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Yep I agree, Calling Parity : (aa)* + neutral symbol was just a way to refer to the definition of Parity. I didn't mean to imply that Parity is as simple as (aa)*. Rather in our proof we treat (aa)* as a subset of Parity (solving Parity would require solving (aa)*) as well. However SSMs are unable to solve (aa)* and thus by extension Parity as well. Regarding something that can be artificially added to SSMs for them to be able to do (aa)* and not Parity. I am not sure, that's a trivial question to answer. We tried to increase the expressivity of SSMs by removing the non-negative assumption in Mamba (replacing the exponentiation with other choices), however, that didn't turn out to be helpful, as breaking the Non-negative assumption broke training, and we weren't able to converge on anything. However, we haven't explored this problem in as much detail, and there could be other ways of doing the same, but that would require breaking either of the Non-negative or Time invariant assumptions as per our findings. Exactly how one does that, without losing out on the advantages offered by SSMs is an open question. Regarding Bounded Dyck with 2 sets of parantheses, the definition of Bounded Dyck(k, m) implies 'k' different kinds of brackets (closing, opening considered different as well) and a depth of m. So, our results and theorems apply to multiple sets of Paranthesis, provided the sets of paranthesis is finite. However, the construction shown in the video was only for 1 set of parentheses. For keeping track of multiple brackets, we again would need flip flop state tracking. The 1st layer would keep track of the depth of the bracket as well as the identity of the bracket. Therefore the space of activations is - {0, ... m} X {all bracket types}. For the 2nd layer, we need to have for each depth, a separate set-reset automaton. With 'm' such automatons, at each depth, we will be able to identify the last bracket at that depth. We can thus deduce the maximum depth at which the last bracket is an opening one, and accordingly be able to predict the next set of valid characters. Thus, we need 'm' automatons that can be simulated by a width of logK , so in total a dimension of O(m logk). I hope I was able to answer your questions !

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this is the comment: I always thought of MLP modules in Transformers as soft key-value memories, where the keys are learned/memorized patterns (contexts, questions), and the values are memorized predictions (groundtruths, answers) that correspond to each learned pattern, assuming we ignore residual connections. If we have to consider residual connections, then the values are probably the updates/corrections to the predictions of the previous layers. so in my intuitive understanding, Transformers are doing the following steps (vaguely): 1. highlighting specific features of the embeddings (by QKV projections) 2. finding & highlighting temporal patterns (by Q @ K.T) 3. representing the highlighted patterns (by AttentionMap @ V) 4. searching for keys (learned patterns) from key-value memory, that are similar to the pattern representations from 3. (by dot product with FFN1 + ReLU) 5. updating predictions using the retrieved values from the key-value memory (by dot product with FFN2 + residual connection) because residual connections exist, patterns and predictions (or input and output) will become inseparable, making it difficult to precisely describe what's happening in each stage.

Sebastien Bubeck's talk was from MIT and published to TH-cam by himself not Microsoft. I think you might be making an unjustified leap assuming what was done to GPT-4 and that it applies generally. It would seem to me that what Bubeck describes as having been lost was trained out of the model as it was able to use such to create very offensive utterances potentially, like creating vectors that might say spell out hatespeech if asked. It seems like Bing's public beta still had shades of this, with users finding and for example posting on Reddit various ways they had found to trick the model into say swearing at a user. If that were the case the case, than it is perhaps better thought of as a business decision rather than something fundamental to how these models can be fine tuned / trained.

I had exactly the same thought. After describing this fascinating pure research, she then proceeded to use it to pervert the LLM in the way you so articulately described. My thought was that only the final answer should be cleaned up, if that is deemed necessary, in a separate step, like maybe with a small language network specialized in such a task, and only for those who request a sanitized answer.

Yes, that's correct. The terminology is confusing though (IF one knows Latin): the 'subject' literally is 'that which is (thrown) UNDER' while the 'object' is 'that which is (thrown) on top' . Everyday sensibilities thus would expect that the object is the one who does sth. and the subject the one which has sth. done TO it. The standard convention is the OPPOSITE however.

@@LGcommaI object generally refers to inert things and the 'subject' is used as English word for persons (King asked his subjects to pay more tax during the drought years...). This could be the reason for English grammar using subject for the actor and object for the acted upon (victim).

hey, not managing to respond from my own account so positing from here - the slides are on my website, which is hosted on github - gailweiss dot github dot io

That construction is not discussed in the published paper, but we will be releasing an arxiv draft with it soon! I will post a link once it exists :)

@@vikingarnirw Thank you! Very cool work.