Fernando Ramirez¹; ¹Congressional Center for Computational Neuroscience (CCCN), Maryland, USA

Appeals to “convergent evidence” are widely used in vision science to justify inferences that integrate results across paradigms, measurement techniques, and species. In contemporary cognitive and systems neuroscience, particularly in studies using multivariate analyses of neural population activity, this strategy is often treated as principled rather than heuristic, notably through “Representational Similarity Analysis” (RSA). Here, I argue that convergent evidence is logically incoherent as a general criterion of evidential validity, and this incoherence linked to foundational assumptions underlying RSA. RSA is often motivated by geometric intuitions related to the Johnson–Lindenstrauss (JL) lemma, which guarantees approximate preservation of Euclidean distances under random linear projections of a fixed set of points. This is taken to license abstraction from measurement and direct comparison of dissimilarity structure across methods. I show that this inference fails on logical grounds: neuroscientific measurements are neither random nor generic projections, and the multivariate patterns analyzed with RSA are constructed by measurement, preprocessing, and normalization operations. Using previously published neuroimaging and electrophysiological datasets together with novel computational modeling and analytical work, I derive necessary conditions under which RSA-based comparisons are valid and illustrate how violations arise in practice. Representational structure is not invariant to translations or rotations in multivariate space when signal imbalances and measurement-scale differences are present. Moreover, empirically observed pattern spaces are typically radial rather than isotropic, so vector length carries representationally relevant information. Under these conditions, RSA outputs that appear similar can support logically incompatible conclusions about the underlying neural code. These failures are compounded by dependence on signal-to-noise regime: different but plausible noise assumptions can flip representational inferences. I conclude that neither convergent evidence nor RSA can serve as general methodological principles in vision science. Valid cross-method inference requires explicit forward models specifying how hypothesized neural representations, noise, and measurement processes jointly generate empirical observations.