Representations that are invariant to translation, scale and other transformations, can considerably reduce the sample complexity of learning, allowing recognition of new object classes from very few examples - a hallmark of human recognition. Empirical estimates of one-dimensional projections of the distribution induced by a group of affine transformations are proven to represent a unique and invariant signature associated with an image. We show how projections yielding invariant signatures for future images can be learned automatically, and updated continuously, during unsupervised visual experience. A module performing filtering and pooling, like simple and complex cells as proposed by Hubel and Wiesel, can compute such estimates. Under this view, a pooling stage estimates a one-dimensional probability distribution. Invariance from observations through a restricted window is equivalent to a sparsity property w.r.t. to a transformation, which yields templates that are a) Gabor for optimal simultaneous invariance to translation and scale or b) very specific for complex, class-dependent transformations such as rotation in depth of faces. Hierarchical architectures consisting of this basic Hubel-Wiesel module inherit its properties of invariance, stability, and discriminability while capturing the compositional organization of the visual world in terms of wholes and parts, and are invariant to complex transformations that may only be locally affine. The theory applies to several existing deep learning convolutional architectures for image and speech recognition. It also suggests that the main computational goal of the ventral stream of visual cortex is to provide a hierarchical representation of new objects which is invariant to transformations, stable, and discriminative for recognition - this representation may be learned in an unsupervised way from natural visual experience.

我们提出了一种基于无监督自动学习的方法，可以学习出具有小样本复杂度的好的表示方法，在视觉对象识别等领域可以得到应用。通过无监督学习期间存储的一组模板，可以对每个图像块计算一种不变而又唯一的（有区分性的）签名，从而从很少的有标记例子中学习图像识别。

分层体系结构中不变表示的无监督学习