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:2609.08851v1 Announce Type: new Abstract: Recent advancements in transformer length generalization theory enable us to reliably predict when a transformer can learn to solve a task. In particul...
arXiv:2603. 19954v2 Announce Type: replace Abstract: Transformers have shown inconsistent success in AI planning tasks, and theoretical understanding of when generalization should be expected has been limited.
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:2601. 22002v5 Announce Type: replace Abstract: Transformers achieve superior performance on many tasks, but impose heavy compute and memory requirements during inference.
arXiv:2410. 11500v2 Announce Type: replace-cross Abstract: In this paper, we establish a collection of covering number bounds for linear function classes under various norm constraints on the inputs and matrices.
arXiv:2606. 08768v1 Announce Type: new Abstract: Transformers consistently fail to learn certain simple functions that are provably expressible with specific parameter settings.
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: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. 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: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 $\Omega(L W \log (T W / L))$.
The paper examines how to allocate attention heads and head dimensions across Transformer layers to balance expressivity and efficiency. It provides a mathematical analysis of early layers’ role in information extraction and characterizes the trade‑off between head count and dimension under a fixed parameter budget. The authors prove a saturation effect of softmax activations, showing that increasing head dimensions yields diminishing returns, especially for long sequences, and propose strategies for efficient parameter allocation across layers.
arXiv:2608.31067v1 Announce Type: new Abstract: Learning generalizable algorithmic computations remains a challenge for neural networks, as reflected in persistent failures on compositional and lengt...