We consider multi-draft speculative sampling, where the proposal sequences are sampled independently from different draft models. At each step, a token-level draft selection scheme takes a list of valid tokens as input and produces an output token whose distribution matches that of the target model. Previous works have demonstrated that the optimal scheme (which maximizes the probability of accepting one of the input tokens) can be cast as a solution to a linear program. In this work we show that the optimal scheme can be decomposed into a two-step solution: in the first step an importance sampling (IS) type scheme is used to select one intermediate token; in the second step (single-draft) speculative sampling is applied to generate the output token. For the case of two identical draft models we further 1) establish a necessary and sufficient condition on the distributions of the target and draft models for the acceptance probability to equal one and 2) provide an explicit expression for the optimal acceptance probability. Our theoretical analysis also motives a new class of token-level selection scheme based on weighted importance sampling. Our experimental results demonstrate consistent improvements in the achievable block efficiency and token rates over baseline schemes in a number of scenarios. The transformer architecture (Vaswani et al., 2017) has revolutionized the field of natural language processing and deep learning. One of the key factors contributing to the success story of transformers, as opposed to prior recurrent-based architectures (Hochreiter and Schmidhuber, 1997; Chung et al., 2014), is their inherent train-time parallelization due to the attention mechanism. This allows for massive scaling and lead to the development of state-of-the-art Large Language Models (LLMs) (Touvron et al., 2023; Achiam et al., 2023; Brown et al., 2020; Chowdhery et al., 2023) which have demonstrated remarkable performance across a wide range of tasks.

Randomized ensemble classifiers (RECs), where one classifier is randomly selected during inference, have emerged as an attractive alternative to traditional ensembling methods for realizing adversarially robust classifiers with limited compute requirements. However, recent works have shown that existing methods for constructing RECs are more vulnerable than initially claimed, casting major doubts on their efficacy and prompting fundamental questions such as: "When are RECs useful?", "What are their limits?", and "How do we train them?". In this work, we first demystify RECs as we derive fundamental results regarding their theoretical limits, necessary and sufficient conditions for them to be useful, and more. Leveraging this new understanding, we propose a new boosting algorithm (BARRE) for training robust RECs, and empirically demonstrate its effectiveness at defending against strong $\ell_\infty$ norm-bounded adversaries across various network architectures and datasets. Our code can be found at https://github.com/hsndbk4/BARRE.

Deep neural networks have achieved state-of-the art performance on various computer vision tasks. However, their deployment on resource-constrained devices has been hindered due to their high computational and storage complexity. While various complexity reduction techniques, such as lightweight network architecture design and parameter quantization, have been successful in reducing the cost of implementing these networks, these methods have often been considered orthogonal. In reality, existing quantization techniques fail to replicate their success on lightweight architectures such as MobileNet. To this end, we present a novel fully differentiable non-uniform quantizer that can be seamlessly mapped onto efficient ternary-based dot product engines. We conduct comprehensive experiments on CIFAR-10, ImageNet, and Visual Wake Words datasets. The proposed quantizer (DBQ) successfully tackles the daunting task of aggressively quantizing lightweight networks such as MobileNetV1, MobileNetV2, and ShuffleNetV2. DBQ achieves state-of-the art results with minimal training overhead and provides the best (pareto-optimal) accuracy-complexity trade-off.