A lot of data these days is synthetically generated. As an example, to make a model good at understanding assembly you simply need to round-trip code through a compiler and disassembler, then train against the source of truth and the assembly. You can generate arbitrary algebra expressions and have it solve it.
A lot of pretraining is also choosing the right type of data, you don't want to just have it ingest garbage (although I read that some amount of garbage actually helps the model be more robust). Pretraining crystallizes a lot of the inductive biases that post-training builds on, so by crafting the right data mixture you can make it easier for it to start off with a good foundation. There is also a lot of focus on mid-training these days, which I understand is basically either the name for the synthetic data stage, or the SFT phase before all the RL
On the face of it, yes? Emotions are very salient part of text, and as a language model you'd hope that it models them. I think the more surprising finding is that J-space is actually less load bearing than you'd assume, that you can ablate a lot of it and enough of the residual stream structure remains that it still produces coherent text.
That's not to dismiss claims of there being an "inner world" or "conscious experience" (which isn't really a falsifiable claim, the whole p-zombie thing). But purely in terms of _why_ you'd expect J-space to contain those things, given that the j-space is a subspace of the residual stream with coordinates we can interpret, it seems like your priors should be that anything that could help accomplish its pretraining & post-training objectives would be captured in there.
And this also helps provide an explanation of some of their claims they observed. For instance, they way they present J-space ablation seems almost mystical, that ablating j-space suddenly turns a "ensouled" model into a robotic one. But j-space is really just a specific subspace within the residual stream, so ablating j-space is not much different than adding a steering vector. And presumably to ablate j-space they nulled out a lot of those dimensions, which would ikely involve nulling out some of of the concepts related to emotion. So their claim could be rephrased as "injecting a steering vector that removes emotional components, results in the model having a robotic voice".
Is it not possible that the interventions were the cause of the disease? There's a lot about the body we don't understand, if you're mainlining supplements daily and doing blood transfusions on the regular you're messing around with a delicate biochemical balance.
Oh I guess another thing related to all of this, is prior work on steering vectors. "Manipulating the j-space" seems not too different from steering, both ultimately work on the residual stream. I think perhaps it makes more sense to think of J-space as just a coordinate system for the residual stream where each coordinate axis is a vocab direction. Compared to vector steering which was much more naive and had to derive the direction via PCA.
>The “J-space” is not a separate, hidden space. It is an alternative coordinate system for intermediate layer activations. Using a Jacobian between the last layer right before unembedding and the intermediate layer, you can “move” rows of the unembedding matrix (corresponding to distinct tokens) into the space that the intermediate activations live in. So each unembedding row/vector has a corresponding vector in the intermediate activation space this way. They use those vectors to generate coordinates for the same intermediate activations (the “J-lens”). Since each coordinate in this alternative coordinate system is now matched with a token, they can now use it to interpret and manipulate the same intermediate activations
>LLMs think in a subconscious space using tokens
narrative is completely misleading because
>(1) It's a coordinate system. Not a new/separate space.
>(2) Tokens only appear because they specifically built the coordinate system using the unembedding vectors of tokens
There is also a good companion piece by Neel Nanda [1] which answers "Why Jacobians rather than linear regression?" which was another question that came to mind
>J-lens beats a plain logit lens on some architectures and does nothing on others, and it isn't about size
The paper talked about this, the jacobian matrix corrects for the shift in basis from initial to final layer compared to logit lens which assumes that the residual remains in the same basis across layers. Maybe the latter is in fact true for some models/architectures so the J-lens doesn't do anything extra?
>"it's a data stream" I knew the answer was going to be reservoir sampling.
But it's only an approximate percentile. Unless the interviewer mentions that an approximate solution is OK, you would be stuck. (And it's not fair to ask the candidate to ask whether an approximate solution is ok given that almost every problem has an easy "approximate" solution which is not explicitly not what they're looking for).
>Maybe we're somehow treating f(0) = 0 so that you can apply it directly
Hm thinking about it a bit more, I think what's going on is that you treat the baseline of hidden layer L at which you apply the J-lens as 0 activation, then apply the activation on top of that and see what direction your future outputs get skewed towards. Even so, you're still throwing away a constant term f(0) since the "true" logits given by the linear approximation would be Unembed{f(0) + J*h)... but I guess it doesn't matter since by linearity we have Unembed{f(0)} + Unembed{(f(h)}, and the baseline is probably just low-frequency noise (like whitespace or punctuation) which while important for actually predicting a next token matching the ground-truth data distribution, is unimportant for the purposes of interpretability of layer L activation.
And for the connection to logit-lens, as they say the J matrix is really just the change of basis matrix (or at least best linear approximation) from layer L to the final hidden layer, very similar to what you'd use in multivariable integration given change of coordinates. I guess you also need some explanation of why we can expect a linear approximation to hold even well even outside the infinitesimal regime though. I don't know enough here so I asked an LLM and it said that you can argue handwavily via the following chain.
