In machine learning and computer vision, M-theory is a learning framework inspired by feed-forward processing in the ventral stream of visual cortex and originally developed for recognition and classification of objects in visual scenes. M-theory was later applied to other areas, such as speech recognition. On certain image recognition tasks, algorithms based on a specific instantiation of M-theory, HMAX, achieved human-level performance. The core principle of M-theory is extracting representations invariant under various transformations of images (translation, scale, 2D and 3D rotation and others). In contrast with other approaches using invariant representations, in M-theory they are not hardcoded into the algorithms, but learned. M-theory also shares some principles with compressed sensing. The theory proposes multilayered hierarchical learning architecture, similar to that of visual cortex.
Intuition
Invariant representations A great challenge in visual recognition tasks is that the same object can be seen in a variety of conditions. It can be seen from different distances, different viewpoints, under different lighting, partially occluded, etc. In addition, for particular classes objects, such as faces, highly complex specific transformations may be relevant, such as changing facial expressions. For learning to recognize images, it is greatly beneficial to factor out these variations. It results in much simpler classification problem and, consequently, in great reduction of sample complexity of the model. A simple computational experiment illustrates this idea. Two instances of a classifier were trained to distinguish images of planes from those of cars. For training and testing of the first instance, images with arbitrary viewpoints were used. Another instance received only images seen from a particular viewpoint, which was equivalent to training and testing the system on invariant representation of the images. One can see that the second classifier performed quite well even after receiving a single example from each category, while performance of the first classifier was close to random guess even after seeing 20 examples. Invariant representations has been incorporated into several learning architectures, such as neocognitrons. Most of these architectures, however, provided invariance through custom-designed features or properties of architecture itself. While it helps to take into account some sorts of transformations, such as translations, it is very nontrivial to accommodate for other sorts of transformations, such as 3D rotations and changing facial expressions. M-theory provides a framework of how such transformations can be learned. In addition to higher flexibility, this theory also suggests how human brain may have similar capabilities.
Templates Another core idea of M-theory is close in spirit to ideas from the field of compressed sensing. An implication from Johnson–Lindenstrauss lemma says that a particular number of images can be embedded into a low-dimensional feature space with the same distances between images by using random projections. This result suggests that dot product between the observed image and some other image stored in memory, called template, can be used as a feature helping to distinguish the image from other images. The template need not to be anyhow related to the image, it could be chosen randomly.
Combining templates and invariant representations The two ideas outlined in previous sections can be brought together to construct a framework for learning invariant representations. The key observation is how dot product between image I {\displaystyle I} and a template t {\displaystyle t} behaves when image is transformed (by such transformations as translations, rotations, scales, etc.). If transformation g {\displaystyle g} is a member of a unitary group of transformations, then the following holds:
⟨ g I , t ⟩ = ⟨ I , g − 1 t ⟩ ( 1 ) {\displaystyle \langle gI,t\rangle =\langle I,g^{-1}t\rangle \qquad (1)}
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