Plus his GitHub. The recently released nanochat https://github.com/karpathy/nanochat is fantastic. Having minimal, understandable and complete examples like that is invaluable for anyone who really wants to understand this stuff.
> Yesterday I was browsing for a Deep Q Learning implementation in TensorFlow (to see how others deal with computing the numpy equivalent of Q[:, a], where a is an integer vector — turns out this trivial operation is not supported in TF). Anyway, I searched “dqn tensorflow”, clicked the first link, and found the core code. Here is an excerpt:
Notice how it's "browse" and "search" not just "I asked chatgpt". Notice how it made him notice a bug
Secondly, the article is from 2016, ChatGPT didn’t exist back then
He's just test driving LLMs, nothing more.
Nobody's asking this core question in podcasts. "How much and how exactly are you using LLMs in your daily flow?"
I'm guessing it's like actors not wanting to watch their own movies.
He's doing a capability check in this video (for the general audience, which is good of course), not attacking a hard problem in ML domain.
Despite this tweet: https://x.com/karpathy/status/1964020416139448359 , I've never seen him citing an LLM helped him out in ML work.
> I think congrats again to OpenAI for cooking with GPT-5 Pro. This is the third time I've struggled on something complex/gnarly for an hour on and off with CC, then 5 Pro goes off for 10 minutes and comes back with code that works out of the box. I had CC read the 5 Pro version and it wrote up 2 paragraphs admiring it (very wholesome). If you're not giving it your hardest problems you're probably missing out.
Later I understood that they don’t need to understand LLMs, and they don’t care how they work. Rather they need to believe and buy into them.
They’re more interested in science fiction discussions — how would we organize a society where all work is done by intelligent machines — than what kinds of tasks are LLMs good at today and why.
And the issue you mention in the last paragraph is very relevant, since the scenario is plausible, so it is something we definitely should be discussing.
Imagine if you were using single layer perceptrons without understanding seperability and going "just a few more tweaks and it will approximate XOR!"
There are things that you just can’t expect from current LLMs that people routinely expect from them.
They start out projects with those expectations. And that’s fine. But they don’t always learn from the outcomes of those projects.
The question here is whether the details are important for the major issues, or whether they can be abstracted away with a vague understanding. To what extent abstracting away is okay depends greatly on the individual case. Abstractions can work over a large area or for a long time, but then suddenly collapse and fail.
The calculator, which has always delivered sufficiently accurate results, can produce nonsense when one approaches the limits of its numerical representation or combines numbers with very different levels of precision. This can be seen, for example, when one rearranges commutative operations; due to rounding problems, it suddenly delivers completely different results.
The 2008 financial crisis was based, among other things, on models that treated certain market risks as independent of one another. Risk could then be spread by splitting and recombining portfolios. However, this only worked as long as the interdependence of the different portfolios was actually quite small. An entire industry, with the exception of a few astute individuals, had abstracted away this interdependence, acted on this basis, and ultimately failed.
As individuals, however, we are completely dependent on these abstractions. Our entire lives are permeated by things whose functioning we simply have to rely on without truly understanding them. Ultimately, it is the nature of modern, specialized societies that this process continues and becomes even more differentiated.
But somewhere there should be people who work at the limits of detailed abstractions and are concerned with researching and evaluating the real complexity hidden behind them, and thus correcting the abstraction if necessary, sending this new knowledge upstream.
The role of an expert is to operate with less abstraction and more detail in her oder his field of expertise than a non-expert -- and the more so, the better an expert she or he is.
I understand how SGD is just taking a step proportional to the gradient and how backprop computes the partial derivative of the loss function with respect to each model weight.
But with more advanced optimizers the gradient is not really used directly. It gets per weight normalization, fudged with momentum, clipped, etc.
So really, how important is computing the exact gradient using calculus, vs just knowing the general direction to step? Would that be cheaper to calculate than full derivatives?
Why would these things be "fudging"? Vanishing gradients (see the initial batch norm paper) are a real thing, and ensuring that the relative magnitudes are in some sense "smooth" between layers allows for an easier optimization problem.
> So really, how important is computing the exact gradient using calculus, vs just knowing the general direction to step? Would that be cheaper to calculate than full derivatives?
Very. In high dimensional space, small steps can move you extremely far from a proper solution. See adversarial examples.
Yes, absolutely -- a lot of ideas inspired by this have been explored in the field of optimization, and also in machine learning. The very idea of "stochastic" gradient descent using mini-batches basically a cheap (hardware compatible) approximation to the gradient for each step.
For a relatively extreme example of how we might circumvent the computational effort of backprop, see Direct Feedback Alignment: https://towardsdatascience.com/feedback-alignment-methods-7e...
Ben Recht has an interesting survey of how various learning algorithms used in reinforcement learning relate with techniques in optimization (and how they each play with the gradient in different ways): https://people.eecs.berkeley.edu/~brecht/l2c-icml2018/ (there's nothing special about RL... as far as optimization is concerned, the concepts work the same even when all the data is given up front rather than generated on-the-fly based on interactions with the environment)
How do you propose calculating the "general direction" ?
And, an example "advanced optimizer" - AdamW - absolutely uses gradients. It just does more, but not less.
