作为一种强大的建模方法，分段线性神经网络（PWLNNS）已在各个领域都被证明是成功的，最近在深度学习中。为了应用PWLNN方法，长期以来一直研究了表示和学习。 1977年，规范表示率先通过增量设计学到了浅层PWLNN的作品，但禁止使用大规模数据的应用。 2010年，纠正的线性单元（RELU）提倡在深度学习中PWLNN的患病率。从那以后，PWLNNS已成功地应用于广泛的任务并实现了有利的表现。在本引物中，我们通过将作品分组为浅网络和深层网络来系统地介绍PWLNNS的方法。首先，不同的PWLNN表示模型是由详细示例构建的。使用PWLNNS，提出了学习数据的学习算法的演变，并且基本理论分析遵循深入的理解。然后，将代表性应用与讨论和前景一起引入。

One of the key challenges in deploying RL to real-world applications is to adapt to variations of unknown environment contexts, such as changing terrains in robotic tasks and fluctuated bandwidth in congestion control. Existing works on adaptation to unknown environment contexts either assume the contexts are the same for the whole episode or assume the context variables are Markovian. However, in many real-world applications, the environment context usually stays stable for a stochastic period and then changes in an abrupt and unpredictable manner within an episode, resulting in a segment structure, which existing works fail to address. To leverage the segment structure of piecewise stable context in real-world applications, in this paper, we propose a \textit{\textbf{Se}gmented \textbf{C}ontext \textbf{B}elief \textbf{A}ugmented \textbf{D}eep~(SeCBAD)} RL method. Our method can jointly infer the belief distribution over latent context with the posterior over segment length and perform more accurate belief context inference with observed data within the current context segment. The inferred belief context can be leveraged to augment the state, leading to a policy that can adapt to abrupt variations in context. We demonstrate empirically that SeCBAD can infer context segment length accurately and outperform existing methods on a toy grid world environment and Mujuco tasks with piecewise-stable context.

尽管已经提出了许多方法来增强对抗性扰动的可转移性，但这些方法是以启发式方式设计的，并且尚不清楚改善对抗性转移性的基本机制。本文总结了在统一视图中以十二个以前的可传递性提高方法共享的共同机制，即这些方法都减少了区域对抗性扰动之间的游戏理论相互作用。为此，我们专注于区域对抗扰动之间所有相互作用的攻击效用，我们首先发现并证明了对抗传递性与相互作用的攻击效用之间的负相关性。基于这一发现，我们从理论上证明并从经验上验证了十二种以前的可传递性提高方法均减少了区域对抗扰动之间的相互作用。更重要的是，我们将相互作用的减少视为增强对抗性转移性的基本原因。此外，我们设计了交互损失，以直接惩罚攻击过程中区域对抗扰动之间的相互作用。实验结果表明，相互作用损失显着提高了对抗扰动的转移性。

世界模型学习基于视觉的交互式系统中动作的后果。但是，在诸如自动驾驶之类的实际情况下，通常存在独立于动作信号的不可控制的动态，因此很难学习有效的世界模型。为了解决这个问题，我们提出了一种新颖的增强学习方法，名为Iso-Dream，该方法在两个方面改善了梦境到控制框架。首先，通过优化逆动力学，我们鼓励世界模型学习隔离状态过渡分支的时空变化的可控和不可控制的来源。其次，我们优化了代理在世界模型的潜在想象中的行为。具体而言，为了估算状态值，我们将不可控制状态推出到未来，并将其与当前可控状态相关联。这样，动态来源的隔离可以极大地使代理商的长期决策受益，例如一种自动驾驶汽车，可以通过预测其他车辆的移动来避免潜在的风险。实验表明，ISO-Dream可以有效地解耦混合动力学，并且在广泛的视觉控制和预测域中明显优于现有方法。

理论上，从理论上分析$ \ ell_ {1} $的典型学习性能 - 正规化的线性回归（$ \ ell_1 $ -linr），用于使用统计力学中的副本方法进行模型选择。对于顺磁阶段的典型随机常规图，获得了对$ \ ell_1 $ -LinR的典型样本复杂度的准确估计。值得注意的是，尽管模型拼写错误，$ \ ell_1 $ -linr是模型选择，其与$ \ ell_ {1} $ - 正常化的逻辑回归（$ \ ell_1 $ -logr），即，$ m = \ mathcal {o} \ left（\ log n \ light）$，其中$ n $是ising模型的变量数。此外，我们提供了一种有效的方法，可以准确地预测$ \ ell_1 $ -Linr的非渐近行为，以便适度$ M，N $，如精度和召回。仿真在理论预测和实验结果之间表现出相当愉快的一致性，即使对于具有许多环路的图表，也支持我们的研究结果。虽然本文主要侧重于$ \ ell_1 $ -Linr，但我们的方法很容易适用于精确地表征广泛类别的$ \ ell_ {1} $的典型学习表演 - 正常化$ M $-estimators，包括$ \ ell_1 $ - LogR和互动筛查。

With the fast development of big data, it has been easier than before to learn the optimal decision rule by updating the decision rule recursively and making online decisions. We study the online statistical inference of model parameters in a contextual bandit framework of sequential decision-making. We propose a general framework for online and adaptive data collection environment that can update decision rules via weighted stochastic gradient descent. We allow different weighting schemes of the stochastic gradient and establish the asymptotic normality of the parameter estimator. Our proposed estimator significantly improves the asymptotic efficiency over the previous averaged SGD approach via inverse probability weights. We also conduct an optimality analysis on the weights in a linear regression setting. We provide a Bahadur representation of the proposed estimator and show that the remainder term in the Bahadur representation entails a slower convergence rate compared to classical SGD due to the adaptive data collection.

