MiTA Attention: Efficient Fast-Weight Scaling via a Mixture of Top-k Activations

The attention operator in Transformers can be viewed as a two-layer fast-weight MLP, whose weights are dynamically instantiated from input tokens and whose width equals sequence length N. As the context extends, the expressive capacity of such an N-width MLP increases, but scaling its fast weights becomes prohibitively expensive for extremely long sequences. Recently, this fast-weight scaling perspective has motivated the Mixture-of-Experts (MoE) attention, which partitions the sequence into fast-weight experts and sparsely routes the tokens to them. In this paper, we elevate this perspective to a unifying framework for a wide range of efficient attention methods by interpreting them as scaling fast weights through routing and/or compression. Then we propose a compress-and-route strategy, which compresses the N-width MLP into a narrower one using a small set of landmark queries and constructs deformable experts by gathering top-k activated key-value pairs for each landmark query. We call this strategy a Mixture of Top-k Activations (MiTA), and refer to the resulting efficient mechanism as MiTA attention. Preliminary experiments on vision tasks demonstrate the promise of our MiTA attention and motivate further investigation on its optimization and broader applications in more challenging settings.

Exploring a Principled Framework for Deep Subspace Clustering

Subspace clustering is a classical unsupervised learning task, built on a basic assumption that high-dimensional data can be approximated by a union of subspaces (UoS). Nevertheless, the real-world data are often deviating from the UoS assumption. To address this challenge, state-of-the-art deep subspace clustering algorithms attempt to jointly learn UoS representations and self-expressive coefficients. However, the general framework of the existing algorithms suffers from a catastrophic feature collapse and lacks a theoretical guarantee to learn desired UoS representation. In this paper, we present a Principled fRamewOrk for Deep Subspace Clustering (PRO-DSC), which is designed to learn structured representations and self-expressive coefficients in a unified manner. Specifically, in PRO-DSC, we incorporate an effective regularization on the learned representations into the self-expressive model, prove that the regularized self-expressive model is able to prevent feature space collapse, and demonstrate that the learned optimal representations under certain condition lie on a union of orthogonal subspaces. Moreover, we provide a scalable and efficient approach to implement our PRO-DSC and conduct extensive experiments to verify our theoretical findings and demonstrate the superior performance of our proposed deep subspace clustering approach. The code is available at https://github.com/mengxianghan123/PRO-DSC.