This paper reads to me as being about fundamental limitations of Transformers and backdoor risk.

The paper starts off by reviewing work which uses an encompassing theoretical model of transformers to prove they're limited to only expressing computations in TC^0 (roughly, upperbounded by set of parallelizable problems that can be solved by relatively shallow circuits).

There's also a reference to a paper which finds that (wrt input problem size), a polynomial number of intermediate scratchpad decoding steps allow transformers to recognize the class of polynomial-time solvable problems, linear steps is context-sensitive languages.

This paper now ask about filler tokens, do they help? The answer is negative except for a very clever exception they work out: problems with demonstrations that can be decomposed to be solvable in parallel. This identifies a practical limitation (transformer next token prediction is not expressive enough to capture all of TC^0) at the same as it identifies a theoretical capability. From the paper:

> Taken together these findings suggest that although current LLMs are unlikely to benefit from filler tokens, this is not an in-principle limitation of current architectures.

If I've understood, this means for learning to use fillers to benefit from CoT data, demonstrations must be structured such that they can be computed in parallel and not as a more natural sequential, instance-adaptive process.

> in order to use filler tokens on natural language data, LLMs would need to discover parallelizable algorithmic solutions given access only to CoT demonstrations lacking parallel structure. By training on instance-adaptive chains of thought, we can study whether models can learn to use filler tokens having seen only more naturalistic chain-of-thought data
>...
> We find that models trained on instance-adaptive CoT data fail to use filler tokens. On filler token sequences, the resulting models remain at, or below, no-intermediate-token, baseline performance, Figure 6. This indicates that there is no transfer from serial, instance-adaptive demonstrations to filler tokens for the 3SUM problem.

It also appears that the parallelizable problem must have a certain amount of structural complexity before a gap appears versus no filler modes (unless using an impractical amount of filler tokens):

> we expect integer addition tasks will not offer suitably rich structures for taking advantage of filler tokens when using large models—natural-language tasks may offer alternatives

Empirically, other papers have shown that LLM performance on complex tasks deteriorates significantly with input length and distractor text. Anyone who has naively attempted to combine RAG with large contexts might also have first hand experience with this.

The reason I consider this to be primarily a backdoor risk is that the kind of data and learning required seems highly unlikely to occur naturally but someone could create documents to introduce triggerable obfuscated computations. While not an issue today, future LLM training might need to filter for data with meaningful parts separated by meaningless patterns of repeated characters.

This paper follows a recent trend of marketing excellent theoretical work as LLMs being capable of secretly plotting behind your back, when the realistic implication is backdoor risk.

An article currently on the first page is relevant:

https://www.strangeloopcanon.com/p/what-can-llms-never-do