To mitigate the negative effect of data heterogeneity (non-IIDness), two common approaches are clustering and personalization.

And, for each of them, the second (final) stripe has 44 options. It could seem that small improvements in efficacy may have only a minor effect on final network accuracy, especially considering the noisiness inherent in large-scale training. Better thanreducing themagnitude oflostweights, though, iscompletely eliminating it - by using the zeros already present in the unstructured sparse weight matrix, it may be possible to find a permutation that does notloseanymagnitude after applying theN:M constraint.

Scaling of Transformers (V aswani et al., 2017) has produced language models (LM) with impressive

This paper advocates a new paradigm Personalized Empirical Risk Minimization (PERM) to facilitate learning from heterogeneous data sources without imposing stringent constraints on computational resources shared by participating devices. In PERM, we aim at learning a distinct model for each client by personalizing the aggregation of local empirical losses by effectively estimating the statistical discrepancy among data distributions, which entails optimal statistical accuracy for all local distributions and overcomes the data heterogeneity issue. To learn personalized models at scale, we propose a distributed algorithm that replaces the standard model averaging with model shuffling to simultaneously optimize PERM objectives for all devices. This also allows to learn distinct model architectures (e.g., neural networks with different number of parameters) for different clients, thus confining to underlying memory and compute resources of individual clients. We rigorously analyze the convergence of proposed algorithm and conduct experiments that corroborates the effectiveness of proposed paradigm.

Logical reasoning over Knowledge Graphs (KGs) is a fundamental technique that can provide an efficient querying mechanism over large and incomplete databases. Current approaches employ spatial geometries such as boxes to learn query representations that encompass the answer entities and model the logical operations of projection and intersection. However, their geometry is restrictive and leads to non-smooth strict boundaries, which further results in ambiguous answer entities. Furthermore, previous works propose transformation tricks to handle unions which results in non-closure and, thus, cannot be chained in a stream. In this paper, we propose a Probabilistic Entity Representation Model (PERM) to encode entities as a Multivariate Gaussian density with mean and covariance parameters to capture its semantic position and smooth decision boundary, respectively. Additionally, we also define the closed logical operations of projection, intersection, and union that can be aggregated using an end-to-end objective function. On the logical query reasoning problem, we demonstrate that the proposed PERM significantly outperforms the state-of-the-art methods on various public benchmark KG datasets on standard evaluation metrics. We also evaluate PERM's competence on a COVID-19 drug-repurposing case study and show that our proposed work is able to recommend drugs with substantially better F1 than current methods. Finally, we demonstrate the working of our PERM's query answering process through a low-dimensional visualization of the Gaussian representations.