How do we know if two systems - biological or artificial - process information in a similar way? Similarity measures such as linear regression, Centered Kernel Alignment (CKA), Normalized Bures Similarity (NBS), and angular Procrustes distance, are often used to quantify this similarity. However, it is currently unclear what drives high similarity scores and even what constitutes a "good" score. Here, we introduce a novel tool to investigate these questions by differentiating through similarity measures to directly maximize the score. Surprisingly, we find that high similarity scores do not guarantee encoding task-relevant information in a manner consistent with neural data; and this is particularly acute for CKA and even some variations of cross-validated and regularized linear regression. We find no consistent threshold for a good similarity score - it depends on both the measure and the dataset. In addition, synthetic datasets optimized to maximize similarity scores initially learn the highest variance principal component of the target dataset, but some methods like angular Procrustes capture lower variance dimensions much earlier than methods like CKA. To shed light on this, we mathematically derive the sensitivity of CKA, angular Procrustes, and NBS to the variance of principal component dimensions, and explain the emphasis CKA places on high variance components. Finally, by jointly optimizing multiple similarity measures, we characterize their allowable ranges and reveal that some similarity measures are more constraining than others. While current measures offer a seemingly straightforward way to quantify the similarity between neural systems, our work underscores the need for careful interpretation. We hope the tools we developed will be used by practitioners to better understand current and future similarity measures.

Understanding how the brain learns may be informed by studying biologically plausible learning rules. These rules, often approximating gradient descent learning to respect biological constraints such as locality, must meet two critical criteria to be considered an appropriate brain model: (1) good neuroscience task performance and (2) alignment with neural recordings. While extensive research has assessed the first criterion, the second remains underexamined. Employing methods such as Procrustes analysis on well-known neuroscience datasets, this study demonstrates the existence of a biologically plausible learning rule — namely e-prop, which is based on gradient truncation and has demonstrated versatility across a wide range of tasks — that can achieve neural data similarity comparable to Backpropagation Through Time (BPTT) when matched for task accuracy. Our findings also reveal that model architecture and initial conditions can play a more significant role in determining neural similarity than the specific learning rule. Furthermore, we observe that BPTT-trained models and their biologically plausible counterparts exhibit similar dynamical properties at comparable accuracies. These results underscore the substantial progress made in developing biologically plausible learning rules, highlighting their potential to achieve both competitive task performance and neural data similarity.

Relational cognition-the ability to infer relationships that generalize to novel combinations of objects-is fundamental to human and animal intelligence. Despite this importance, it remains unclear how relational cognition is implemented in the brain due in part to a lack of hypotheses and predictions at the levels of collective neural activity and behavior. Here we discovered, analyzed, and experimentally tested neural networks (NNs) that perform transitive inference (TI), a classic relational task (if A > B and B > C, then A > C). We found NNs that (i) generalized perfectly, despite lacking overt transitive structure prior to training, (ii) generalized when the task required working memory (WM), a capacity thought to be essential to inference in the brain, (iii) emergently expressed behaviors long observed in living subjects, in addition to a novel order-dependent behavior, and (iv) expressed different task solutions yielding alternative behavioral and neural predictions. Further, in a large-scale experiment, we found that human subjects performing WM-based TI showed behavior inconsistent with a class of NNs that characteristically expressed an intuitive task solution. These findings provide neural insights into a classical relational ability, with wider implications for how the brain realizes relational cognition.