Amodal perception requires inferring the full shape of an object that is partially occluded.

A.1 Proof of FAT-Clipping - PR For notional clarity, we have the following update: Local update: x The first inequality follows from the strongly-convex property, i.e., Assumption 4. (Bounded Stochastic Gradient V ariance) There exists a constant Assumption 5. (Bounded Gradient) There exists a constant We remark that for any stochastic estimator satisfies the above conditions, the above inequalities hold. The proof is the exactly same as that in original proof [18]. Theorem 6. Suppose f is We run a convolutional neural network (CNN) model on CIFAR-10 dataset using FedAvg. CNN architecture is shown in Table 2. To simulate data heterogeneity across clients, we manually The dataset and model are taken from [45]. This implies that the gradient noise is fat-tailed.

In recent years, the recommendation content on e-commerce platforms has become increasingly rich -- a single user feed may contain multiple entities, such as selling products, short videos, and content posts. To deal with the multi-entity recommendation problem, an intuitive solution is to adopt the shared-network-based architecture for joint training. The idea is to transfer the extracted knowledge from one type of entity (source entity) to another (target entity). However, different from the conventional same-entity cross-domain recommendation, multi-entity knowledge transfer encounters several important issues: (1) data distributions of the source entity and target entity are naturally different, making the shared-network-based joint training susceptible to the negative transfer issue, (2) more importantly, the corresponding feature schema of each entity is not exactly aligned (e.g., price is an essential feature for selling product while missing for content posts), making the existing methods no longer appropriate. Recent researchers have also experimented with the pre-training and fine-tuning paradigm. Again, they only consider the scenarios with the same entity type and feature systems, which is inappropriate in our case. To this end, we design a pre-training & fine-tuning based Multi-entity Knowledge Transfer framework called MKT. MKT utilizes a multi-entity pre-training module to extract transferable knowledge across different entities. In particular, a feature alignment module is first applied to scale and align different feature schemas. Afterward, a couple of knowledge extractors are employed to extract the common and entity-specific knowledge. In the end, the extracted common knowledge is adopted for target entity model training. Through extensive offline and online experiments, we demonstrated the superiority of MKT over multiple State-Of-The-Art methods.

A key assumption in most existing works on FL algorithms' convergence analysis is that the noise in stochastic first-order information has a finite variance. Although this assumption covers all light-tailed (i.e., sub-exponential) and some heavy-tailed noise distributions (e.g., log-normal, Weibull, and some Pareto distributions), it fails for many fat-tailed noise distributions (i.e., ``heavier-tailed'' with potentially infinite variance) that have been empirically observed in the FL literature. To date, it remains unclear whether one can design convergent algorithms for FL systems that experience fat-tailed noise. This motivates us to fill this gap in this paper by proposing an algorithmic framework called FAT-Clipping (\ul{f}ederated \ul{a}veraging with \ul{t}wo-sided learning rates and \ul{clipping}), which contains two variants: FAT-Clipping per-round (FAT-Clipping-PR) and FAT-Clipping per-iteration (FAT-Clipping-PI). Specifically, for the largest $\alpha \in (1,2]$ such that the fat-tailed noise in FL still has a bounded $\alpha$-moment, we show that both variants achieve $\mathcal{O}((mT)^{\frac{2-\alpha}{\alpha}})$ and $\mathcal{O}((mT)^{\frac{1-\alpha}{3\alpha-2}})$ convergence rates in the strongly-convex and general non-convex settings, respectively, where $m$ and $T$ are the numbers of clients and communication rounds. Moreover, at the expense of more clipping operations compared to FAT-Clipping-PR, FAT-Clipping-PI further enjoys a linear speedup effect with respect to the number of local updates at each client and being lower-bound-matching (i.e., order-optimal). Collectively, our results advance the understanding of designing efficient algorithms for FL systems that exhibit fat-tailed first-order oracle information.