In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerful technique for constructing estimates of the Hessian which can be used to perform approximate Newton steps. This involves multiplication by a random sketching matrix, which introduces a trade-off between the computational cost of sketching and the convergence rate of the optimization algorithm. A theoretically desirable but practically much too expensive choice is to use a dense Gaussian sketching matrix, which produces unbiased estimates of the exact Newton step and which offers strong problem-independent convergence guarantees. We show that the Gaussian sketching matrix can be drastically sparsified, significantly reducing the computational cost of sketching, without substantially affecting its convergence properties. This approach, called Newton-LESS, is based on a recently introduced sketching technique: LEverage Score Sparsified (LESS) embeddings. We prove that Newton-LESS enjoys nearly the same problem-independent local convergence rate as Gaussian embeddings, not just up to constant factors but even down to lower order terms, for a large class of optimization tasks. In particular, this leads to a new state-of-the-art convergence result for an iterative least squares solver. Finally, we extend LESS embeddings to include uniformly sparsified random sign matrices which can be implemented efficiently and which perform well in numerical experiments.

Learning in a multi-target environment without prior knowledge about the targets requires a large amount of samples and makes generalization difficult. To solve this problem, it is important to be able to discriminate targets through semantic understanding. In this paper, we propose goal-aware cross-entropy (GACE) loss, that can be utilized in a self-supervised way using auto-labeled goal states alongside reinforcement learning. Based on the loss, we then devise goal-discriminative attention networks (GDAN) which utilize the goal-relevant information to focus on the given instruction. We evaluate the proposed methods on visual navigation and robot arm manipulation tasks with multi-target environments and show that GDAN outperforms the state-of-the-art methods in terms of task success ratio, sample efficiency, and generalization. Additionally, qualitative analyses demonstrate that our proposed method can help the agent become aware of and focus on the given instruction clearly, promoting goal-directed behavior.

Knowledge Distillation (KD) is a well-known training paradigm in deep neural networks where knowledge acquired by a large teacher model is transferred to a small student. KD has proven to be an effective technique to significantly improve the student's performance for various tasks including object detection. As such, KD techniques mostly rely on guidance at the intermediate feature level, which is typically implemented by minimizing an ℓp-norm distance between teacher and student activations during training. In this paper, we propose a replacement for the pixel-wise independent ℓp-norm based on the structural similarity (SSIM) [28]. By taking into account additional contrast and structural cues, feature importance, correlation and spatial dependence in the feature space are considered in the loss formulation. Extensive experiments on MSCOCO [16] demonstrate the effectiveness of our method across different training schemes and architectures. Our method adds only little computational overhead, is straightforward to implement and at the same time it significantly outperforms the standard ℓp-norms. Moreover, more complex state-of-the-art KD methods [13, 33] using attention-based sampling mechanisms are outperformed, including a +3.5 AP gain using a Faster R-CNN R-50 [21] compared to a vanilla model.

Distributionally robust optimization (DRO) is a widely-used approach to learn models that are robust against distribution shift. Compared with the standard optimization setting, the objective function in DRO is more difficult to optimize, and most of the existing theoretical results make strong assumptions on the loss function.

Knowledge Distillation (KD) aims at transferring the knowledge of a wellperformed neural network (the teacher) to a weaker one (the student). A peculiar phenomenon is that a more accurate model doesn't necessarily teach better, and temperature adjustment can neither alleviate the mismatched capacity. To explain this, we decompose the efficacy of KD into three parts: correct guidance, smooth regularization, and class discriminability. The last term describes the distinctness of wrong class probabilities that the teacher provides in KD. Complex teachers tend to be over-confident and traditional temperature scaling limits the efficacy of class discriminability, resulting in less discriminative wrong class probabilities. Therefore, we propose Asymmetric Temperature Scaling (ATS), which separately applies a higher/lower temperature to the correct/wrong class. ATS enlarges the variance of wrong class probabilities in the teacher's label and makes the students grasp the absolute affinities of wrong classes to the target class as discriminative as possible. Both theoretical analysis and extensive experimental results demonstrate the effectiveness of ATS.

Knowledge Distillation (KD) aims at transferring the knowledge of a wellperformed neural network (the teacher) to a weaker one (the student). A peculiar phenomenon is that a more accurate model doesn't necessarily teach better, and temperature adjustment can neither alleviate the mismatched capacity. To explain this, we decompose the efficacy of KD into three parts: correct guidance, smooth regularization, and class discriminability. The last term describes the distinctness of wrong class probabilities that the teacher provides in KD. Complex teachers tend to be over-confident and traditional temperature scaling limits the efficacy of class discriminability, resulting in less discriminative wrong class probabilities. Therefore, we propose Asymmetric Temperature Scaling (ATS), which separately applies a higher/lower temperature to the correct/wrong class. ATS enlarges the variance of wrong class probabilities in the teacher's label and makes the students grasp the absolute affinities of wrong classes to the target class as discriminative as possible. Both theoretical analysis and extensive experimental results demonstrate the effectiveness of ATS.