Personalized federated learning (PFL) has been widely investigated to address the challenge of data heterogeneity, especially when a single generic model is inadequate in satisfying the diverse performance requirements of local clients simultaneously. Existing PFL methods are inherently based on the idea that the relations between the generic global and personalized local models are captured by the similarity of model weights. Such a similarity is primarily based on either partitioning the model architecture into generic versus personalized components, or modeling client relationships via model weights. To better capture similar (yet distinct) generic versus personalized model representations, we propose spectral distillation, a novel distillation method based on model spectrum information. Building upon spectral distillation, we also introduce a co-distillation framework that establishes a two-way bridge between generic and personalized model training. Moreover, to utilize the local idle time in conventional PFL, we propose a waitfree local training protocol. Through extensive experiments on multiple datasets over diverse heterogeneous data settings, we demonstrate the outperformance and efficacy of our proposed spectral co-distillation method, as well as our wait-free training protocol.

Modern convolutional neural networks (CNNs) have massive identical convolution blocks, and, hence, recursive sharing of parameters across these blocks has been proposed to reduce the amount of parameters. However, naive sharing of parameters poses many challenges such as limited representational power and the vanishing/exploding gradients problem of recursively shared parameters. In this paper, we present a recursive convolution block design and training method, in which a recursively shareable part, or a filter basis, is separated and learned while effectively avoiding the vanishing/exploding gradients problem during training. We show that the unwieldy vanishing/exploding gradients problem can be controlled by enforcing the elements of the filter basis orthonormal, and empirically demonstrate that the proposed orthogonality regularization improves the flow of gradients during training. Experimental results on image classification and object detection show that our approach, unlike previous parameter-sharing approaches, does not trade performance to save parameters and consistently outperforms overparameterized counterpart networks. This superior performance demonstrates that the proposed recursive convolution block design and the orthogonality regularization not only prevent performance degradation, but also consistently improve the representation capability while a significant amount of parameters are recursively shared.

We present and analyze an algorithm for optimizing smooth and convex or strongly convex objectives using minibatch stochastic gradient estimates. The algorithm is optimal with respect to its dependence on both the minibatch size and minimum expected loss simultaneously. This improves over the optimal method of Lan [17], which is insensitive to the minimum expected loss; over the optimistic acceleration of Cotter et al. [10], which has suboptimal dependence on the minibatch size; and over the algorithm of Liu and Belkin [19], which is limited to least squares problems and is also similarly suboptimal with respect to the minibatch size.

We organize our supplementary document as follows: 1. Results on additional dataset 2. Results for limited data settings on YFCC26k and GWS15k datasets 3. Additional Ablations (a) Gallery Size (b) Queue Length (c) ση for Batch GPS noise (d) ση for Queue GPS noise (e) σ for Random Fourier Features (f) Number of hierarchies (M) 4. Different selection choices for GPSGallery Construction (a) Evenly Spaced GPSCoordinates (b) Test Set GPSCoordinates 5. Analysis of Runtime and Memory Footprint 6. Motivations for using Pretrained CLIP as Image encoder Backbone 7. Qualitative Demonstration (a) Hierarchical learning in our location encoder L () (b) GeoCLIP with Image Query (c) Distribution of correct predictions of GeoCLIP on different datasets (d) GeoCLIP with Text Query 8. Discussion on Ethical Issues and Possible Mitigation In section 4.1 of the main paper, we demonstrated the performance of our GeoCLIP method on Im2GPS3k [2] and GWS15k [1] datasets and compared them with the state-of-the-art methods. Here, we perform experiments on another dataset YFCC26k [6]. The results are provided in Table 1. This result highlights that GeoCLIP performs well across datasets, being useful across different data distributions. GeoCLIP achieves decent performance across datasets even when the training data is significantly reduced. 2 We show the efficacy of GeoCLIP on limited training samples of Im2GPS3k in section 4.2 of the main paper. Now, we further investigate the performance of GeoCLIP for limited data settings on other datasets (YFCC26k and GWS15k).