linear_combinatori_probabi

hope you won't get shocked by the ping like I did, as always.

@Jakobian what are you learning?

Hi, I need an expert for my question on NFA: math.stackexchange.com/q/4928500/390226. Cannot figure this out :(

Could someone who knows about NFA help me with this question? math.stackexchange.com/q/4924750/390226. It's about the implication of transition functions' value being an empty set. The thread has become a bit long, and I (unfortunately) suspect that the existing (only) answer hasn't resolved my confusion.

@robjohn Hi sorry for direct tagging, if you have time could you help me with a simple(?) problem I asked yesterday but I didn't get an answer: chat.stackexchange.com/transcript/message/63837804#63837804. The context is some lines above the linked comment cus I made a typo in my formula.

So it just stated as a lemma that $T(i)$ is decreasing function and the proof is just one-liner: by observation from the definition of $T(i)$. Lol

indeed a good question, and as you said these are just objects so without a context it's hard to reason about. apologies for this.

the other way, it's $T(0) > T(n)$. The ML context is that we're doing backward propagation.

exactly.

I used to like math seriously then realized that I'm really bad at math so now I'm doing computer science and realize... it is still about math, lol.

Yes :) I know Ted he helped me a lot years ago. (I also subscribed to his lectures on YouTube, but that's off-topic :P)

but yes, when I said I want to prove that $T(i)$ is a decreasing function I do mean: $T(i)$ decreases when $i$ increases. (not saying you didn't get it, just want to put emphasis on this)

The formula is the definition of $T(i)$. The calculation is done reversely. The base case is $T(n)$, and finally it will reach $T(0)$ and that's the answer.

But from my current understanding, the formula itself depends on zero knowledge of ML. There is no hidden relation between $T(i),d_i,d_s,g_k$. Except for the function $T(i)$, all these variables can be thought of as just some positive integers from a log file.

We can assume that $d_i = g_i$ (let me omit the context), and for simplicity we can assume that $d_i$ are all small integers like $1<d_i<100$. $T(i)$ is a function for the calculation of memory usage. Thanks for your reply anyway.

my bad eyes typing these formulas with a small font size.

there should be a $d_s$ inside the parentheses of the only summation.

Lol, you're right I made a typo

my apologies that this formula might not be well-defined (I'm not the one who first wrote it) and you might have questions like "what is $d_i, g_k$" all I can say is that this is a formula from Machine Learning and $d,g$ mean data, gradient respectively. I cannot provide more details.

What I want to do is that I want to prove that $T(i)$ is a decreasing function. (those $d_i, g_k$, given any $i,k$ are all positive integers.)

$$ T(i)=\min_{i<j<n}( \max{(d_i+T(j))}, \max_{k}{((\sum_{s=i}^{k})+g_k+g_{k+1}} )) $$

Now define a function $T(i)$ as follow:

Given two positive variables $i,j$, and $i < j < n$, where $n$ is a fixed positive integer.

Here is the description of my problem:

I'm not the author of the math formula so forgiving me that in some cases it might not be well-defined.

Hi, could anyone help me with some simple math formulas?

paper books make me calm

I read pdfs but I enjoy read textbook, two different worlds

I once forked a Repo. on GitHub about pdfs and received an email, saying that I (and those other users that forked it) are violating some laws

because they're exp as fu*k

I once obsessed in choosing calculus text book like choosing a laptop

I'm so dumb

So instead I gave up choosing laptop and spent about $80 buying introduction to algorithm 4ed. I'm so smart

set = sad

I remember that set theory made me upset

Choosing either brand and/or hardware specs doesn't help in calculating my combinatorics problems lol

Sorry for hijacking the thread, but I just want to say that my disability in making decisions just helped me saving money on choosing a new laptop. I go with my old PC :)

and realized that I cannot eat all of it

with extra noodle

I bought some noodles for dinner

Hi

It's called "Box of Chinese chives"(word by word translated) in my country.

Momo so good to eat

hola

The paper is about reducing GPU memory by recomputing some of the intermediate results (between layers)

I'm reading Alg.2. I don't understand how it work, especially the line nested in the double-for-loop: a[v] = new node [...]

arxiv.org/pdf/1604.06174.pdf

It's OK. The pseudo-code is from a paper

@Mithical Hi, could you help me understanding a piece of pseudo-code related to deep learning?