arXiv:2607. 18759v1 Announce Type: new Abstract: Transformers with relative positional encodings often extrapolate to sequences longer than those seen during training, whereas transformers with learned absolute encodings typically do not.
By Subham Singh, Ashutosh Mishra, Subha Raut
The paper investigates how large language models can accurately copy long repeated strings, a task that standard transformers struggle with due to overrun or truncation. It proposes a two‑layer transformer using RoPE‑style rotations (VO‑rotations) with small prime periods to encode distances modulo primes, enabling the model to distinguish all necessary positions via the Chinese Remainder Theorem and correctly terminate copying. Experiments show that baseline transformers fail on long repeats, while the VO‑based model generalizes to lengths up to about 5005 with near‑perfect accuracy.
By Anxin Guo, Tianlong Huang, Chenxiao Yang, Zhiyuan Li
The paper proposes a content‑based addressing scheme for long‑context models that replaces the growing token counter in Rotary Position Embedding (RoPE) with unit‑level addresses derived from the content of each unit. By dividing the token stream into units, the method preserves local RoPE behavior while allowing new units to be addressed via learned content maps, avoiding positional mismatches when extending context length. Experiments on character‑level Tiny Shakespeare show that a model trained on 256‑character contexts achieves lower perplexity at 4096 characters using this scheme, and a second diagnostic demonstrates retrieval of multiple serialized facts.
By Mahesh Godavarti
The paper presents quantitative generalization bounds for fixed‑precision transformer models, addressing both in‑distribution statistical generalization and length generalization. It derives guarantees based on model parameters, quantization space, and alphabet size, and shows how training length and sample size trade off, with longer training being exponentially more efficient. Experiments confirm the theoretical predictions.
By Marius Henry, Michael Rizvi-Martel, Michael Hahn
arXiv:2607. 07678v1 Announce Type: new Abstract: Rotary Position Embeddings (RoPE) provide transformers with a fixed grid of positional frequencies, yet trained models use these frequencies highly non-uniformly.
By Xinyi Wu, Siyuan Liu, Ali Jadbabaie
The paper introduces GAPE (Gated Adaptive Positional Encoding), a drop‑in augmentation for rotary positional encodings that adds content‑aware bias to attention logits while preserving rotary geometry. GAPE uses a query‑dependent gate to contract irrelevant context and a key‑dependent gate to keep salient distant tokens, leading to exponential attenuation of weakly protected context. Experiments show that GAPE improves long‑context robustness, extrapolating up to eight times the training length, and can be retrofitted into a pretrained 7B model without losing benchmark performance.
By Riccardo Ali, Alessio Borgi, Mario Severino, Pietro Li\`o, Christopher Irwin