given experiment

Suppose :

• s total subjects
• g total gestures
• r total reps per gesture
• N classes per task
• k samples per task class
• 1 query gesture per task, belongs to one of the N classes of that task

Experiments 1, 2b, 3

The number of possible N-tuples of gestures chosen from the total g available is $\binom{g}{N} = \frac{g!}{N!(g-N)!}$ Given that one of the N chosen classes will also be chosen as the query one that gives us $\binom{N}{1} = N$ possible query classes per chosen N-tuple therefore resulting in $N\times\binom{g}{N}$ possible N-tuples,query gesture that comprise the task

For a given set of N classes, chosen query class there $s\_r = s\times r$ possible combinations of subject, rep for a given gesture number. There are N classes and for N-1 of those we need to chose k (s,r) pairs of the s_r available and from the query one we shall choose k+1. Thie leads us to:

• $\binom{s\_r }{k}$ possible combinations of samples for N-1 of the chosen classes
• $\binom{s\_r}{k+1}$ combinations for the chosen query class

Thus resulting in: $\binom{s\_r}{k}^{N-1}\times\binom{s\_r}{k+1}$ total combinations over all classes for a given N-tuple of categories and a chosen query category.

For all possible N-tuples this will result in: $N\times\binom{g}{N}\times\binom{s\_r}{k}^{N-1}\times\binom{s\_r}{k+1}$ possible tasks for these experiments

Experiment 2a

Again the number of possible N-tuples of classes (+a chosen query class) is $N\times\binom{g}{N}$ This time for a given set of N classes, the samples are all chosen from the same subject. Therefore, for a given subject, for each class of the support set we need to choose k of the available r repetitions (g,s are constant). This is a total of $\binom{r}{k}$ possible combinatins of k samples per class for the non-query classes. For the query one the number will be $\binom{r}{k+1}$. This means that there are:

• $\binom{r}{k}$ possible combinations of samples for the N-1 non-query classes
• $\binom{r}{k+1}$ combinations of sample keys for the query class

In total: $\binom{r}{k}^{N-1} \times\binom{r}{k+1}$ possible tasks for given subject number, N-tiple of classes and query class. Given that any of the s subjects could be randomly chosen for a task this means that the total available tasks for a set of N classes are $s\times\binom{r}{k}^{N-1} \times\binom{r}{k+1}$

For all possible N-tuples this will result in: $N \times \binom{g}{N} \times s \times\binom{r}{k}^{N-1} \times \binom{r}{k+1}$ possible tasks for experiment 2a