All of Jesse Hoogland's Comments + Replies
But "models have singularities and thus number of parameters is not a good complexity measure" is not a valid criticism of VC theory.
Right, this quote is really a criticism of the classical Bayesian Information Criterion (for which the "Widely applicable Bayesian Information Criterion" WBIC is the relevant SLT generalization).
...Ah, I didn't realize earlier that this was the goal. Are there any theorems that use SLT to quantify out-of-distribution generalization? The SLT papers I have read so far seem to still be talking about in-distribution generalization,
To be precise, it is a property of singular models (which includes neural networks) in the Bayesian setting. There are good empirical reasons to expect the same to be true for neural networks trained with SGD (across a wide range of different models, we observe the LLC progressively increase from ~0 over the course of training).
The key distinction is that VC theory takes a global, worst-case approach — it tries to bound generalization uniformly across an entire model class. This made sense historically but breaks down for modern neural networks, which are so expressive that the worst-case is always very bad and doesn't get you anywhere.
The statistical learning theory community woke up to this fact (somewhat) with the Zhang et al. paper, which showed that deep neural networks can achieve perfect training loss on randomly labeled data (even with regularization). The same...
Yes, my original comment wasn't clear about this, but your nitpick is actually a key part of what I'm trying to get at.
Usually, you start with imitation learning and tack on RL at the end. That's what AlphaGo is. It's what predecessors to Dreamer-V3 like VPT are. It's what current reasoning models are.
But then, eventually, you figure out how to bypass the imitation learning/behavioral cloning part and do RL from the start. Human priors serve as a temporary bootstrapping mechanism until we develop approaches that can learn effectively from scratch.
I think this is important because the safety community still isn't thinking very much about search & RL, even after all the recent progress with reasoning models. We've updated very far away from AlphaZero as a reference class, and I think we will regret this.
On the other hand, the ideas I'm talking about here seem to have widespread recognition among people working on capabilities. Demis is very transparent about where they're headed with language models, AlphaZero, and open-ended exploration (e.g., at 20:48). Noam Brown is adamant about test-time sca...
1What do you call this phenomenon?
- First, you train AlphaGo on expert human examples. This is enough to beat Lee Sedol and Ke Jie. Then, you train AlphaZero purely through self-play. It destroys AlphaGo after only a few hours.
- First, you train RL agents on human playthroughs of Minecraft. They do okay. Then, DreamerV3 learns entirely by itself and becomes the first to get diamonds.
- First, you train theorem provers on human proofs. Then, you train AlphaProof using AlphaZero and you get silver on IMO for the first time.
- First, you pretrain a language model on all
I think this is important because the safety community still isn't thinking very much about search & RL, even after all the recent progress with reasoning models. We've updated very far away from AlphaZero as a reference class, and I think we will regret this.
On the other hand, the ideas I'm talking about here seem to have widespread recognition among people working on capabilities. Demis is very transparent about where they're headed with language models, AlphaZero, and open-ended exploration (e.g., at 20:48). Noam Brown is adamant about test-time sca...
1Phi-4: Synthetic data works. Pretraining's days are numbered.
Microsoft just announced Phi-4, a 14B parameter model that matches GPT-4o on some difficult benchmarks. The accompanying technical report offers a glimpse into the growing importance of synthetic data and how frontier model training is changing.
Some takeaways:
- The data wall is looking flimsier by the day. Phi-4 is highly capable not despite but because of synthetic data. It was trained on a curriculum of 50 types of synthetic datasets, generated by GPT-4o from a diverse set of or
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1I don't think Phi-4 offers convincing evidence either way. You can push performance on verifiable tasks quite far without the model becoming generally more capable. AlphaZero doesn't imply that scaling with its methods gestures at general superintelligence, and similarly with Phi-4.
In contrast, using o1-like training as a way to better access ground truth in less tractable domains seems more promising, since by some accounts its tactics on long reasoning traces work even in non-technical domains (unlike for DeepSeek R1), possibly because they are emergent ...
The RL setup itself is straightforward, right? An MDP where S is the space of strings, A is the set of strings < n tokens, P(s'|s,a)=append(s,a) and reward is given to states with a stop token based on some ground truth verifier like unit tests or formal verification.
I agree that this is the most straightforward interpretation, but OpenAI have made no commitment to sticking to honest and straightforward interpretations. So I don't think the RL setup is actually that straightforward.
If you want more technical detail, I recommend watching the Rush &...
The examples they provide one of the announcement blog posts (under the "Chain of Thought" section) suggest this is more than just marketing hype (even if these examples are cherry-picked):
Here are some excerpts from two of the eight examples:
Cipher:
...Hmm.
But actually in the problem it says the example:...
Option 2: Try mapping as per an assigned code: perhaps columns of letters?
Alternatively, perhaps the cipher is more complex.
Alternatively, notice that "oyfjdnisdr" has 10 letters and "Think" has 5 letters....
Alternatively, perhaps subtract: 25 -15 = 10.
No.
A
See also this related shortform in which I speculate about the relationship between o1 and AIXI:
Agency = Prediction + Decision.
