This latter observation is expected given the different design objectives. Recall that this choice was made as computing the double derivative terms would have required extra communication bandwidth as well increased computational load. The number of participating clients is set to 10. Comparison with personalized FL: Performance with both unseen/seen classes at deployment. Specifically, we decrease the number of data in each episode from 6000 to 1200 in CIFAR-100, so that each user holds only 120 images.

We also show that the ILFO problem is strictly harder than the standard IL problem by presenting an exponential sample complexity separation between IL and ILFO.

We also show that the ILFO problem is strictly harder than the standard IL problem by presenting an exponential sample complexity separation between IL and ILFO.

Given the differences between the training procedures of the model presented in Section 6.2, and those All models in Section 6.3 were trained with stochastic gradient descent on batches of size All models presented in this paper make use of the same 3-Layer MLP for parameterizing the encoders and decoders. This is then divided into 18 capsules, each of 18 dimensions. The decoder layers then have output sizes (450, 675, 4096). For all topographic models (TV AE and BubbleV AE) in Section 6.3, the global topographic organization afforded by These values were chosen to be sufficiently large to achieve notably lower equivariance error than the V AE baseline, and thus demonstrate the impact of topographic organization without temporal coherence. The results of all models are shown in Section B below.

Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs).

The core idea of contrastive learning is to pull the textual and visual representations of matched text-video pairs together and push the representations of unmatched text-video pairs apart.

A.1 Gradients for the entropy approximation Following the arguments in [13], we can compute the gradient of the term in (13) using θ A.2 Gradients for the penalty function We used the following penalty function h( x) = ( x δ) A.3 Gradients for the energy error We can write the energy error as (q We generalise the arguments from [14], Lemma 7. Proceeding by induction over n, we have for the case n = 1, for any v R The suggested approach can perform poorly for non-convex potentials or even convex potentials such as arsing in a logistic regression model for some data sets. We illustrate here how to learn a reasonable proposal for a general potential function by considering some version of position-dependent preconditioning. The transformation f as well as U generally depend on some parameters θ that we again omit for a less convoluted notation. Our approach can be seen as an alternative for instance to [31] where such a transformation is first learned by trying to approximate π with a standard Gaussian density using variational inference, while the HMC hyperparameters are adapted in a second step using Bayesian optimisation. The motivation for stopping the gradients comes from considering the special case f: z null Cz that corresponds to the position-independent preconditioning scheme above.

Despite the remarkable success of graph neural networks (GNNs) for graph representation learning, they are generally built on the (unreliable) i.i.d.