It is proved that this construction preserves local RoPE exactly, leaves the attention comparison between two fixed tokens unchanged when other units are inserted or reordered, and does not create new relative rotations merely because more units are added.
Abstract
Rotary position embedding (RoPE) uses each token's integer position to determine the rotation applied inside attention. This works well for local token order, but increasing context length creates a positional train-test mismatch: RoPE produces relative rotations at offsets not seen during training. Methods that rescale, interpolate, randomize, or bias positions specify how attention handles those offsets, but still derive positional information from a growing token counter. We instead divide a token stream into units, retain ordinary RoPE positions within each unit, and assign every completed unit an address computed from its content. Adding units then applies the same learned map to new content rather than extending a positional range or an identifier table. We prove that this construction preserves local RoPE exactly, leaves the attention comparison between two fixed tokens unchanged when other units are inserted or reordered, and does not create new relative rotations merely because more units are added. In a character-level Tiny Shakespeare diagnostic, all-token validation perplexity remains approximately constant from contexts of 256 to 4096 characters. A second diagnostic shows that content-based addressing can retrieve and use information from multiple serialized facts. These are controlled shallow experiments, not scale benchmarks, but they support a direct prescription: use position to address locally and content to address across units.
Rotary Position Embedding (RoPE) encodes token positions by rotating each two-dimensional channel of the query and key vectors at a channel-specific frequency, making the attention logits invariant to a common shift of positions. However, this rotation is periodic, and it leads to position aliasing where relative posit...
Guan-Cheng Du, Luo-Tian Huang, Shaowen Wang et al.· 0 citations
Aperture stores Fourier moments of the token's weighted support at the model's rotary frequencies, and it is proved that these moments have minimal real dimension among continuous states sufficient for the selected expected rotary interactions.
A hierarchical rotary positional encoding (hRoPE) that represents paragraph, sentence, and token indices as separate channels, hold the token sequence fixed, intervene on the paragraph coordinate $p_1$, and measure cross-paragraph attention with a token-distance-exact estimator is used.
This paper derives the specific class of matrices where this cancellation is exact under RoPE if and only if $M$ commutes with RoPE's per-position rotation, and derives the specific class of matrices where this holds.
Training-free token reduction accelerates vision transformers by removing redundant tokens across layers, recovering most of the original accuracy at a fraction of the compute. These methods, however, are designed and evaluated primarily on clean data, and under real-world distribution shift their accuracy gap to the u...
Analytic-Walk Rotary Positional Encodings (AW-RoPE), which place the rotations on edges and sum the transported features over all walks, so contributions along different routes can reinforce or cancel and prove forward and parameter-derivative truncation bounds at fixed inputs and parameters.
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.