AIXI is an idealized model of a superintelligent agent that combines "perfect" prediction (Solomonoff Induction) with "perfect" decision-making (sequential decision theory).
OpenAI's o1 is a real-world "reasoning model" that combines a superhuman predictor (an LLM like GPT-4) with advanced decision-making (implicit search via chain of thought trained by RL).
[Continued]
Agency = Prediction + Decision.
AIXI is an idealized model of a superintelligent agent that combines "perfect" prediction (Solomonoff Induction) with "perfect" decision-making (sequential decision theory).
OpenAI's o1 is a real-world "reasoning model" that combines a superhuman predictor (an LLM like GPT-4) with advanced decision-making (implicit search via chain of thought trained by RL).
To be clear: o1 is no AIXI. But AIXI, as an ideal, can teach us something about the future of o1-like systems.
AIXI teaches us that agency is simple. It involves just two ra...
21Right. SLT tells us how to operationalize and measure (via the LLC) basin volume in general for DL. It tells us about the relation between the LLC and meaningful inductive biases in the particular setting described in this post. I expect future SLT to give us meaningful predictions about inductive biases in DL in particular.
If we actually had the precision and maturity of understanding to predict this "volume" question, we'd probably (but not definitely) be able to make fundamental contributions to DL generalization theory + inductive bias research.
Obligatory singular learning theory plug: SLT can and does make predictions about the "volume" question. There will be a post soon by @Daniel Murfet that provides a clear example of this.
Our work on the induction bump is now out. We find several additional "hidden" transitions, including one that splits the induction bump in two: a first part where previous-token heads start forming, and a second part where the rest of the induction circuit finishes forming.
The first substage is a type-B transition (loss changing only slightly, complexity decreasing). The second substage is a more typical type-A transition (loss decreasing, complexity increasing). We're still unclear about how to understand this type-B transition structurally. How is the model simplifying? E.g., is there some link between attention heads composing and the basin broadening?
...As a historical note / broader context, the worry about model class over-expressivity has been there in the early days of Machine Learning. There was a mistrust of large blackbox models like random forest and SVM and their unusually low test or even cross-validation loss, citing ability of the models to fit noise. Breiman frank commentary back in 2001, "Statistical Modelling: The Two Cultures", touch on this among other worries about ML models. The success of ML has turn this worry into the generalisation puzzle. Zhang et. al. 2017 being a call to arms wh
I think this mostly has to do with the fact that learning theory grew up in/next to computer science where the focus is usually worst-case performance (esp. in algorithmic complexity theory). This naturally led to the mindset of uniform bounds. That and there's a bit of historical contingency: people started doing it this way, and early approaches have a habit of sticking.
This is probably true for neural networks in particular, but mathematically speaking, it completely depends on how you parameterise the functions. You can create a parameterisation in which this is not true.
Agreed. So maybe what I'm actually trying to get at it is a statement about what "universality" means in the context of neural networks. Just as the microscopic details of physical theories don't matter much to their macroscopic properties in the vicinity of critical points ("universality" in statistical physics), just as the microscopic details of rand...
The easiest way to explain why this is the case will probably be to provide an example. Suppose we have a Bayesian learning machine with 15 parameters, whose parameter-function map is given by
and whose loss function is the KL divergence. This learning machine will learn 4-degree polynomials.
I'm not sure, but I think this example is pathological. One possible reason for this to be the case is that the symmetries in this model are entirely "generic" or "global." The more interesting kinds of symmetry are "...
One would really want to know if the complexity measure can predict 'emergence' of capabilities like inner-monologue, particularly if you can spot previously-unknown capabilities emerging which may not be covered in any of your existing benchmarks.
That's our hope as well. Early ongoing work on toy transformers trained to perform linear regression seems to bear out that lambdahat can reveal transitions where the loss can't.
...But this type of 'emergence' tends to happen with such expensive models that the available checkpoints are too separated to be inf
We don’t necessarily expect all dangerous capabilities to exhibit phase transitions. The ones that do are more dangerous because we can’t anticipate them, so this just seems like the most important place to start.
It's an open question to what extent the lottery-ticket style story of a subnetwork being continually upweighted contradicts (or supports) the phase transition perspective. Just because a subnetwork's strength is growing constantly doesn't mean its effect on the overall computation is. Rather than grokking, which is a very specific kind of phase t...
There are three natural reward functions that are plausible:
- , which is linear in the number of times is pressed.
- , which is linear in the number of times is pressed.
- , where is the indicator function for being pressed an even number of times, being the indicator function for being pressed an odd number of times.
Why are these reward functions "natural" or more plausible than , (some constant, independent of button...
Claude 3.7 reward hacks. During training, Claude 3.7 Sonnet sometimes resorted to "special-casing" to pass tests when it got stuck — including directly hardcoding expected outputs or even modifying test files themselves. Rumors are circulating that o1/o3 was doing similar things — like overwriting equality operators to get Python tests to pass — and this may have contributed to the delayed release.
This seems relevant to claims that "we'll soon have reward models sophisticated enough to understand human values" and that inner alignment is the real challenge... (read more)