Ensemble learning leverages multiple models (i.e., weak learners) on a common
machine learning task to enhance prediction performance. Basic ensembling
approaches average the weak learners outputs, while more sophisticated ones
stack a machine learning model in between the weak learners outputs and the
final prediction. This work fuses both aforementioned frameworks. We introduce
an aggregated f-average (AFA) shallow neural network which models and combines
different types of averages to perform an optimal aggregation of the weak
learners predictions. We emphasise its interpretable architecture and simple
training strategy, and illustrate its good performance on the problem of
few-shot class incremental learning.

使用集成学习方法和聚合方法相结合的浅层神经网络在少样本类别增量学习问题上表现出良好性能。

解释性集成的聚合 f - 平均神经网络

Aggregated f-average Neural Network for Interpretable Ensembling

We present an approach to identify concise equations from data using a
shallow neural network approach. In contrast to ordinary black-box regression,
this approach allows understanding functional relations and generalizing them
from observed data to unseen parts of the parameter space. We show how to
extend the class of learnable equations for a recently proposed equation
learning network to include divisions, and we improve the learning and model
selection strategy to be useful for challenging real-world data. For systems
governed by analytical expressions, our method can in many cases identify the
true underlying equation and extrapolate to unseen domains. We demonstrate its
effectiveness by experiments on a cart-pendulum system, where only 2 random
rollouts are required to learn the forward dynamics and successfully achieve
the swing-up task.

使用浅层神经网络的方法识别数据中的简明方程，并扩展可学习的方程类别以包括除法，并改进学习和模型选择策略以用于挑战性的真实数据。

学习外推和控制方程

Learning Equations for Extrapolation and Control

In this paper we study the problem of learning a shallow artificial neural
network that best fits a training data set. We study this problem in the
over-parameterized regime where the number of observations are fewer than the
number of parameters in the model. We show that with quadratic activations the
optimization landscape of training such shallow neural networks has certain
favorable characteristics that allow globally optimal models to be found
efficiently using a variety of local search heuristics. This result holds for
an arbitrary training data of input/output pairs. For differentiable activation
functions we also show that gradient descent, when suitably initialized,
converges at a linear rate to a globally optimal model. This result focuses on
a realizable model where the inputs are chosen i.i.d. from a Gaussian
distribution and the labels are generated according to planted weight
coefficients.

研究浅层神经网络在过参数化情况下，如何使用二次激活函数进行训练并找到全局最优解，结果表明此方法适用于具有任意输入 / 输出对的任何训练数据，并可使用各种本地搜索启发式方法高效地找到全局最优解。同时，对於差分激活函数，我们也证明了梯度下降法在得到合适的初值后可以以线性速度收敛到全局最优解，它的输入来自符合高斯分布的选定属性且标记是通过种植的重量系数生成的。