This supplementary provides additional experiments as well as details that are required to reproduce our results. These were not included in the main paper due to space limitations. The supplementary is arranged as follows: Section A: Details on Modelling - Section A.1 Details of Theoretical Modelling - Section A.2 Additional Details on CLEAM Algorithm - Section A.3 Details on Fairness Metric - Section A.4 Details of Significance of the Baseline Errors Section B: Deeper Analysis on Error in Fairness Measurement Section C: Validating Statistical Model for Classifier Output - Section C.1 Validation of Sample-Based Estimate vs Model-Based Estimate - Section C.2 Goodness-of-Fit Test: ˆpfrom the Real GANs with Our Theoretical Model Section D: Additional Experimental Results - Section D.1 Experimental Results with Standard Deviation - Section D.2 Experimental Setup for Diversity - Section D.3 Measuring Varying Degrees of Bias (Gender and BlackHair) - Section D.4 Measuring Varying Degrees of ...

Large language models (LLMs) exhibit in-context learning abilities which enable the same model to perform several tasks without any task-specific training. In contrast, traditional adaptation approaches, such as fine-tuning, modify the underlying models for each specific task. In-context learning, however, consistently underperforms task-specific tuning approaches even when presented with the same examples. While most existing approaches (e.g., prompt engineering) focus on the LLM's learned representations to patch this performance gap, our experiments actually reveal that LLM representations contain sufficient information to make good predictions. As such, we focus on the LLM's reasoning abilities and demonstrate that this performance gap exists due to their inability to perform simple probabilistic reasoning tasks. This raises an intriguing question: Are LLMs actually capable of learning how to reason in a task-agnostic manner? We answer this in the affirmative and, as a proof of concept, propose TART which generically improves an LLM's reasoning abilities using a synthetically trained reasoning module.

Robust reinforcement learning (RL) is to find a policy that optimizes the worstcase performance over an uncertainty set of MDPs. In this paper, we focus on model-free robust RL, where the uncertainty set is defined to be centering at a misspecified MDP that generates a single sample trajectory sequentially, and is assumed to be unknown. We develop a sample-based approach to estimate the unknown uncertainty set, and design robust Q-learning algorithm (tabular case) and robust TDC algorithm (function approximation setting), which can be implemented in an online and incremental fashion. For the robust Q-learning algorithm, we prove that it converges to the optimal robust Q function, and for the robust TDC algorithm, we prove that it converges asymptotically to some stationary points. Unlike the results in [Roy et al., 2017], our algorithms do not need any additional conditions on the discount factor to guarantee the convergence. We further characterize the finite-time error bounds of the two algorithms, and show that both the robust Qlearning and robust TDC algorithms converge as fast as their vanilla counterparts (within a constant factor). Our numerical experiments further demonstrate the robustness of our algorithms. Our approach can be readily extended to robustify many other algorithms, e.g., TD, SARSA, and other GTD algorithms.

Due to the high price and heavy energy consumption of GPUs, deploying deep models on IoT devices such as microcontrollers makes significant contributions for ecological AI. Conventional methods successfully enable convolutional neural network inference of high resolution images on microcontrollers, while the framework for vision transformers that achieve the state-of-the-art performance in many vision applications still remains unexplored. In this paper, we propose a hardware-algorithm co-optimizations method called MCUFormer to deploy vision transformers on microcontrollers with extremely limited memory, where we jointly design transformer architecture and construct the inference operator library to fit the memory resource constraint. More specifically, we generalize the one-shot network architecture search (NAS) to discover the optimal architecture with highest task performance given the memory budget from the microcontrollers, where we enlarge the existing search space of vision transformers by considering the low-rank decomposition dimensions and patch resolution for memory reduction. For the construction of the inference operator library of vision transformers, we schedule the memory buffer during inference through operator integration, patch embedding decomposition, and token overwriting, allowing the memory buffer to be fully utilized to adapt to the forward pass of the vision transformer. Experimental results demonstrate that our MCUFormer achieves 73.62% top-1 accuracy on ImageNet for image classification with 320KB memory on STM32F746 microcontroller.

The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixedpoints of a deep neural network. We also present numerical results comparing the recovery performance of PnP/RED in compressive sensing against that of recent compressive sensing algorithms based on generative models. Our numerical results suggest that PnP with a pre-trained artifact removal network provides significantly better results compared to the existing state-of-the-art methods.