Learning efficient and interpretable policies has been a challenging task in reinforcement learning (RL), particularly in the visual RL setting with complex scenes. While neural networks have achieved competitive performance, the resulting policies are often over-parameterized black boxes that are difficult to interpret and deploy efficiently. More recent symbolic RL frameworks have shown that high-level domain-specific programming logic can be designed to handle both policy learning and symbolic planning. However, these approaches rely on coded primitives with little feature learning, and when applied to high-dimensional visual scenes, they can suffer from scalability issues and perform poorly when images have complex object interactions. To address these challenges, we propose \textit{Differentiable Symbolic Expression Search} (DiffSES), a novel symbolic learning approach that discovers discrete symbolic policies using partially differentiable optimization. By using object-level abstractions instead of raw pixel-level inputs, DiffSES is able to leverage the simplicity and scalability advantages of symbolic expressions, while also incorporating the strengths of neural networks for feature learning and optimization. Our experiments demonstrate that DiffSES is able to generate symbolic policies that are simpler and more and scalable than state-of-the-art symbolic RL methods, with a reduced amount of symbolic prior knowledge.

We consider the problem of estimating a multivariate function $f_0$ of bounded variation (BV), from noisy observations $y_i = f_0(x_i) + z_i$ made at random design points $x_i \in \mathbb{R}^d$, $i=1,\ldots,n$. We study an estimator that forms the Voronoi diagram of the design points, and then solves an optimization problem that regularizes according to a certain discrete notion of total variation (TV): the sum of weighted absolute differences of parameters $\theta_i,\theta_j$ (which estimate the function values $f_0(x_i),f_0(x_j)$) at all neighboring cells $i,j$ in the Voronoi diagram. This is seen to be equivalent to a variational optimization problem that regularizes according to the usual continuum (measure-theoretic) notion of TV, once we restrict the domain to functions that are piecewise constant over the Voronoi diagram. The regression estimator under consideration hence performs (shrunken) local averaging over adaptively formed unions of Voronoi cells, and we refer to it as the Voronoigram, following the ideas in Koenker (2005), and drawing inspiration from Tukey's regressogram (Tukey, 1961). Our contributions in this paper span both the conceptual and theoretical frontiers: we discuss some of the unique properties of the Voronoigram in comparison to TV-regularized estimators that use other graph-based discretizations; we derive the asymptotic limit of the Voronoi TV functional; and we prove that the Voronoigram is minimax rate optimal (up to log factors) for estimating BV functions that are essentially bounded.

Gradient-based explanation is the cornerstone of explainable deep networks, but it has been shown to be vulnerable to adversarial attacks. However, existing works measure the explanation robustness based on $\ell_p$-norm, which can be counter-intuitive to humans, who only pay attention to the top few salient features. We propose explanation ranking thickness as a more suitable explanation robustness metric. We then present a new practical adversarial attacking goal for manipulating explanation rankings. To mitigate the ranking-based attacks while maintaining computational feasibility, we derive surrogate bounds of the thickness that involve expensive sampling and integration. We use a multi-objective approach to analyze the convergence of a gradient-based attack to confirm that the explanation robustness can be measured by the thickness metric. We conduct experiments on various network architectures and diverse datasets to prove the superiority of the proposed methods, while the widely accepted Hessian-based curvature smoothing approaches are not as robust as our method.

Benefiting from its single-photon sensitivity, single-photon avalanche diode (SPAD) array has been widely applied in various fields such as fluorescence lifetime imaging and quantum computing. However, large-scale high-fidelity single-photon imaging remains a big challenge, due to the complex hardware manufacture craft and heavy noise disturbance of SPAD arrays. In this work, we introduce deep learning into SPAD, enabling super-resolution single-photon imaging over an order of magnitude, with significant enhancement of bit depth and imaging quality. We first studied the complex photon flow model of SPAD electronics to accurately characterize multiple physical noise sources, and collected a real SPAD image dataset (64 $\times$ 32 pixels, 90 scenes, 10 different bit depth, 3 different illumination flux, 2790 images in total) to calibrate noise model parameters. With this real-world physical noise model, we for the first time synthesized a large-scale realistic single-photon image dataset (image pairs of 5 different resolutions with maximum megapixels, 17250 scenes, 10 different bit depth, 3 different illumination flux, 2.6 million images in total) for subsequent network training. To tackle the severe super-resolution challenge of SPAD inputs with low bit depth, low resolution, and heavy noise, we further built a deep transformer network with a content-adaptive self-attention mechanism and gated fusion modules, which can dig global contextual features to remove multi-source noise and extract full-frequency details. We applied the technique on a series of experiments including macroscopic and microscopic imaging, microfluidic inspection, and Fourier ptychography. The experiments validate the technique's state-of-the-art super-resolution SPAD imaging performance, with more than 5 dB superiority on PSNR compared to the existing methods.