A.1 CIFAR-10 dataset Figure 6 displays test accuracy curves for all six backbone algorithms under three distinct imbalance parameters: 2{ 0.3,1,10}. The results clearly demonstrate that FedNAR outperforms the baselines, particularly in scenarios with imbalanced data. A.2 Shakespeare dataset The experimental results presented in Figure 7 and 8 showcase the outcomes of experiments performed on the Shakespeare dataset. Six backbone algorithms were utilized, with initial weight decay values selected from {10 3,10 4}. These findings serve as evidence that FedNAR, as an adaptive weight decay scheduling algorithm, exhibits effectiveness across various initial weight decay values.

Let (x,y)be a binary classification task that admits a smooth separator as in Assumption 1. Then, there exists an RLC with neural network fθ and absolutely continuous randomness source u (Assumption 2) that is universal in the limit, i.e., Fθ (x) = y(x), x X, and makes random predictions that are correct with probability P(maj({sgn( a Further, if p is the number of parameters used by a deterministic neural network with one hidden layer to achieve zero-error in the task, fθ has at most p p +O(1)parameters. Since Assumption 1 holds3, there exists a single hidden-layer neural network N that, like s, achieves zero-error in this task [8]. Further, since sgn is nonpolynomial, we can use it as the nonlinearity of this network [21]. Putting it all together, there exists a number of hidden units M and parameters bj,oj R,wj Rd for j = 1,...,M such that N(x):= Note that this means we can achieve zero-error in classification, N(x) = y(x), x X.

Image super-resolution (SR) aims to learn a mapping from low-resolution (LR) to high-resolution (HR) using paired HR-LR training images. Conventional SR methods typically gather the paired training data by synthesizing LR images from HR images using a predetermined degradation model, e.g., Bicubic down-sampling.

In-context learning (ICL) of large language models has proven to be a surprisingly effective method of learning a new task from only a few demonstrative examples. In this paper, we shed light on the efficacy of ICL from the viewpoint of statistical learning theory. We develop approximation and generalization error analyses for a transformer model composed of a deep neural network and one linear attention layer, pretrained on nonparametric regression tasks sampled from general function spaces including the Besov space and piecewise $\gamma$-smooth class. In particular, we show that sufficiently trained transformers can achieve -- and even improve upon -- the minimax optimal estimation risk in context by encoding the most relevant basis representations during pretraining. Our analysis extends to high-dimensional or sequential data and distinguishes the \emph{pretraining} and \emph{in-context} generalization gaps, establishing upper and lower bounds w.r.t.

Existing large language models (LLMs) can only afford fix-sized inputs due to the input length limit, preventing them from utilizing rich long-context information from past inputs. To address this, we propose a framework, Language Models Augmented with Long-Term Memory (LONGMEM), which enables LLMs to memorize long history. We design a novel decoupled network architecture with the original backbone LLM frozen as a memory encoder and an adaptive residual side-network as a memory retriever and reader. Such a decoupled memory design can easily cache and update long-term past contexts for memory retrieval without suffering from memory staleness. Enhanced with memory-augmented adaptation training, LONGMEM can thus memorize long past context and use long-term memory for language modeling.

Data pruning, which aims to downsize a large training set into a small informative subset, is crucial for reducing the enormous computational costs of modern deep learning. Though large-scale data collections invariably contain annotation noise and numerous robust learning methods have been developed, data pruning for the noise-robust learning scenario has received little attention. With state-ofthe-art Re-labeling methods that self-correct erroneous labels while training, it is challenging to identify which subset induces the most accurate re-labeling of erroneous labels in the entire training set.