Self-supervised learning stops at shared content: record each instance's augmentation strength and the coordinates line up

Self-supervised learning previously guaranteed only that the content shared across views is recovered as a whole block; which coordinate inside that block corresponds to which factor was not determined by the theory. Shared-content theory identifies content only up to an invertible transformation, so replacing horizontal and vertical position by their sum and difference leaves the observation law unchanged. In a conditional Gaussian model, as long as the conditional covariance of content stays constant across instances, rotations and other mixtures still satisfy conditional independence and preserve the observation law, so they cannot be ruled out.

Letting each instance's content variances respond to a recorded augmentation strength makes coordinates distinguishable, because different coordinates have different response slopes to that strength. Earlier approaches took the identifying variation from the data source itself; here the augmentation design creates the variance variation while keeping each instance's content mean stable. Within a conditional Gaussian comparison class, coordinates with pairwise distinct response slopes are identified up to permutation, scaling and translation, while coordinates with equal slopes are identified only as a block.

The learner pools variance responses across instances using the recorded strengths, so each instance needs only a few views. Estimating variances separately for each instance gives estimates too noisy to reveal a response when only two views are available. In synthetic experiments, when the view count drops from four to two, the pooled estimator reaches Amari error 0.030, whereas the separate estimator at two views is on average worse than a random rotation.

On dSprites, moderate strength variation moves individual coordinates closer to the corresponding generative factors while prediction from the whole representation changes little. Without strength variation the coordinates mix the factors, with off-diagonal correlations up to 0.31 and factor alignment of 0.837. At strength variation 0.5, off-diagonal correlations fall to at most 0.03 and factor alignment rises to 0.932, while five-neighbor block prediction moves from 0.88 to 0.85, indicating the information remains in the representation but is carried by different coordinates.

The identification guarantee concerns a conditional Gaussian comparison class, not the trained learner; the image experiments test the design and do not satisfy the theorem's assumptions. The dSprites and Shapes3D augmentations target known factors, even when the coordinate-to-factor assignment is learned. Held-out instances share the benchmarks and augmentation distributions with training, so they test transfer to new instances rather than to new intervention families or unseen factor combinations. The authors propose future work on how to choose strengths for reliable recovery and on what identifying information richer self-supervised augmentation pipelines supply.

The image experiments depart from the theorem's hypotheses in several ways: the content law can be degenerate, source factors that no augmentation targets are constant within an instance, and nonlinear encoder responses, clipping and resampling can all break the ideal variance law. The dSprites zoom is applied about the image center rather than the sprite, so the position covariance is neither exactly diagonal nor exactly log-affine. At strength variation 1 both alignment and block prediction deteriorate sharply, and that setting also raises the expected squared shift by about four times, so the effect of greater strength variation cannot be separated from that of larger shifts. On Shapes3D a smooth two-coordinate representation of continuous hue lies on a curve and does not satisfy the theorem's Gaussian setting, so the grouping results are selective and imperfect.