With the inspiration of vision transformers, the concept of depth-wise convolution revisits to provide a large Effective Receptive Field (ERF) using Large Kernel (LK) sizes for medical image segmentation. However, the segmentation performance might be saturated and even degraded as the kernel sizes scaled up (e.g., $21\times 21\times 21$) in a Convolutional Neural Network (CNN). We hypothesize that convolution with LK sizes is limited to maintain an optimal convergence for locality learning. While Structural Re-parameterization (SR) enhances the local convergence with small kernels in parallel, optimal small kernel branches may hinder the computational efficiency for training. In this work, we propose RepUX-Net, a pure CNN architecture with a simple large kernel block design, which competes favorably with current network state-of-the-art (SOTA) (e.g., 3D UX-Net, SwinUNETR) using 6 challenging public datasets. We derive an equivalency between kernel re-parameterization and the branch-wise variation in kernel convergence. Inspired by the spatial frequency in the human visual system, we extend to vary the kernel convergence into element-wise setting and model the spatial frequency as a Bayesian prior to re-parameterize convolutional weights during training. Specifically, a reciprocal function is leveraged to estimate a frequency-weighted value, which rescales the corresponding kernel element for stochastic gradient descent. From the experimental results, RepUX-Net consistently outperforms 3D SOTA benchmarks with internal validation (FLARE: 0.929 to 0.944), external validation (MSD: 0.901 to 0.932, KiTS: 0.815 to 0.847, LiTS: 0.933 to 0.949, TCIA: 0.736 to 0.779) and transfer learning (AMOS: 0.880 to 0.911) scenarios in Dice Score.

This paper presents a new generalization error analysis for the Decentralized Stochastic Gradient Descent (D-SGD) algorithm based on algorithmic stability. The obtained results largely improve upon state-of-the-art results, and even invalidate their claims that the communication graph has a detrimental effect on generalization. For instance, we show that in convex settings, D-SGD has the same generalization bounds as the classical SGD algorithm, no matter the choice of graph. We exhibit that this counter-intuitive result comes from considering the average of local parameters, which hides a final global averaging step incompatible with the decentralized scenario. In light of this observation, we advocate to analyze the supremum over local parameters and show that in this case, the graph does have an impact on the generalization. Unlike prior results, our analysis yields non-vacuous bounds even for non-connected graphs.

Previous work optimizes traditional active learning (AL) processes with incremental neural network architecture search (Active-iNAS) based on data complexity change, which improves the accuracy and learning efficiency. However, Active-iNAS trains several models and selects the model with the best generalization performance for querying the subsequent samples after each active learning cycle. The independent training processes lead to an insufferable computational budget, which is significantly inefficient and limits search flexibility and final performance. To address this issue, we propose a novel active strategy with the method called structured variational inference (SVI) or structured neural depth search (SNDS) whereby we could use the gradient descent method in neural network depth search during AL processes. At the same time, we theoretically demonstrate that the current VI-based methods based on the mean-field assumption could lead to poor performance. We apply our strategy using three querying techniques and three datasets and show that our strategy outperforms current methods.

Modern machine learning paradigms, such as deep learning, occur in or close to the interpolation regime, wherein the number of model parameters is much larger than the number of data samples. In this work, we propose a regularity condition within the interpolation regime which endows the stochastic gradient method with the same worst-case iteration complexity as the deterministic gradient method, while using only a single sampled gradient (or a minibatch) in each iteration. In contrast, all existing guarantees require the stochastic gradient method to take small steps, thereby resulting in a much slower linear rate of convergence. Finally, we demonstrate that our condition holds when training sufficiently wide feedforward neural networks with a linear output layer.

Most prior results on differentially private stochastic gradient descent (DP-SGD) are derived under the simplistic assumption of uniform Lipschitzness, i.e., the per-sample gradients are uniformly bounded. We generalize uniform Lipschitzness by assuming that the per-sample gradients have sample-dependent upper bounds, i.e., per-sample Lipschitz constants, which themselves may be unbounded. We provide principled guidance on choosing the clip norm in DP-SGD for convex over-parameterized settings satisfying our general version of Lipschitzness when the per-sample Lipschitz constants are bounded; specifically, we recommend tuning the clip norm only till values up to the minimum per-sample Lipschitz constant. This finds application in the private training of a softmax layer on top of a deep network pre-trained on public data. We verify the efficacy of our recommendation via experiments on 8 datasets. Furthermore, we provide new convergence results for DP-SGD on convex and nonconvex functions when the Lipschitz constants are unbounded but have bounded moments, i.e., they are heavy-tailed.

Stochastic gradient-based optimization methods, such as L-SVRG and its accelerated variant L-Katyusha (Kovalev et al., 2020), are widely used to train machine learning models. The theoretical and empirical performance of L-SVRG and L-Katyusha can be improved by sampling observations from a non-uniform distribution (Qian et al., 2021). However, designing a desired sampling distribution requires prior knowledge of smoothness constants, which can be computationally intractable to obtain in practice when the dimension of the model parameter is high. To address this issue, we propose an adaptive sampling strategy for L-SVRG and L-Katyusha that can learn the sampling distribution with little computational overhead, while allowing it to change with iterates, and at the same time does not require any prior knowledge of the problem parameters. We prove convergence guarantees for L-SVRG and L-Katyusha for convex objectives when the sampling distribution changes with iterates. Our results show that even without prior information, the proposed adaptive sampling strategy matches, and in some cases even surpasses, the performance of the sampling scheme in Qian et al. (2021). Extensive simulations support our theory and the practical utility of the proposed sampling scheme on real data.

