Positional encoding (PE) is widely viewed as necessary for transformers to process ordered sequences: without them, the next-token map appears permutation-invariant in its context tokens. This intuition underlies all prior universality results, which rely on positional information to prove that transformers with chain-of-thought can perform arbitrary computation, i.
arXiv:2606. 01532v1 Announce Type: new Abstract: Positional encoding (PE) is widely viewed as necessary for transformers to process ordered sequences: without them, the next-token map appears permutation-invariant in its context tokens.
arXiv:2604. 25800v2 Announce Type: replace Abstract: Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness.
arXiv:2607. 17710v1 Announce Type: new Abstract: Large Language Models (LLMs) have had a remarkable impact across many areas of machine learning.
arXiv:2607. 26988v1 Announce Type: cross Abstract: What types of decision problems can a causally masked, finite-precision transformer solve for inputs of arbitrary length?
arXiv:2606. 19697v1 Announce Type: cross Abstract: The increasing popularity of \emph{reasoning} models -- language models that output a series of reasoning or thought tokens before producing an answer -- is justified, in part, by theoretical results showing that chain-of-thought (CoT) transformers can simulate Turing machines, and thus perform arbitrary computation.
arXiv:2608. 11909v1 Announce Type: new Abstract: Two accounts recur in explanations of the success of rotary position embeddings (RoPE).
arXiv:2511. 05963v4 Announce Type: replace Abstract: Transformers replace recurrence with a memory that grows with sequence length and self-attention that enables ad-hoc lookups over past tokens.
arXiv:2603. 17019v2 Announce Type: replace Abstract: A central question in the debate over large language models is whether transformers can learn rules they have never seen, or whether they can only interpolate: predict new cases from their similarity to training examples.
arXiv:2605. 18079v2 Announce Type: replace Abstract: Existing expressivity results for transformers typically rely on hardmax attention, high precision, and other architectural modifications that disconnect them from the models used in practice.
arXiv:2510. 18315v2 Announce Type: replace-cross Abstract: We investigate how embedding dimension affects the emergence of an internal "world model" in a transformer trained with reinforcement learning to perform bubble-sort-style adjacent swaps.
We present a theoretical framework to explain the emergence of inductive reasoning abilities in Transformer language models. While previous works on Transformer learning dynamics have so far been mostly tied to specific tasks, we study a generalized class of inductive tasks that unifies several synthetic tasks known in the literature, including in-context n-grams and multi-hop reasoning.
arXiv:2608. 09432v1 Announce Type: cross Abstract: Transformer-based language models rely on self-attention, whose computation is permutation-equivariant and therefore lacks an intrinsic mechanism for representing token order.