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Of All StrIPEs: Investigating Structure-informed Positional Encoding for Efficient Music Generation

Manvi Agarwal, Changhong Wang, Gael Richard

TL;DR

This work investigates structure-informed positional encoding for efficient music generation by unifying RFF-based PEs and rotation-based PEs under a kernelized attention framework. It introduces RoPEPool, which adds cross-dimension pooling to RoPE, enabling causal, temporal interactions and greater expressivity. Through synthetic analyses and melody-harmonization experiments on the POP909-derived dataset, RoPEPool with rich structural priors outperforms RoPE, F-StrIPE, and other baselines, with performance correlating to the mutual information between content and context. The findings illuminate how content-context interactions in attention kernels drive learnability, offering a principled, scalable approach to structure-aware music generation with practical implications for other sequence modeling tasks.

Abstract

While music remains a challenging domain for generative models like Transformers, a two-pronged approach has recently proved successful: inserting musically-relevant structural information into the positional encoding (PE) module and using kernel approximation techniques based on Random Fourier Features (RFF) to lower the computational cost from quadratic to linear. Yet, it is not clear how such RFF-based efficient PEs compare with those based on rotation matrices, such as Rotary Positional Encoding (RoPE). In this paper, we present a unified framework based on kernel methods to analyze both families of efficient PEs. We use this framework to develop a novel PE method called RoPEPool, capable of extracting causal relationships from temporal sequences. Using RFF-based PEs and rotation-based PEs, we demonstrate how seemingly disparate PEs can be jointly studied by considering the content-context interactions they induce. For empirical validation, we use a symbolic music generation task, namely, melody harmonization. We show that RoPEPool, combined with highly-informative structural priors, outperforms all methods.

Of All StrIPEs: Investigating Structure-informed Positional Encoding for Efficient Music Generation

TL;DR

This work investigates structure-informed positional encoding for efficient music generation by unifying RFF-based PEs and rotation-based PEs under a kernelized attention framework. It introduces RoPEPool, which adds cross-dimension pooling to RoPE, enabling causal, temporal interactions and greater expressivity. Through synthetic analyses and melody-harmonization experiments on the POP909-derived dataset, RoPEPool with rich structural priors outperforms RoPE, F-StrIPE, and other baselines, with performance correlating to the mutual information between content and context. The findings illuminate how content-context interactions in attention kernels drive learnability, offering a principled, scalable approach to structure-aware music generation with practical implications for other sequence modeling tasks.

Abstract

While music remains a challenging domain for generative models like Transformers, a two-pronged approach has recently proved successful: inserting musically-relevant structural information into the positional encoding (PE) module and using kernel approximation techniques based on Random Fourier Features (RFF) to lower the computational cost from quadratic to linear. Yet, it is not clear how such RFF-based efficient PEs compare with those based on rotation matrices, such as Rotary Positional Encoding (RoPE). In this paper, we present a unified framework based on kernel methods to analyze both families of efficient PEs. We use this framework to develop a novel PE method called RoPEPool, capable of extracting causal relationships from temporal sequences. Using RFF-based PEs and rotation-based PEs, we demonstrate how seemingly disparate PEs can be jointly studied by considering the content-context interactions they induce. For empirical validation, we use a symbolic music generation task, namely, melody harmonization. We show that RoPEPool, combined with highly-informative structural priors, outperforms all methods.

Paper Structure

This paper contains 27 sections, 24 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Transformers, Attention and Positional Encoding
  4. Efficient Attention with Positional Information
  5. Rotary Positional Encoding
  6. Methods
  7. F-StrIPE: Fast, Structure-informed Positional Encoding
  8. Interpreting PE-enriched Attention through Kernels
  9. Comparing Rotation-based and RFF-based PEs
  10. RoPEPool: Gaining expressivity using simple operations
  11. A Simplified Analysis of F-StrIPE$_1$, RoPE and RoPEPool
  12. Experiments
  13. Dataset and Input Representation
  14. Task: Melody Harmonization
  15. Model and Training
  16. ...and 12 more sections

Figures (4)

  • Figure 1: Top: Efficient attention enriched with positional information can be viewed as a Tensor Product Kernel operating on context similarity and content similarity. Bottom: Relationship of the three positional encoding methods discussed in this paper (RoPE, F-StrIPE and RoPEPool)
  • Figure 2: Generating a toy dataset to study the characteristics of different positional encoding methods for the $D=2$ setting
  • Figure 3: Different PE methods exhibit different trade-offs between content and context
  • Figure 4: Performance as a function of how much information about the data distribution is contained in the positional information; drawn from the in-domain results in Table \ref{['tab:results']}