Federated learning (FL) is a distributed paradigm that coordinates massive local clients to collaboratively train a global model via stage-wise local training processes on the heterogeneous dataset. Previous works have implicitly studied that FL suffers from the "client-drift" problem, which is caused by the inconsistent optimum across local clients. However, till now it still lacks solid theoretical analysis to explain the impact of this local inconsistency. To alleviate the negative impact of the "client drift" and explore its substance in FL, in this paper, we first design an efficient FL algorithm FedInit, which allows employing the personalized relaxed initialization state at the beginning of each local training stage.

The neural population spiking activity recorded by intracortical brain-computer interfaces (iBCIs) contain rich structure. Current models of such spiking activity are largely prepared for individual experimental contexts, restricting data volume to that collectable within a single session and limiting the effectiveness of deep neural networks (DNNs). The purported challenge in aggregating neural spiking data is the pervasiveness of context-dependent shifts in the neural data distributions. However, large scale unsupervised pretraining by nature spans heterogeneous data, and has proven to be a fundamental recipe for successful representation learning across deep learning. We thus develop Neural Data Transformer 2 (NDT2), a spatiotemporal Transformer for neural spiking activity, and demonstrate that pretraining can leverage motor BCI datasets that span sessions, subjects, and experimental tasks. NDT2 enables rapid adaptation to novel contexts in downstream decoding tasks and opens the path to deployment of pretrained DNNs for iBCI control.

Robotic applications often involve working in environments that are uncertain, dynamic, and partially observable. Recently, diffusion models have been proposed for learning trajectory prediction models trained from expert demonstrations, which can be used for planning in robot tasks. Such models have demonstrated a strong ability to overcome challenges such as multi-modal action distributions, highdimensional output spaces, and training instability. It is crucial to quantify the uncertainty of these dynamics models when using them for planning. In this paper, we quantify the uncertainty of diffusion dynamics models using Conformal Prediction (CP).

We consider the class of noisy multi-layered sigmoid recurrent neural networks with w (unbounded) weights for classification of sequences of length T, where independent noise distributed according to N(0,σ2)is added to the output of each neuron in the network. Our main result shows that the sample complexity of PAC learning this class can be bounded by O(wlog(T/σ)). For the non-noisy version of the same class (i.e., σ = 0), we prove a lower bound of Ω(wT) for the sample complexity. Our results indicate an exponential gap in the dependence of sample complexity on T for noisy versus non-noisy networks. Moreover, given the mild logarithmic dependence of the upper bound on 1/σ, this gap still holds even for numerically negligible values of σ.1