We introduce a modified incremental learning algorithm for evolving Granular
Neural Network Classifiers (eGNN-C+). We use double-boundary hyper-boxes to
represent granules, and customize the adaptation procedures to enhance the
robustness of outer boxes for data coverage and noise suppression, while
ensuring that inner boxes remain flexible to capture drifts. The classifier
evolves from scratch, incorporates new classes on the fly, and performs local
incremental feature weighting. As an application, we focus on the
classification of emotion-related patterns within electroencephalogram (EEG)
signals. Emotion recognition is crucial for enhancing the realism and
interactivity of computer systems. We extract features from the Fourier
spectrum of EEG signals obtained from 28 individuals engaged in playing
computer games -- a public dataset. Each game elicits a different predominant
emotion: boredom, calmness, horror, or joy. We analyze individual electrodes,
time window lengths, and frequency bands to assess the accuracy and
interpretability of resulting user-independent neural models. The findings
indicate that both brain hemispheres assist classification, especially
electrodes on the temporal (T8) and parietal (P7) areas, alongside
contributions from frontal and occipital electrodes. While patterns may
manifest in any band, the Alpha (8-13Hz), Delta (1-4Hz), and Theta (4-8Hz)
bands, in this order, exhibited higher correspondence with the emotion classes.
The eGNN-C+ demonstrates effectiveness in learning EEG data. It achieves an
accuracy of 81.7% and a 0.0029 II interpretability using 10-second time
windows, even in face of a highly-stochastic time-varying 4-class
classification problem.

我们介绍了一种改进的增量学习算法，用于进化颗粒神经网络分类器（eGNN-C+）。我们使用双边界超立方体来表示颗粒，并自定义适应过程以增强外部边界对数据覆盖和噪声抑制的鲁棒性，同时确保内部边界保持灵活以捕捉漂移。分类器从头开始进化，即时融入新的类别，并进行局部增量特征加权。作为应用，我们专注于对脑电图（EEG）信号中与情绪相关的模式的分类。情绪识别对于增强计算机系统的逼真性和交互性至关重要。我们从 28 个参与玩电脑游戏的个体获得的 EEG 信号的傅立叶频谱中提取特征 - 这是一个公共数据集。每个游戏引发不同的主导情绪：无聊、平静、恐惧或喜悦。我们分析个体电极、时间窗口长度和频带，以评估用户无关的神经模型的准确性和可解释性。研究结果表明，两个大脑半球都有助于分类，尤其是颞叶（T8）和顶叶（P7）区域的电极，并且前额叶和枕叶电极也对分类有贡献。虽然模式可能表现在任何频带上，但阿尔法波（8-13Hz）、δ（1-4Hz）波和 θ（4-8Hz）波以此顺序与情绪类别有更高的相关性。eGNN-C + 在学习 EEG 数据方面表现出有效性。即使在高度随机的时间变化的 4 类分类问题面前，它在 10 秒时间窗口内达到了 81.7% 的准确性和 0.0029 II 的可解释性。

EGNN-C+：可解释的演化粒状神经网络及其在弱监督脑电数据流分类中的应用

EGNN-C+: Interpretable Evolving Granular Neural Network and Application  in Classification of Weakly-Supervised EEG Data Streams

We present a novel approach to non-convex optimization with certificates,
which handles smooth functions on the hypercube or on the torus. Unlike
traditional methods that rely on algebraic properties, our algorithm exploits
the regularity of the target function intrinsic in the decay of its Fourier
spectrum. By defining a tractable family of models, we allow at the same time
to obtain precise certificates and to leverage the advanced and powerful
computational techniques developed to optimize neural networks. In this way the
scalability of our approach is naturally enhanced by parallel computing with
GPUs. Our approach, when applied to the case of polynomials of moderate
dimensions but with thousands of coefficients, outperforms the state-of-the-art
optimization methods with certificates, as the ones based on Lasserre's
hierarchy, addressing problems intractable for the competitors.

通过利用目标函数傅里叶频谱在衰减方面的本质，我们提出了一种新颖的具有证书的非凸优化方法，该方法处理超立方体或环面上的平滑函数。

GloptiNets：带证书的可扩展非凸优化

GloptiNets: Scalable Non-Convex Optimization with Certificates

This paper presents a significant improvement for the synthesis of texture
images using convolutional neural networks (CNNs), making use of constraints on
the Fourier spectrum of the results. More precisely, the texture synthesis is
regarded as a constrained optimization problem, with constraints conditioning
both the Fourier spectrum and statistical features learned by CNNs. In contrast
with existing methods, the presented method inherits from previous CNN
approaches the ability to depict local structures and fine scale details, and
at the same time yields coherent large scale structures, even in the case of
quasi-periodic images. This is done at no extra computational cost. Synthesis
experiments on various images show a clear improvement compared to a recent
state-of-the art method relying on CNN constraints only.

本文使用卷积神经网络和傅里叶频谱以及统计特征约束来实现纹理合成，并实验表明与现有方法相比具有更好的性能。

卷积神经网络和频谱约束下的纹理合成

Texture Synthesis Through Convolutional Neural Networks and Spectrum  Constraints

In this article we develop quantum algorithms for learning and testing
juntas, i.e. Boolean functions which depend only on an unknown set of k out of
n input variables. Our aim is to develop efficient algorithms:
- whose sample complexity has no dependence on n, the dimension of the domain
the Boolean functions are defined over;
- with no access to any classical or quantum membership ("black-box")
queries. Instead, our algorithms use only classical examples generated
uniformly at random and fixed quantum superpositions of such classical
examples;
- which require only a few quantum examples but possibly many classical
random examples (which are considered quite "cheap" relative to quantum
examples).
Our quantum algorithms are based on a subroutine FS which enables sampling
according to the Fourier spectrum of f; the FS subroutine was used in earlier
work of Bshouty and Jackson on quantum learning. Our results are as follows:
- We give an algorithm for testing k-juntas to accuracy $\epsilon$ that uses
$O(k/\epsilon)$ quantum examples. This improves on the number of examples used
by the best known classical algorithm.
- We establish the following lower bound: any FS-based k-junta testing
algorithm requires $\Omega(\sqrt{k})$ queries.
- We give an algorithm for learning $k$-juntas to accuracy $\epsilon$ that
uses $O(\epsilon^{-1} k\log k)$ quantum examples and $O(2^k \log(1/\epsilon))$
random examples. We show that this learning algorithms is close to optimal by
giving a related lower bound.

该研究文章讨论了发展基于量子算法用于学习和测试仅依赖于 k 个输入变量的布尔函数（即 juntas）的有效算法，并着重于在没有经典或量子会员资格（“黑盒”）查询的情况下实现高效算法，其中量子算法仅需少量输入样本但可能需要许多经典随机样本，并阐述了算法的上下界。