PolySketchFormer: Fast Transformers via Sketching Polynomial Kernels

Core Concepts

Polynomial attention with high degree can replace softmax attention without sacrificing model quality, leading to a linear-time Transformer architecture.

Abstract

1. Introduction

Self-attention mechanisms in Transformers pose computational bottlenecks.
Efficient transformers aim to address scalability issues.
Vanilla transformers dominate due to practical training speedups.
2. Polynomial Attention and Approximation

Kernel-based methods offer efficient n × n attention computation.
Approximate feature mapping for polynomial kernels is explored.
3. Dealing with Causal Masks

Block-based lower triangular multiplication for handling causal masks efficiently.
4. Experiments

Synthetic tasks measure content-aware reasoning and memorization capabilities.
Real-world datasets train decoder-only models mirroring GPT-2 family scales.

Stats

Context Length µs/token: Vanilla Softmax, Polysketch, FlashAttention (Block = 256), FlashAttention (Block = 512)
Train Step latency per token comparison between GPT-2 small style models with different attention mechanisms.

Quotes

Key Insights Distilled From

PolySketchFormer

by Praneeth Kac... at arxiv.org 03-19-2024

https://arxiv.org/pdf/2310.01655.pdf

Deeper Inquiries

How does the PolysketchFormer approach compare to other efficient transformer architectures

PolysketchFormer offers a significant improvement over other efficient transformer architectures in terms of training speed and model quality. By leveraging polynomial kernels for attention mechanisms, PolysketchFormer achieves linear-time polynomial attention with approximation guarantees, allowing for faster training and deployment of large-scale Transformer-based language models. Compared to approaches like FlashAttention and Performer, PolysketchFormer demonstrates superior performance in handling long contexts without sacrificing model quality.

What are the implications of using polynomial kernels for attention mechanisms in language modeling

Using polynomial kernels for attention mechanisms in language modeling has several implications. Firstly, it allows for the replacement of softmax attention with high-degree polynomial attention without compromising model quality. This approach addresses the computational bottleneck associated with self-attention mechanisms by providing a more efficient alternative that scales well with sequence length. Additionally, the concept of sketching polynomial kernels enables the computation of approximate feature mappings that maintain non-negativity properties crucial for stable training processes.

How can the concept of sketching be applied in other areas beyond language modeling

The concept of sketching can be applied beyond language modeling to various domains where matrix computations are involved. In fields such as image processing, computer vision, recommendation systems, and natural language processing tasks other than modeling languages (e.g., sentiment analysis or text summarization), sketching techniques can help optimize computations involving large matrices efficiently. By approximating complex operations through sketches while maintaining accuracy guarantees, these techniques can enhance the scalability and performance of machine learning algorithms across diverse applications.