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Title: Morpho-MNIST: Quantitative Assessment and Diagnostics for Representation Learning

Paper content:
Revealing latent structure in data is an active field of research, having introduced exciting technologies such as variational autoencoders and adversarial networks, and is essential to push machine learning towards unsupervised knowledge discovery.
However, a major challenge is the lack of suitable benchmarks for an objective and quantitative evaluation of learned representations.
To address this issue we introduce Morpho-MNIST, a framework that aims to answer: "to what extent has my model learned to represent specific factors of variation in the data?"
We extend the popular MNIST dataset by adding a morphometric analysis enabling quantitative comparison of trained models, identification of the roles of latent variables, and characterisation of sample diversity.
We further propose a set of quantifiable perturbations to assess the performance of unsupervised and supervised methods on challenging tasks such as outlier detection and domain adaptation.
A key factor for progress in machine learning has been the availability of well curated, easy-to-use, standardised and sufficiently large annotated datasets for benchmarking different algorithms and models.
This has led to major advances in speech recognition, computer vision, and natural language processing.
A commonality between these tasks is their natural formulation as supervised learning tasks, wherein performance can be measured in terms of accuracy on a test set.The general problem of representation learning (i.e. to reveal latent structure in data) is more difficult to assess due the lack of suitable benchmarks.
Although the field is very active, with many recently proposed techniques such as probabilistic autoencoders and adversarial learning, it is less clear where the field stands in terms of progress or which approaches are more expressive for specific tasks.
The lack of reproducible ways to quantify performance has led to subjective means of evaluation: visualisation techniques have been used to show low-dimensional projections of the latent space and visual inspection of generated or reconstructed samples are popular to provide subjective measures of descriptiveness.
On the other hand, the quality of sampled images generally tells us little about how well the learned representations capture known factors of variation in the training distribution.
In order to advance progress, the availability of tools for objective assessment of representation learning methods seems essential yet lacking.
This paper introduces Morpho-MNIST, a collection of shape metrics and perturbations, in a step towards quantitative assessment of representation learning.
We build upon one of the most popular machine learning benchmarks, MNIST, which despite its shortcomings remains widely used.
While MNIST was originally constructed to facilitate research in image classification, in the form of recognising handwritten digits BID17 , it has found its use in representation learning, for example, to demonstrate that the learned latent space yields clusters consistent with digit labels.
Methods aiming to disentangle the latent space claim success if individual latent variables capture specific style variations (e.g. stroke thickness, sidewards leaning digits and other visual characteristics).The
main appeal of selecting MNIST as a benchmark for representation learning is that, while manifesting complex interactions between pixel intensities and underlying shapes, it has well understood and easily measurable factors of variation. More
generally, MNIST remains popular in practice due to several factors: it allows reproducible comparisons with previous results reported in the literature; the dataset is sufficiently large for its complexity and consists of small, two-dimensional greyscale images defining a tractable ten-class classification problem; computation and memory requirements
With Morpho-MNIST we provide a number of mechanisms to quantitatively assess representation learning with respect to measurable factors of variation in the data.
We believe that this is an important asset for future research on generative models, and we would like to emphasize that the proposed morphometrics can be used post hoc to evaluate already trained models, potentially revealing novel insights and interesting observations.A similar morphometry approach could be used with other datasets such as dSprites, e.g. estimating shape location and size, number of objects/connected components.
Perhaps some generic image metrics may be useful for analysis on other datasets, e.g. relating to sharpness or colour diversity, or we could even consider using the output of object detectors (analogously to the Inception-based scores; e.g. number/class of objects, bounding boxes etc.).
In future work we plan to include additional perturbations, for example, mimicking imaging artefacts commonly observed in medical imaging modalities to add further complexity and realism.

assistant: text: This paper introduces Morpho-MNIST, a collection of shape metrics and perturbations, in a step towards quantitative evaluation of representation learning.