Implicitly, SAEs are trying to model activations across a context window, shaped like (n_ctx, n_emb). But today's SAEs ignore the token axis, modeling such activations as lists of n_ctx IID samples from a distribution over n_emb-dim vectors.

I suspect SAEs could be much better (at reconstruction, sparsity and feature interpretability) if they didn't make this modeling choice -- for instance by "looking back" at earlier tokens using causal attention.

Assorted arguments to this effect:

• There is probably a lot of compressible redundancy in LLM activations across the token axis, because most ways of combining textual features (given any intuitive notion of "textual feature") across successive tokens are either very unlikely under the data distribution, or actually impossible.
  • For example, you're never going to see a feature that means "we're in the middle of a lengthy monolingual English passage" at position j and then a feature that means "we're in the middle of a lengthy monolingual Chinese passage" at position j+1. 
  • In other words, the intrinsic dimensionality of window activations is probably a lot less than n_ctx * n_emb, but SAEs don't exploit this.
• [Another phrasing of the previous point.] Imagine that someone handed you a dataset of (n_ctx, n_emb)-shaped matrices, without telling you where they're from.  (But in fact they're LLM activations, the same ones we train SAEs on.). And they said "OK, your task is to autoencode these things."
  • I think you would quickly notice, just by doing exploratory data analysis, that the data has a ton of structure along the first axis: the rows of each matrix are very much not independent.  And you'd design your autoencoder around this fact.
  • Now someone else comes to you and says "hey look at my cool autoencoder for this problem. It's actually just an autoencoder for individual rows, and then I autoencode a matrix by applying it separately to the rows one by one."
  • This would seem bizarre -- you'd want to ask this person what the heck they were thinking.
  • But this is what today's SAEs do.
• We want features that "make sense," "are interpretable." In general, such features will be properties of regions of text (phrases, sentences, passages, or the whole text at once) rather than individual tokens.
  • Intuitively, such a feature is equally present at every position within the region.  An SAE has to pay a high L1 cost to activate the feature over and over at all those positions.
  • This could lead to an unnatural bias to capture features that are relatively localized, and not capture those that are less localized.
  • Or, less-localized features might be captured but with "spurious localization":
    • Conceptually, the feature is equally "true" of the whole region at once.
    • At some positions in the region, the balance between L1/reconstruction tips in favor of reconstruction, so the feature is active.
    • At other positions, the balance tips in favor of L1, and the feature is turned off.
    • To the interpreter, this looks like a feature that has a clear meaning at the whole-region level, yet flips on and off in a confusing and seemingly arbitrary pattern within the region.
  • The "spurious localization" story feels like a plausible explanation for the way current SAE features look.
    • Often if you look at the most-activating cases, there is some obvious property shared by the entire texts you are seeing, but the pattern of feature activation within each text is totally mysterious.  Many of the features in the Anthropic Sonnet paper look like this to me.
    • Descriptions of SAE features typically round this off to a nice-sounding description at the whole-text level, ignoring the uninterpretable pattern over time.  You're being sold an "AI agency feature" (or whatever), but what you actually get is a "feature that activates at seemingly random positions in AI-agency-related texts."
• An SAE that could "look back" at earlier positions might be able to avoid paying "more than one token's worth of L1" for a region-level feature, and this might have a very nice interpretation as "diffing" the text.
  • I'm imagining that a very non-localized (intuitive) feature, such as "this text is in English," would be active just once at the first position where the property it's about becomes clearly true.
    • Ideally, at later positions, the SAE encoder would look back at earlier activations and suppress this feature here because it's "already been accounted for," thus saving some L1.
    • And the decoder would also look back (possibly reusing the same attention output or something) and treat the feature as though it had been active here (in the sense that "active here" would mean in today's SAEs), thus preserving reconstruction quality.
  • In this contextual SAE, the features now express only what is new or unpredictable-in-advance at the current position: a "diff" relative to all the features at earlier positions.
    • For example, if the language switches from English to Cantonese, we'd have one or more feature activations that "turn off" English and "turn on" Cantonese, at the position where the switch first becomes evident.
    • But within the contiguous, monolingual regions, the language would be implicit in the features at the most recent position where such a "language flag" was set.  All the language-flag-setting features would be free to turn off inside these regions, freeing up L0/L1 room for stuff we don't already know about the text.
  • This seems like it would allow for vastly higher sparsity at any given level of reconstruction quality -- and also better interpretability at any given level of sparsity, because we don't have the "spurious localization" problem.
  • (I don't have any specific architecture for this in mind, though I've gestured towards one above.  It's of course possible that this might just not work, or would be very tricky.  One danger is that the added expressivity might make your autoencoder "too powerful," with opaque/polysemantic/etc. calculations chained across positions that recapitulate in miniature the original problem of interpreting models with attention; it may or may not be tough to avoid this in practice.)
• At any point before the last attention layer, LLM activations at individual positions are free to be "ambiguous" when taken out of context, in the sense that the same vector might mean different things in two different windows.  The LLM can always disambiguate them as needed with attention, later.
  • This is meant as a counter to the following argument: "activations at individual positions are the right unit of analysis, because they are what the LLM internals can directly access (read off linearly, etc.)"
  • If we're using a notion of "what the LLM can directly access" which (taken literally) implies that it can't "directly access" other positions, that seems way too limiting -- we're effectively pretending the LLM is a bigram model.

I do a lot of "mundane utility" work with chat LLMs in my job^[1], and I find there is a disconnect between the pain points that are most obstructive to me and the kinds of problems that frontier LLM providers are solving with new releases.

