Bidirectional representational alignment between biological and artificial neural networks
Authors: Samuel Kostousov, Abhinn Kaushik, Brokoslaw Laschowski
Organizations: Department of Physics, University of Toronto, Toronto, ON, Canada · Department of Computer Science, University of Toronto, Toronto, ON, Canada · Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada; and the KITE Research Institute, University Health Network, Toronto, ON, Canada
Recent work has shown that representational alignment between biological and artificial neural networks is asymmetric: model representations predict neural responses much better than neural responses predict model representations. This asymmetry raises the question of whether representational geometry contributes to bidirectional representational alignment. We hypothesized that steering representational geometry during training can systematically influence bidirectional alignment. To test this hypothesis, we developed a computational framework that integrates spectral regularization with bidirectional predictivity analyses. As an initial demonstration, we evaluated our framework using self-supervised contrastive vision models. Steering the spectral geometry of the learned representations substantially increased reverse predictivity with modest reductions in forward predictivity, yielding a 55% relative improvement in bidirectional predictivity. These improvements were accompanied by reduced effective dimensionality and a reorganization of the shared representational subspace, within which forward and reverse predictivity became approximately symmetric at intermediate spectral exponents. Overall, these findings demonstrate that representational geometry can be systematically steered to modulate bidirectional representational alignment between biological and artificial neural networks.
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Fig. 1: Our computational framework for studying the relationship between representational geometry and bidirectional representational alignment between biological and artificial neural networks. During training, a standard learning objective is combined with spectral regularization to steer the spectral geometry of the learned representations by regularizing the spectral decay exponent. During validation, bidirectional predictivity is evaluated using forward and reverse predictivity on stimuli with neural data.
Fig. 2: Forward and reverse explained variance across the measured spectral exponents for λ=3 . The white point is the unregularized baseline. Error bars represent the median absolute deviation.
Fig. 3: Forward and reverse explained variance across the measured spectral exponents for λ=2 . The white point is the unregularized baseline. Error bars represent the median absolute deviation.
Fig. 4: Reverse explained variance as a function of the measured spectral exponent α and regularization strength λ . The white point is the unregularized baseline. Error bars represent the median absolute deviation.
Fig. 5: Distributions of reverse explained variance across model units for λ=3 . The white distribution is the unregularized baseline. Error bands are the standard error of the mean.
Fig. 6: Bidirectional predictivity as a function of the measured spectral exponent α for models with λ=3 . The white point is the unregularized baseline. Error bars represent the median absolute deviation.
Fig. 7: Distributions of forward explained variance across recorded neurons for models with λ=3 . The white distribution represents the unregularized baseline. Error bands are the standard error of the mean.
Fig. 8: Forward explained variance as a function of the measured spectral exponent α and spectral regularization strength λ . The white point is the unregularized baseline. Error bars are the median absolute deviation.
Fig. 9: Forward and reverse explained variance for common model units (top 20% ranked by reverse predictivity). The white point denotes the unregularized baseline. Error bars are the median absolute deviation.
Fig. 10: Forward and reverse explained variance for unique model units (bottom 20% ranked by reverse predictivity). The white point denotes the unregularized baseline. Error bars are the median absolute deviation.
Fig. 11: Effective dimensionality as a function of the measured spectral exponent α . The white point represents the unregularized baseline. Error bars represent the median absolute deviation.
Activation-alignment measures such as Representational Similarity Analysis (RSA), Canonical Correlation Analysis (CCA), and Centered Kernel Alignment (CKA) are widely used to compare biological and artificial neural representations. Recent theoretical work interprets many of these methods as assessing agreement between optimal linear readouts over broad families of global tasks. However, agreement at the level of global readouts does not determine how a system uses local stimulus evidence. Specifically, representations may align in activation space yet differ in their sensitivity to small perturbations. To address this challenge, we introduce a complementary framework based on local decodable information, which focuses on a representation's ability, under noise, to discriminate small perturbations within a specified stimulus-coordinate subspace. Building on Fisher information and local representation geometry, we summarize each representation using the expected projected pullback/Fisher metric over that subspace. This formulation induces a second-moment family of local discrimination tasks, for which the resulting operator provides a minimal, complete dataset-level summary of expected discriminability. We compare these regularized signatures using a log-spectral distance on the manifold of symmetric positive definite (SPD) matrices, yielding the Spectral Riemannian Alignment Score (S-RAS) and a uniform multiplicative certificate over the corresponding family of lifted task values. Empirically, this framework enables the recovery of corresponding layers across independently trained artificial neural networks, supports transferable class-conditional probes, reveals controlled dissociations between standard and robust training, and uncovers stimulus-coordinate family effects across mouse visual cortex using the Allen Brain Observatory static gratings dataset.
Amirhossein Yavari, Farnaz Zamani Esfahlani
Stephenson School of Biomedical Engineering, University of Oklahoma · Data Science and Analytics Institute, University of Oklahoma
We propose the Neural Functional Alignment Space (NFAS), a brain-referenced representational framework for characterizing artificial neural networks on equal functional grounds. NFAS departs from conventional alignment approaches that rely on layer-wise features or task-specific activations by modeling the intrinsic dynamical evolution of stimulus representations across network depth. Specifically, we model layer-wise embeddings as a depth-wise dynamical trajectory and apply Dynamic Mode Decomposition (DMD) to extract the stable mode. This representation is then projected into a biologically anchored coordinate system defined by distributed neural responses. We also introduce the Signal-to-Noise Consistency Index (SNCI) to quantify cross-model consistency at the modality level. Across 45 pretrained models spanning vision, audio, and language, NFAS reveals structured organization within this brain-referenced space, including modality-specific clustering and cross-modal convergence in integrative cortical systems. Our findings suggest that representation dynamics provide a principled basis for
Ruiyu Yan, Hanqi Jiang, Yi Pan +4
Tandon School of Engineering, New York University, Brooklyn, NY 11201, USA · School of Computing, University of Georgia, Athens, GA 30602, USA · Department of Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA +1
The feedback alignment (FA) algorithm offers a biologically plausible alternative to backpropagation (BP) for training neural networks yet notably fails to scale to convolutional architectures. Modifications have been proposed to address this limitation, but at questionable cost to biological plausibility. In this paper, we evaluate five learning algorithms including modified FA and standard BP, applied to the same convolutional architecture with the CIFAR-10 dataset. We provide a tripartite comparative analysis focusing on biological plausibility, interpretability, and computational complexity. Our results indicate that modified FA algorithms converge on internal representations that are structurally similar to those produced by backpropagation. In particular, it appears the functional success of modified FA algorithms may be rooted in their ability to mimic the representational geometry of backpropagation, converging on similar representations despite relying on fundamentally different weight update mechanisms.