Therefore, with high probability the term DE is small. Next, we show that DE is governed by the variance of sim( x, y) for unmatched pairs.

We introduce an Outlier-Efficient Modern Hopfield Model (termed $\mathtt{OutEffHop}$) and use it to address the outlier-induced challenge of quantizing gigantic transformer-based models. Our main contribution is a novel associative memory model facilitating \textit{outlier-efficient} associative memory retrievals. Interestingly, this memory model manifests a model-based interpretation of an outlier-efficient attention mechanism ($\text{Softmax}_1$): it is an approximation of the memory retrieval process of $\mathtt{OutEffHop}$. Methodologically, this allows us to debut novel outlier-efficient Hopfield layers a powerful attention alternative with superior post-quantization performance. Theoretically, the Outlier-Efficient Modern Hopfield Model retains and improves the desirable properties of the standard modern Hopfield models, including fixed point convergence and exponential storage capacity. Empirically, we demonstrate the proposed model's efficacy across large-scale transformer-based and Hopfield-based models (including BERT, OPT, ViT and STanHop-Net), benchmarking against state-of-the-art methods including $\mathtt{Clipped\_Softmax}$ and $\mathtt{Gated\_Attention}$. Notably, $\mathtt{OutEffHop}$ achieves on average $\sim$22+\% reductions in both average kurtosis and maximum infinity norm of model outputs accross 4 models.

Multi-hop inference is necessary for machine learning systems to successfully solve tasks such as Recognising Textual Entailment and Machine Reading. In this work, we demonstrate the effectiveness of adaptive computation for learning the number of inference steps required for examples of different complexity and that learning the correct number of inference steps is difficult. We introduce the first model involving Adaptive Computation Time which provides a small performance benefit on top of a similar model without an adaptive component as well as enabling considerable insight into the reasoning process of the model.

We consider the problem of classification when inputs correspond to sets of vectors. This setting occurs in many problems such as the classification of pieces of mail containing several pages, of web sites with several sections or of images that have been pre-segmented into smaller regions. We propose generalizations of the restricted Boltzmann machine (RBM) that are appropriate in this context and explore how to incorporate different assumptions about the relationship between the input sets and the target class within the RBM. In experiments on standard multiple-instance learning datasets, we demonstrate the competitiveness of approaches based on RBMs and apply the proposed variants to the problem of incoming mail classification.