I'd say llm inference requires both memory capacity and bandwidth. Cerebras provides bandwidth with on-chip SRAM, but not capacity (an entire wafer has only 44GB SRAM).
Indeed, and even if the cost per wafer was 300K, since about say 20-50 wafers are needed, its still 6MM to 15MM for the system. So likely it would appear this is VC subsidized.
I recently came across a critique of the Turing test that seems relevant here. Given the test's limited duration (five minutes in this study) and the constrained rate of human communication, it’s theoretically possible to anticipate every possible human response and prepare prewritten replies in advance. If such a giant lookup table successfully deceives the interrogator most of the time, would we then consider it intelligent?
Thank you for the great discussion. You've put your finger on the right thing I think. We can now dispense with the old VC-type thinking (i.e., that it's because the hypothesis space is not complex enough that we get generalization). Instead now the real question is this: is it the loss landscape itself, or the particular way in which the landscape is searched that leads to good generalization in deep learning.
One can think of perhaps an "exhaustive" search with say God's computer of the loss landscape and pick an arbitrary point among all the points that minimize (or are close to the minimum). Or with our computers we can merely sample. But in both cases, it's hard to see how one would avoid picking "memorization" solutions in the loss landscape. Recall that in an over-parameterized setting, there will be many solutions that have the same low training loss but very different test losses. The reference in my original post [1] shows a nice example with a toy overparameterized linear model (Section 3) where multiple linear models fit the training data but they have very different generalizations. (It also shows why GD ends up picking the better-generalizing solution.)
Now people have argued that the curvature around the solution is a distinguishing factor between well-generalizing solutions and not. Though already now we are moving into the territory of how to sample the space i.e. the specifics of the searching algorithm (a direction you may not like), but even if we press ahead, it's not a satisfactory explanation since in a linear model with L2 loss, the curvature is the same everywhere as Zhang et al. pointed out. So the curvature theories fail for the simplest case already unless one believes that somehow linear models are fundamentally different from deeper and non-linear models.
[1] points out other troubling facts about the curvature explanation (Section 12), but one I like more than the others is the following: As per curvature theories the reason for good generalization at the start of the training process is fundamentally different from the reason from good generalization at the end of the training process. (As always, generalization is just the difference between test and training, and so good generalization is when that difference is small; not necessarily that the test loss is small.) At the start of the GD training process curvature theories would not be applicable (we just picked a random point after all) and so they would hold that we get good (in fact, perfect) generalization because we didn't look at the training data. However, at the end of training, they say we have good generalization because we found a shallow minima. This lack of continuity is disconcerting. In contrast, stability based arguments provide a continuous explanation: the longer you run SGD the less stable it is (so don't run it too long and you'll be fine since you'll achieve an acceptable tradeoff between lowering the loss and overfitting).
Thank you, this makes sense. I am thinking of this as an abstraction/refinement process where an abstract notion of the longer completion is refined into a cogent whole that satisfies the notion of a good completion. I look forward to reading your paper to understand the "backward chaining" aspect and the evidence for it.
Thank you. In my mind, "planning" doesn’t necessarily imply higher-order reasoning but rather some form of search, ideally with backtracking. Of course, architecturally, we know that can’t happen during inference. Your example of the indefinite article is a great illustration of how this illusion of planning might occur. I wonder if anyone at Anthropic could compare the two cases (some sort of minimal/differential analysis) and share their insights.
Yes, and that's the problem. What Zhang et al [2] showed convincingly in the Rethinking paper is that just focusing on the hypothesis space cannot be enough since the same hypothesis space fits real and random data so it's already too large. Therefore, these methods that focus on the hypothesis space have to talk about a bias in practice towards a better subspace, and that already requires studying the specific optimization algorithm in order to understand why it picks certain hypothesis over others in the space.
But once you are ready to do that then algorithmic stability is enough. You don't then need to think about Bayesian ensembles, or other proxies/simplifications etc. but can focus on just the specific learning setup you have. BTW algorithmic stability is not a new idea. An early version showed up within a few years of VC theory in the 80s in order to understand why nearest neighbors generalizes (it wasn't called algorithmic stability then though).
If you are interested in this, also recommend [3].
Agreed, but PAC-Bayes or other descendants of VC theory is probably not the best explanation. The notion of algorithmic stability provides a (much) more compelling explanation. See [1] (particularly Sections 11 and 12)