1) Something about stein's lemma saying taking expectation of gradient gives you a global linear best-fit in the OLS sense) (this seems intuitive I guess, even if I don't know the details).
2) Because of the resnet type structure of LLMs which passes through the residual added with some delta (attention + MLP), overall residual stream doesn't undergo any "wild" nonlinearities. So it's plausible that a linear approximation might work. If you think about it, even the "naive" logit lens works fairly well.
3) Semantic meaning is encoded in angle rather than magnitude of vectors (linear representation hypothesis). I'm not sure I fully buy this outside of simple word2vec style embeddings, but assuming it holds for both the intermediary and final layers, then conversion is just a rotation, and even if the magnitudes are off it doesn't matter much for recovering the underlying concept.
Part of the annoying thing is that if you're working on a product which uses LLMs, at some level you run out of levers to pull in terms of being able to fix things. At best you're stacking hacks on top of hacks to prevent unwanted output, but at the end of the day if the LLM really decides it simply doesn't want to follow your instructions, you can't do much other than resign to adding *IMPORTANT* and hoping the next model fixes it.
The experience is much closer to working with an external API that you don't have control over and which simply doesn't do what the documentation says. Those have always been the most frustrating parts of programming, but at least previously you could reverse engineer the actual implementation to work around bugs. You can't even do that now because the "boundary" randomly change every day.
The details seem to be present in the paper (section 2.1). I'm still trying to understand, but it seems instead of computing gradients with respect to cross-entropy loss for the 1-hot "next word" vs output logits, you compute the gradient for the last hidden layer with respect to some middle layer L. This gives you a `hidden x hidden` jacobian matrix, hence the "J-lens". They don't just do this for the last hidden layer of the current token, but the last hidden layers of all subsequent tokens too, and average them. And then repeat for a bunch of documents like in pre-training.
It's still not clear to me intuitively what this represents though. I get that it somehow encodes a link between future words the model says and the current activation, but the confusing thing is that I always think of derivatives and gradients as basically a "sensitivity" between output & input, i.e. if you nudge the input x by h, the output changes by h * f'(x). So then on the face of it applying the J-lens matrix directly to a given activation rather than a small perterbation seems like a "type" issue.
Maybe we're somehow treating f(0) = 0 so that you can apply it directly? Or is there some shift invariance somehow? ignoring that, I do see how it's like selecting a linear combination of the directions, and then it can maybe be represented as "possible continuations" in the same way the gradient is usually thought of as tangent space. Maybe that's what the other commenters meant by information geometric approach.
Other things i'm not clear about is how this is related to two other interprability methods:
* SAE (sparse auto encoder) they showed a few months back, where you train an autoencoder directly off of the hidden states/residual stream to convert it into words. The doc only mentions it briefly, but it seems that j-lens is sensitive to things that SAE are not. They're both working off of the same residual stream so clearly the the inputs must be there, but for some reason SAEs can't detect it while J-lens can (they seem to hint at some explanation but it's over my head)
* Logit lens. This was a more primitive technique that simply applies the unembedding matrix directly to the residual stream. I do like that they mention it:
>The J-lens can be understood as a principled refinement of the logit lens. While the logit lens assumes that representations use the same coordinates in all layers, the Jacobian lens corrects for representational changes that take place across layers, allowing it to uncover meaningful information in earlier layers where the logit lens produces uninterpretable readouts... The J-lens can be understood as the principled correction: J_l is precisely the average linear map that relates layer-l directions to their final-layer counterparts.
Was that ever solved? It seems that entire retort faded overnight, yet to my knowledge there was never any systematic analysis on cause or tokenizer change that fixed it. Maybe we just decided that this failure mode doesn't have any practical bearing given the existence of tool-use?
I wonder how they detect it, is it for known IOCs that they've already found elsewhere, or do they have heuristic detection that flags things that might need further investigation.
in case you don't know, there's back and made by incase. The first manufacturing run completely sold out I think, it's backordered until sep 2026. The matias is... not a good replacement, see https://news.ycombinator.com/item?id=46388976
Isn't that one of the reasons why KL-divergence is used, at least in DPO/RL for LLM? Otherwise the model can effectively cheat and mode collapse. For pre-training against a 1-hot label the KL-divergence should be equivalent to cross-entropy anyway.
> thought for like 20 minutes then just told me it was all "inevitable"
I have in mind an image of ASI as something that's able to seamlessly work across time as if it was weaving cloth. Reasoning about not just first or second order effects, but able to richly play with the nature of causality itself. In the limit, it effects change far into the distant future simply by making only the most minute change in the present then sitting back and waiting for things to play out.
For an AI that can do this, things like "managing subagents" or "context compaction" become child's play. Perhaps we'll know if we're getting close by seeing how well models do at prediction markets.
Would you be better off pooling that money with some hackerspace group and then setting up shared inference infra, so that way you at least get better utilization?
A great variant of the gay jailbreak
https://news.ycombinator.com/item?id=47977134