Displaced dynamics of binary mixtures in linear and nonlinear optical lattices

The dynamical behavior of matter wave solitons of two-component Bose-Einstein condensates (BEC) in combined linear and nonlinear optical lattices (OLs) is investigated. In particular, the dependence of the frequency of the oscillating dynamics resulting from initially slightly displaced components is investigated both analytically, by means of a variational effective potential approach for the reduced collective coordinate dynamics of the soliton, and numerically, by direct integrations of the mean field equations of the BEC mixture. We show that for small initial displacements binary solitons can be viewed as point masses connected by elastic springs of strengths related to the amplitude of the OL and to the intra and inter-species interactions. Analytical expressions of symmetric and anti-symmetric mode frequencies, are derived and occurrence of beatings phenomena in the displaced dynamics is predicted. These expressions are shown to give a very good estimation of the oscillation frequencies for different values of the intra-species interatomic scattering length, as confirmed by direct numerical integrations of the mean field Gross-Pitaevskii equations (GPE) of the mixture. The possibility to use displaced dynamics for indirect measurements of BEC mixture characteristics such as number of atoms and interatomic interactions is also suggested.Comment: 8 pages, 21 figure

CoDeC: Communication-Efficient Decentralized Continual Learning

Training at the edge utilizes continuously evolving data generated at different locations. Privacy concerns prohibit the co-location of this spatially as well as temporally distributed data, deeming it crucial to design training algorithms that enable efficient continual learning over decentralized private data. Decentralized learning allows serverless training with spatially distributed data. A fundamental barrier in such distributed learning is the high bandwidth cost of communicating model updates between agents. Moreover, existing works under this training paradigm are not inherently suitable for learning a temporal sequence of tasks while retaining the previously acquired knowledge. In this work, we propose CoDeC, a novel communication-efficient decentralized continual learning algorithm which addresses these challenges. We mitigate catastrophic forgetting while learning a task sequence in a decentralized learning setup by combining orthogonal gradient projection with gossip averaging across decentralized agents. Further, CoDeC includes a novel lossless communication compression scheme based on the gradient subspaces. We express layer-wise gradients as a linear combination of the basis vectors of these gradient subspaces and communicate the associated coefficients. We theoretically analyze the convergence rate for our algorithm and demonstrate through an extensive set of experiments that CoDeC successfully learns distributed continual tasks with minimal forgetting. The proposed compression scheme results in up to 4.8x reduction in communication costs with iso-performance as the full communication baseline

Homogenizing Non-IID datasets via In-Distribution Knowledge Distillation for Decentralized Learning

Decentralized learning enables serverless training of deep neural networks (DNNs) in a distributed manner on multiple nodes. This allows for the use of large datasets, as well as the ability to train with a wide variety of data sources. However, one of the key challenges with decentralized learning is heterogeneity in the data distribution across the nodes. In this paper, we propose In-Distribution Knowledge Distillation (IDKD) to address the challenge of heterogeneous data distribution. The goal of IDKD is to homogenize the data distribution across the nodes. While such data homogenization can be achieved by exchanging data among the nodes sacrificing privacy, IDKD achieves the same objective using a common public dataset across nodes without breaking the privacy constraint. This public dataset is different from the training dataset and is used to distill the knowledge from each node and communicate it to its neighbors through the generated labels. With traditional knowledge distillation, the generalization of the distilled model is reduced because all the public dataset samples are used irrespective of their similarity to the local dataset. Thus, we introduce an Out-of-Distribution (OoD) detector at each node to label a subset of the public dataset that maps close to the local training data distribution. Finally, only labels corresponding to these subsets are exchanged among the nodes and with appropriate label averaging each node is finetuned on these data subsets along with its local data. Our experiments on multiple image classification datasets and graph topologies show that the proposed IDKD scheme is more effective than traditional knowledge distillation and achieves state-of-the-art generalization performance on heterogeneously distributed data with minimal communication overhead