arXiv:2606. 09731v1 Announce Type: new Abstract: We tightly characterize the VC dimension of depth-$L$ Transformers with a total of $W$ parameters, mapping an input sequence of length $T$ to a single output, establishing an upper bound of $O(L W \log (T W))$ and a nearly matching lower bound of $\Omega(L W \log (T W / L))$.
arXiv:2607. 11760v1 Announce Type: new Abstract: A theoretical understanding of Transformers is crucial to better understand the capacities and limitations of large language models (LLMs).
arXiv:2601. 22002v5 Announce Type: replace Abstract: Transformers achieve superior performance on many tasks, but impose heavy compute and memory requirements during inference.
arXiv:2605. 22223v2 Announce Type: replace Abstract: We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively.
arXiv:2606. 29331v1 Announce Type: new Abstract: Scientific discovery via symbolic regression is often viewed as statistically and computationally intractable because the hypothesis space of expressions grows combinatorially with depth.
arXiv:2603. 02238v2 Announce Type: replace Abstract: Length generalization is a key property of a learning algorithm that enables it to make correct predictions on inputs of any length, given finite training data.
arXiv:2608. 06337v1 Announce Type: cross Abstract: A monotone adversary observes an i.
arXiv:2608. 06363v1 Announce Type: cross Abstract: Let $H\subseteq\{-1,+1\}^X$ be a class of finite VC dimension $d\ge1$.
arXiv:2608. 04288v1 Announce Type: new Abstract: Calibration requires a predictor to be unbiased after conditioning on its own predictions.
arXiv:2607. 19573v1 Announce Type: cross Abstract: Structural generalization has been measured repeatedly by several benchmarks, yet it has never been formally defined.
arXiv:2606. 11437v1 Announce Type: cross Abstract: Efficiently sampling from a complex probability distribution is a fundamental problem which has become increasingly pertinent in recent years with the rise of generative AI, as sophisticated sampling procedures from LLMs have been proposed to solve challenging reasoning problems.
arXiv:2608. 12671v1 Announce Type: new Abstract: Multi-layer transformers form the critical component of essentially all large language models (LLMs) in use today.
arXiv:2607. 07423v1 Announce Type: new Abstract: We prove that, in the realizable PAC setting, the sample complexity of exact-trace learning for full autoregressive Chain-of-Thought traces is upper bounded by the standard multiclass rate of the local next-token class, where this rate is governed by the Daniely--Shalev-Shwartz dimension.