Pruning schemes have been widely used in practice to reduce the complexity of trained models with a massive number of parameters. In fact, several practical studies have shown that if a pruned model is fine-tuned with some gradient-based updates it generalizes well to new samples. Although the above pipeline, which we refer to as pruning + fine-tuning, has been extremely successful in lowering the complexity of trained models, there is very little known about the theory behind this success. In this paper, we address this issue by investigating the pruning + fine-tuning framework on the overparameterized matrix sensing problem with the ground truth $U_\star \in \mathbb{R}^{d \times r}$ and the overparameterized model $U \in \mathbb{R}^{d \times k}$ with $k \gg r$. We study the approximate local minima of the mean square error, augmented with a smooth version of a group Lasso regularizer, $\sum_{i=1}^k \| U e_i \|_2$. In particular, we provably show that pruning all the columns below a certain explicit $\ell_2$-norm threshold results in a solution $U_{\text{prune}}$ which has the minimum number of columns $r$, yet close to the ground truth in training loss. Moreover, in the subsequent fine-tuning phase, gradient descent initialized at $U_{\text{prune}}$ converges at a linear rate to its limit. While our analysis provides insights into the role of regularization in pruning, we also show that running gradient descent in the absence of regularization results in models which {are not suitable for greedy pruning}, i.e., many columns could have their $\ell_2$ norm comparable to that of the maximum. To the best of our knowledge, our results provide the first rigorous insights on why greedy pruning + fine-tuning leads to smaller models which also generalize well.

Exploration remains a key challenge in deep reinforcement learning (RL). Optimism in the face of uncertainty is a well-known heuristic with theoretical guarantees in the tabular setting, but how best to translate the principle to deep reinforcement learning, which involves online stochastic gradients and deep network function approximators, is not fully understood. In this paper we propose a new, differentiable optimistic objective that when optimized yields a policy that provably explores efficiently, with guarantees even under function approximation. Our new objective is a zero-sum two-player game derived from endowing the agent with an epistemic-risk-seeking utility function, which converts uncertainty into value and encourages the agent to explore uncertain states. We show that the solution to this game minimizes an upper bound on the regret, with the 'players' each attempting to minimize one component of a particular regret decomposition. We derive a new model-free algorithm which we call 'epistemic-risk-seeking actor-critic' (ERSAC), which is simply an application of simultaneous stochastic gradient ascent-descent to the game. Finally, we discuss a recipe for incorporating off-policy data and show that combining the risk-seeking objective with replay data yields a double benefit in terms of statistical efficiency. We conclude with some results showing good performance of a deep RL agent using the technique on the challenging 'DeepSea' environment, showing significant performance improvements even over other efficient exploration techniques, as well as improved performance on the Atari benchmark.

We study the SAM (Sharpness-Aware Minimization) optimizer which has recently attracted a lot of interest due to its increased performance over more classical variants of stochastic gradient descent. Our main contribution is the derivation of continuous-time models (in the form of SDEs) for SAM and two of its variants, both for the full-batch and mini-batch settings. We demonstrate that these SDEs are rigorous approximations of the real discrete-time algorithms (in a weak sense, scaling linearly with the learning rate). Using these models, we then offer an explanation of why SAM prefers flat minima over sharp ones~--~by showing that it minimizes an implicitly regularized loss with a Hessian-dependent noise structure. Finally, we prove that SAM is attracted to saddle points under some realistic conditions. Our theoretical results are supported by detailed experiments.

Understanding the gradient variance of blackbox Despite the advances of BBVI, little is known about its theoretical variational inference (BBVI) is a crucial step properties. Even when restricted to the locationscale for establishing its convergence and developing family (Definition 2), it is unknown whether BBVI algorithmic improvements. However, existing is guaranteed to converge without having to modify the studies have yet to show that the gradient variance algorithms used in practice, for example, by enforcing of BBVI satisfies the conditions used to bounded domains, bounded support, bounded gradients, study the convergence of stochastic gradient descent and such. This theoretical insight is necessary since BBVI (SGD), the workhorse of BBVI. In this methods are known to be less robust (Yao et al., 2018; work, we show that BBVI satisfies a matching Dhaka et al., 2020; Welandawe et al., 2022; Dhaka et al., bound corresponding to the condition used 2021; Domke, 2020) compared to other inference methods in the SGD literature when applied to smooth and such as Markov chain Monte Carlo. Although progress has quadratically-growing log-likelihoods. Our results been made to formalize the theory of BBVI with some generality, generalize to nonlinear covariance parameterizations the gap between our understanding of BBVI and the widely used in the practice of BBVI.