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Werestructured the textsuch that the NSM isbetter and earlier introduced inthe main text, add derivation7 details and provide the experimental results. Previously unexplained terms (e.g., the offset parameter to the noise)8 are now elaborated. We have not attempted NSMs in a (deep) RL framework as we are not aware of convincing9 theoretical/practical work on successful deep RL with binary neural networks. Reviewer 2 Abbreviation SNN (Stochastic Neural Network) was changed to StNN. We suggest "Inherent Weight17 Normalization inStochastic Neural Networks" asalessconfusing title.

Then we use a 3D garment decoder to decode the sewing pattern embedding into a 3D garment using the UV-position maps with masks.

Multiplicative stochasticity such as Dropout improves the robustness and gener-alizability deep neural networks. Here, we further demonstrate that always-on multiplicative stochasticity combined with simple threshold neurons provide a sufficient substrate for deep learning machines. We call such models Neural Sampling Machines (NSM). We find that the probability of activation of the NSM exhibits a self-normalizing property that mirrors Weight Normalization, a previously studied mechanism that fulfills many of the features of Batch Normalization in an online fashion. The normalization of activities during training speeds up convergence by preventing internal covariate shift caused by changes in the distribution of inputs. The always-on stochasticity of the NSM confers the following advantages: the network is identical in the inference and learning phases, making the NSM a suitable substrate for continual learning, it can exploit stochasticity inherent to a physical substrate such as analog non-volatile memories for in memory computing, and it is suitable for Monte Carlo sampling, while requiring almost exclusively addition and comparison operations. We demonstrate NSMs on standard classification benchmarks (MNIST and CIFAR) and event-based classification benchmarks (N-MNIST and DVS Gestures). Our results show that NSMs perform comparably or better than conventional artificial neural networks with the same architecture.

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Thank you all reviewers for your in-depth comments. We fixed the typos and abbreviations indicated by reviewer 1 in the text. Previously unexplained terms ( e.g., the offset parameter to the noise) We improved the SI by elaborating on Figure 3, fixing missing sections (4.3) and detailing the DVS Abbreviation SNN (Stochastic Neural Network) was changed to StNN. Klambauer et al. in 2017 indeed introduced Our work is different in terms of objective and results. Regarding Eq. (7), our calculations confirm the derivative w.r.t.

In practical applications, lattice quantizers leverage discrete lattice points to approximate arbitrary points in the lattice. An effective lattice quantizer significantly enhances both the accuracy and efficiency of these approximations. In the context of high-dimensional lattice quantization, previous work proposed utilizing low-dimensional optimal lattice quantizers and addressed the challenge of determining the optimal length ratio in orthogonal splicing. Notably, it was demonstrated that fixed length ratios and orthogonality yield suboptimal results when combining low-dimensional lattices. Building on this foundation, another approach employed gradient descent to identify optimal lattices, which inspired us to explore the use of neural networks to discover matrices that outperform those obtained from orthogonal splicing methods. We propose two novel approaches to tackle this problem: the Household Algorithm and the Matrix Exp Algorithm. Our results indicate that both the Household Algorithm and the Matrix Exp Algorithm achieve improvements in lattice quantizers across dimensions 13, 15, 17 to 19, 21, and 22. Moreover, the Matrix Exp Algorithm demonstrates superior efficacy in high-dimensional settings.

In this paper, we propose a novel Neural Sewing Machine (NSM), a learning-based framework for structure-preserving 3D garment modeling, which is capable of learning representations for garments with diverse shapes and topologies and is successfully applied to 3D garment reconstruction and controllable manipulation. To model generic garments, we first obtain sewing pattern embedding via a unified sewing pattern encoding module, as the sewing pattern can accurately describe the intrinsic structure and the topology of the 3D garment. Then we use a 3D garment decoder to decode the sewing pattern embedding into a 3D garment using the UV-position maps with masks. To preserve the intrinsic structure of the predicted 3D garment, we introduce an inner-panel structure-preserving loss, an inter-panel structure-preserving loss, and a surface-normal loss in the learning process of our framework. We evaluate NSM on the public 3D garment dataset with sewing patterns with diverse garment shapes and categories.

Multiplicative stochasticity such as Dropout improves the robustness and gener- alizability deep neural networks. Here, we further demonstrate that always-on multiplicative stochasticity combined with simple threshold neurons provide a suf- ficient substrate for deep learning machines. We call such models Neural Sampling Machines (NSM). We find that the probability of activation of the NSM exhibits a self-normalizing property that mirrors Weight Normalization, a previously studied mechanism that fulfills many of the features of Batch Normalization in an online fashion. The normalization of activities during training speeds up convergence by preventing internal covariate shift caused by changes in the distribution of inputs.