The rapid progress seen in terms of large-scale generative AI is largely based on the attention mechanism. It is conversely non-trivial to conceive small-scale applications for which attention-based architectures outperform traditional approaches, such as multi-layer perceptrons or recurrent networks. We examine this problem in the context of 'task switching'. In this framework models work on ongoing token sequences with the current task being determined by stochastically interspersed control tokens. We show that standard transformers cannot solve a basic task switching reference model based on finite domain arithmetics which contains subtasks dedicated to increment / addition / reverse copy / context (IARC). We show that transformers, long short-term memory recurrent networks (LSTM), and plain multi-layer perceptrons (MLPs) achieve similar, but only modest prediction accuracies. We enlarge our comparative study by including an extension of the standard transformer architecture to its non-translational invariant counterpart, the cisformer, and an alternative attention mechanism, extensive attention. A combination of the latter is found to be the only model able to achieve considerable performance levels, of around 95%. Our results indicate that the workings of attention can be understood better, and even improved, when comparing qualitatively different formulations in task-switching settings.

We propose a novel attention mechanism, named Cog Attention, that enables attention weights to be negative for enhanced expressiveness, which stems from two key factors: (1) Cog Attention can shift the token deletion and copying function from a static OV matrix to dynamic QK inner products, with the OV matrix now focusing more on refinement or modification. The attention head can simultaneously delete, copy, or retain tokens by assigning them negative, positive, or minimal attention weights, respectively. As a result, a single attention head becomes more flexible and expressive. (2) Cog Attention improves the model's robustness against representational collapse, which can occur when earlier tokens are over-squashed into later positions, leading to homogeneous representations. Negative weights reduce effective information paths from earlier to later tokens, helping to mitigate this issue. We develop Transformer-like models which use Cog Attention as attention modules, including decoder-only models for language modeling and U-ViT diffusion models for image generation. Experiments show that models using Cog Attention exhibit superior performance compared to those employing traditional softmax attention modules. Our approach suggests a promising research direction for rethinking and breaking the entrenched constraints of traditional softmax attention, such as the requirement for non-negative weights.

Attention involves comparing query and key vectors in terms of a scalar product, $\mathbf{Q}^T\mathbf{K}$, together with a subsequent softmax normalization. Classicaly, parallel/orthogonal/antiparallel queries and keys lead to large/intermediate/small attention weights. Here we study expressive attention (EA), which is based on $(\mathbf{Q}^T\mathbf{K})^2$, the squared dot product. In this case attention is enhanced when query and key are either parallel or antiparallel, and suppressed for orthogonal configurations. For a series of autoregressive prediction tasks, we find that EA performs at least as well as the standard mechanism, dot-product attention (DPA). Increasing task complexity, EA is observed to outperform DPA with increasing margins, which also holds for multi-task settings. For a given model size, EA manages to achieve 100\% performance for a range of complexity levels not accessible to DPA.