I would pay a premium for an LLM API that was better tailored to my needs, even if the LLM was behind the frontier in terms of raw intelligence.  Raw intelligence is rarely the limiting factor on what I am trying to do.  I am not asking for anything especially sophisticated, merely something very specific, which I need to be done exactly as specified.

It is demoralizing to watch the new releases come out, one after the next.  The field is overcrowded with near-duplicate copies of the same very specific thing, the frontier "chat" LLM, modeled closely on ChatGPT (or perhaps I should say modeled closely on Anthropic's HHH Assistant concept, since that came first).  If you want this exact thing, you have many choices -- more than you could ever need.  But if its failure modes are problematic for you, you're out of luck.

Some of the things I would pay a premium for:

• Tuning that "bakes in" the idea that you are going to want to use CoT in places where it is obviously appropriate.  The model does not jump to conclusions; it does not assert something in sentence #1 and then justify it in sentences #2 through #6; it moves systematically from narrow claims to broader ones.  This really ought to happen automatically, but failing that, maybe some "CoT mode" that can be reliably triggered with a special string of words.
  • Getting chat LLMs to do 0-shot CoT is still (!) kind of a crapshoot.  It's ridiculous.  I shouldn't have to spend hours figuring out the magic phrasing that will make your model do the thing that you know I want, that everyone always wants, that your own "prompting guide" tells me I should want.
• Really good instruction-following, including CoT-like reviewing and regurgitation of instruction text as needed.
  • Giving complex instructions to chat LLMs is still a crapshoot.  Often what one gets is a sort of random mixture of "actually following the damn instructions" and "doing something that sounds, out of context, like a prototypical 'good' response from an HHH Assistant -- even though in context it is not 'helpful' because it flagrantly conflicts with the instructions."
  • "Smarter" chat LLMs are admittedly better at this than their weaker peers, but they are still strikingly bad at it, given how easy instruction-following seems in principle, and how capable they are at various things that seem more difficult.
  • It's 2024, the whole selling point of these things is that you write verbal instructions and they follow them, and yet I have become resigned to the idea that they will just ignore half of my instructions half of the time.  Something is wrong with this picture!
• Quantified uncertainty.  Some (reliable) way of reporting how confident they are about a given answer, and/or how likely it is that they will be able to perform a given task, and/or similar things.
  • Anthropic published some promising early work on this back in mid-2022, the P(IK) thing.  When I first read that paper, I was expecting something like that to get turned into a product fairly soon.  Yet it's mid-2024, and still nothing, from any LLM provider.
• A more humanlike capacity to write/think in an exploratory, tentative manner without immediately trusting what they've just said as gospel truth.  And the closely related capacity to look back at something they've written and think "hmm, actually no, that argument didn't work," and then try something else.  A certain quality of looseness, of "slack," of noncommittal just-trying-things-out, which is absolutely required for truly reliable reasoning and which is notably absent in today's "chat" models.
  • I think this stuff is inherently kind of hard for LLMs, even ignoring the distortions introduced by instruction/chat tuning.  LLMs are trained mostly on texts that capture the final products of human thought, without spelling out all the messy intermediate steps, all the failed attempts and doubling back on oneself and realizing one isn't making any sense and so on.  That tends to stay inside one's head, if one is a human.
  • But, precisely because this is hard for LLMs (and so doesn't come for free with better language modeling, or comes very slowly relative to other capabilities), it ought to be attacked as a research problem unto itself.

I get the sense that much of this is downstream from the tension between the needs of "chat users" -- people who are talking to these systems as chatbots, turn by turn -- and the needs of people like me who are writing applications or data processing pipelines or whatever.

People like me are not "chatting" with the LLM.  We don't care about its personality or tone, or about "harmlessness" (typically we want to avoid refusals completely).  We don't mind verbosity, except insofar as it increases cost and latency (very often there is literally no one reading the text of the responses, except for a machine that extracts little pieces of them and ignores the rest).

But we do care about the LLM's ability to perform fundamentally easy but "oddly shaped" and extremely specific business tasks.  We need it to do such tasks reliably, in a setting where there is no option to write customized follow-up messages to clarify and explain things when it fails.  We also care a lot about cost and latency, because we're operating at scale; it is painful to have to spend tokens on few-shot examples when I just know the model could 0-shot the task in principle, and no, I can't just switch to the most powerful available model the way all the chat users do, those costs really add up, yes GPT-4-insert-latest-suffix-here is much cheaper than GPT-4 at launch but no, it is still not worth the extra money at scale, not for many things at least.

It seems like what happened was:

• The runaway success of ChatGPT caused a lot of investment in optimizing inference for ChatGPT-like models
• As a result, no matter what you want to do with an LLM, a ChatGPT-like model is the most cost-effective option
• Social dynamics caused all providers "in the game" to converge around this kind of model -- everyone wants to prove that, yes, they are "in the game," meaning they have to compare their model to the competition in an apples-to-apples manner, meaning they have to build the same kind of thing that the competition has built
• It's mid-2024, there are a huge number of variants of the Anthropic HHH Assistant bot with many different options at each of several price/performance points, and absolutely nothing else
• It turns out the Anthropic HHH Assistant bot is not ideal for a lot of use cases, there would be tremendous value in building better models for those use cases, but no one (?) is doing this because ... ??  (Here I am at a loss.  If your employer is doing this, or wants to, please let me know!)

1. ^{^}

   And I work on tools for businesses that are using LLMs themselves, so I am able to watch what various others are doing in this area as well, and where they tend to struggle most.