> how important is computing the exact gradient using calculus
Normally the gradient is computed with a small "minibatch" of examples, meaning that on average over many steps the true gradient is followed, but each step individually never moves exacty along the true gradient. This noisy walk is actually quite beneficial for the final performance of the network https://arxiv.org/abs/2006.15081 , https://arxiv.org/abs/1609.04836 so much so that people started wondering what is the best way to "corrupt" this approximate gradient even more to improve performance https://arxiv.org/abs/2202.02831 (and many other works relating to SGD noise)
> vs just knowing the general direction to step
I can't find relevant papers now, but I seem to recall that the Hessian eigenvalues of the loss function decay rather quickly, which means that taking a step in most directions will not change the loss very much. That is to say, you have to know which direction to go quite precisely for an SGD-like method to work. People have been trying to visualize the loss and trajectory taken during optimization https://arxiv.org/pdf/1712.09913 , https://losslandscape.com/
Non-stochastic gradient descent has to optimize over the full dataset. This doesn't matter for non-machine learning applications, because often there is no such thing as a dataset in the first place and the objective has a small fixed size. The gradient here is exact.
With stochastic gradient descent you're turning gradient descent into an online algorithm, where you process a finite subset of the dataset at a time. Obviously the gradient is no longer exact, you still have to calculate it though.
Seems like "exactness" is not that useful of a property for optimization. Also, I can't stress it enough, but calculating first order derivatives is so cheap there is no need to bother. It's roughly 2x the cost of evaluating the function in the first place.
It's second order derivatives that you want to approximate using first order derivatives. That's how BFGS and Gauss-Newton work.
9 years ago, 365 points, 101 comments
I told everyone this was the best single exercise of the whole year for me. It aligns with the kind of activity that I benefit immensely but won't do by myself, so this push was just perfect.
If you are teaching, please consider this kind of assignments.
P.S. Just checked now and it's still in the syllabus :)
I made a UI that showed how the weights and biases changed throughout the training iterations.
I really hate what Twitter did to blogging…
Diving through the abstraction reveals some of those.
You've also missed the point of the article, if you're building novel model architectures you can't magic away the leakiness. You need to understand the back prop behaviours of the building blocks you use to achieve a good training run. Ignore these and what could be a good model architecture with some tweaks will either entirely fail to train or produce disappointing results.
Perhaps you're working at a level of bolting pre built models together or training existing architectures on new datasets but this course operates below that level to teach you how things actually work.
> As a developer, you just pick the best one and find good hparams for it
It would be more correct to say: "As a developer, (not researcher), whose main goal is to get a good model working — just pick a proven architecture, hyperparameters, and training loop for it."
Because just picking the best optimizer isn't enough. Some of the issues in the article come from the model design, e.g. sigmoids, relu, RNNs. And some of the issues need to be addressed in the training loop, e.g. gradient clipping isn't enabled by default in most DL frameworks.
And it should be noted that the article is addressing people on the academic / research side, who would benefit from a deeper understanding.
Back propagation is reverse mode auto differentiation. They are the same thing.
And for those who don't understand what back propagation is, it is just an efficient method to calculate the gradient for all parameters.
def clipped_error(x):
return tf.select(tf.abs(x) < 1.0,
0.5 * tf.square(x),
tf.abs(x) - 0.5) # condition, true, false
joshdavham•4h ago
It's a bit snarky of me, but whenever I see some web developer or product person with a strong opinion about AI and its future, I like to ask "but can you at least tell me how gradient descent works?"
I'd like to see a future where more developers have a basic understanding of ML even if they never go on to do much of it. I think we would all benefit from being a bit more ML-literate.
kojoru•3h ago
joshdavham•3h ago
For example, I believe that if we were to ask the average developer about why LLM's behave randomly, they would not be able to answer. This to me exposes a fundamental hole in their knowledge of AI. Obviously one shouldn't feel bad about not knowing the answer, but I think we'd benefit from understanding the basic mathematical and statistical underpinnings on these things.
Al-Khwarizmi•23m ago
All you need is:
- Basic understanding of how a Markov chain can generate text (generating each word using corpus statistics on the previous few words).
- Understanding that you can then replace the Markov chain with a neural model which gives you more context length and more flexibility (words are now in a continuous space so you don't need to find literally the same words, you can exploit synonyms, similarity, etc., plus massive training data also helps).
- Finally, you add the instruction tuning (among all the plausible continuations the model could choose, teach it to prefer the ones human prefer - e.g. answering a question rather than continuing with a list of similar questions. You give the model cookies or slaps so it learns to prefer the answers humans prefer).
- But the core is still like in the Markov chain (generating each word using corpus statistics on the previous words).
I often give dissemination talks on LLMs to the general public and I have the feeling that with this mental model, you can basically know everything a lay user needs to know about how they work (you can explain things like hallucinations, stochastic nature, relevance of training data, relevance of instruction tuning, dispelling myths like "they always choose the most likely word", etc.) without any calculus at all; although of course this is subjective and maybe some people will think that explaining it in this way is heresy.
lock1•3h ago
Plus, I don't think a "gotcha" question like "what is gradient descent" will give you a good signal about someone if it get popularized. It probably will lead to the present-day OOP cargo cult, where everyone just memorizes whatever their lecturer/bootcamp/etc and repeats it to you without actually understanding what it does, why it's the preferred method over other strategies, etc.
joshdavham•38m ago
We could also say AI-literate too, I suppose. I guess I just like to focus on ML generally because 1) most modern AI is possible only due to ML and 2) it’s more narrow and emphasizes the low level of how AI works.
confirmmesenpai•2h ago
augment_me•2h ago
There is no need for the knowledge that you propose in a world where this is solved, you will achieve more goals by utilizing higher-level tools.
joshdavham•34m ago