The anisotropic Kerr nonlinear refractive index of the beta-barium borate (\beta-BaB2O4) nonlinear crystal

We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (\beta-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant $\chi^{(3)}$ cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments in the literature are analyzed and we correct the data from some of the experiments for contributions from cascading as well as for updated material parameters. We find that the Kerr nonlinear tensor component responsible for self-phase modulation in cascading is considerably larger than what has been used to date. We evaluate the impact of using such a cubic anisotropic response in ultrafast cascading experiments.Comment: Updated version, comments on experiments from the literature welcom

Generalized Nonlinear Wave Equation in Frequency Domain

We interpret the forward Maxwell equation with up to third order induced polarizations and get so called nonlinear wave equation in frequency domain (NWEF), which is based on Maxwell wave equation and using slowly varying spectral amplitude approximation. The NWEF is generalized in concept as it directly describes the electric field dynamics rather than the envelope dynamics and because it concludes most current-interested nonlinear processes such as three-wave mixing, four-wave-mixing and material Raman effects. We give two sets of NWEF, one is a 1+1D equation describing the (approximated) planar wave propagation in nonlinear bulk material and the other corresponds to the propagation in a waveguide structure.Comment: Equation Derivation

Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities

We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency. Numerical results show that compressed pulses with less than three-cycle duration can be achieved even when the compression factor is very large, and in contrast to standard soliton compression, these compressed pulses have minimal pedestal and high quality factor

Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

We interpret the purely spectral forward Maxwell equation with up to 3${^{\rm rd}}$ order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named nonlinear wave equation in frequency domain, includes both quadratic and cubic nonlinearities, delayed Raman effects and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due to competition between self-steepening, Raman effects and self-steepening-like effects from cascading originating in the group-velocity mismatch between the pump and second harmonic. We analyze the first-order contributions, and show that this balance can be broken to create fast or slow pulses. Through further simulations we demonstrate few-cycle compressed solitons in extremely short crystals, where spectral phenomena such as blue/red shifting, non-stationary radiation in accordance with the non-local phase matching condition and dispersive-wave generation are observed and marked, which help improving the experimental knowledge of cascading nonlinear soliton pulse compression

RobustMQ: Benchmarking Robustness of Quantized Models

Quantization has emerged as an essential technique for deploying deep neural networks (DNNs) on devices with limited resources. However, quantized models exhibit vulnerabilities when exposed to various noises in real-world applications. Despite the importance of evaluating the impact of quantization on robustness, existing research on this topic is limited and often disregards established principles of robustness evaluation, resulting in incomplete and inconclusive findings. To address this gap, we thoroughly evaluated the robustness of quantized models against various noises (adversarial attacks, natural corruptions, and systematic noises) on ImageNet. The comprehensive evaluation results empirically provide valuable insights into the robustness of quantized models in various scenarios, for example: (1) quantized models exhibit higher adversarial robustness than their floating-point counterparts, but are more vulnerable to natural corruptions and systematic noises; (2) in general, increasing the quantization bit-width results in a decrease in adversarial robustness, an increase in natural robustness, and an increase in systematic robustness; (3) among corruption methods, \textit{impulse noise} and \textit{glass blur} are the most harmful to quantized models, while \textit{brightness} has the least impact; (4) among systematic noises, the \textit{nearest neighbor interpolation} has the highest impact, while bilinear interpolation, cubic interpolation, and area interpolation are the three least harmful. Our research contributes to advancing the robust quantization of models and their deployment in real-world scenarios.Comment: 15 pages, 7 figure

Isolation and Induction: Training Robust Deep Neural Networks against Model Stealing Attacks

Despite the broad application of Machine Learning models as a Service (MLaaS), they are vulnerable to model stealing attacks. These attacks can replicate the model functionality by using the black-box query process without any prior knowledge of the target victim model. Existing stealing defenses add deceptive perturbations to the victim's posterior probabilities to mislead the attackers. However, these defenses are now suffering problems of high inference computational overheads and unfavorable trade-offs between benign accuracy and stealing robustness, which challenges the feasibility of deployed models in practice. To address the problems, this paper proposes Isolation and Induction (InI), a novel and effective training framework for model stealing defenses. Instead of deploying auxiliary defense modules that introduce redundant inference time, InI directly trains a defensive model by isolating the adversary's training gradient from the expected gradient, which can effectively reduce the inference computational cost. In contrast to adding perturbations over model predictions that harm the benign accuracy, we train models to produce uninformative outputs against stealing queries, which can induce the adversary to extract little useful knowledge from victim models with minimal impact on the benign performance. Extensive experiments on several visual classification datasets (e.g., MNIST and CIFAR10) demonstrate the superior robustness (up to 48% reduction on stealing accuracy) and speed (up to 25.4x faster) of our InI over other state-of-the-art methods. Our codes can be found in https://github.com/DIG-Beihang/InI-Model-Stealing-Defense.Comment: Accepted by ACM Multimedia 202

Outlier Suppression+: Accurate quantization of large language models by equivalent and optimal shifting and scaling

Quantization of transformer language models faces significant challenges due to the existence of detrimental outliers in activations. We observe that these outliers are asymmetric and concentrated in specific channels. To address this issue, we propose the Outlier Suppression+ framework. First, we introduce channel-wise shifting and scaling operations to eliminate asymmetric presentation and scale down problematic channels. We demonstrate that these operations can be seamlessly migrated into subsequent modules while maintaining equivalence. Second, we quantitatively analyze the optimal values for shifting and scaling, taking into account both the asymmetric property and quantization errors of weights in the next layer. Our lightweight framework can incur minimal performance degradation under static and standard post-training quantization settings. Comprehensive results across various tasks and models reveal that our approach achieves near-floating-point performance on both small models, such as BERT, and large language models (LLMs) including OPTs, BLOOM, and BLOOMZ at 8-bit and 6-bit settings. Furthermore, we establish a new state of the art for 4-bit BERT