Decoding Alignment without Encoding Alignment: A critique of similarity analysis in neuroscience

The gist Decoding approaches are widely used in neuroscience and machine learning to compare stimulus representations across neural systems, such as different brain regions, organisms, and deep learning models.

Critique of Similarity Analysis

The paper demonstrates a fundamental weakness behind this approach: it is misleading to assume that representational geometry is representative of a neuronal population as a whole, when such representations may actually be shaped by a very small subset of neurons. We show that the complementary encoding paradigm addresses this issue directly: it characterizes how neurons are organized globally in terms of their responses to a set of data, providing insight into how the decoding representation is implemented by neurons within a population. We demonstrate across experiments in biological systems and deep learning models that (i) surprisingly, similar decoding behavior and high representational alignment can arise from small, non-representative subpopulations of neurons; and critically, (ii), alignment metrics are insensitive to encoding manifold topology (how function is distributed across neurons), despite this being a key signature of differentiation across biological systems We provide a Neural Manifold Explorer tool.

Encoding vs. Decoding Manifolds

The paper introduces the complementary encoding paradigm which characterizes how neurons are organized globally in terms of their responses to a set of data, providing insight into how the decoding representation is implemented by neurons within a population. The encoding manifold represents neurons as points in stimulus-response space. Each point on the encoding manifold is a neuron; nearby neurons are similarly tuned. The global topology of this neural point cloud—whether it forms discrete clusters, as in retinal ganglion cell types, or a smooth continuum, as in mouse V1—directly reflects the functional architecture of the population.

Insensitivity to Topology

Alignment metrics are insensitive to encoding manifold topology (how function is distributed across neurons), despite this being a key signature of differentiation across biological systems A controlled MNIST experiment provides causal evidence: decoding metrics remain unchanged even when encoding topology is causally manipulated via the training loss. Overall, similarity in decoding behavior, as measured by classic alignment metrics, does not imply similarity in function or computation.

Complementary Diagnostics

We therefore propose using encoding manifolds and GromovWasserstein distance as complementary diagnostics for any decoding-based similarity claim. GWmax = GW(Efull, Ecoll) and Ecoll collapses all points to their centroid, thereby measuring a baseline on the maximal distance all points could travel.

Population-Size Sweep Results

First we show that decoding scores can be reproduced by a small fraction of neurons. Across biological systems, all metrics saturate near ceiling at or above 5% of neurons under information-maximizing selection strategies. This raises a fundamental question: if decoding metrics can be matched by a handful of neurons, what functional role do the remaining neurons play.

Topological Manipulation

We construct subpopulations with identical size but fundamentally different coverage of the encoding manifold: one continuous and distributed, the other locally clustered. Despite clear topological differences, RSA, CKA, and Procrustes R2 remain near-ceiling across systems and metrics. GW similarity thus provides a complementary, encoding-side measure that captures precisely what decoding metrics are blind to.

Causal Dissociation

The dissociation is not a ceiling effect: at λ = 10, where decoding metrics are near ceiling, GW similarity has fallen to 0.52, indicating a substantially reorganized internal structure. Thus the insensitivity of decoding metrics to encoding topology is a structural property of the metrics themselves, not a feature of the specific biological or neural network data analyzed in the preceding sections.

Conclusion

Our results do not invalidate decoding-based similarity metrics; rather, they delimit what those metrics can support. We therefore recommend complementing decoding-based comparisons with encoding manifolds and GW-based measures of functional organization. A model may match biological responses while implementing a fundamentally different internal organization.

Methods Summary

The encoding manifold is constructed following the three-stage pipeline of Dyballa et al. (2024): (1) nonnegative tensor factorization to embed neurons into a stimulus-response space (Williams et al., 2018), (2) adaptive graph construction via IAN (Dyballa and Zucker, 2023), and (3) diffusion maps for dimensionality reduction.

Decoding Metrics

The eight complementary metrics organized into two groups are four static metrics that operate on time-averaged representations and four trajectory metrics that characterize temporal dynamics<ref:2605.

1. Improve model comparison by using encoding manifolds as a complementary diagnostic tool to decoding metrics, as similarity in decoding behavior, as measured by classic alignment metrics, does not imply similarity in function or computation. This allows researchers to determine if two systems are functionally distinct beyond encoding manifold topology.

2. Develop model evaluation protocols that explicitly compare internal functional organization by using Gromov-Wasserstein distance to quantify encoding manifold coverage, as GW measures how well the internal pairwise-distance structure of one point cloud can be matched to that of another. This provides a measure for functional alignment rather than just behavioral alignment.

3. Design neural network training objectives that explicitly control encoding topology by adding auxiliary losses like Lcluster, as this allows researchers to establish causal rather than merely correlational evidence that decoding metrics are insensitive to internal functional organization. The paper demonstrates that even when decoding metrics remain near ceiling, GW similarity can show a substantially reorganized internal structure, indicating functional differences.

4. Implement subpopulation selection strategies based on encoding manifold coverage, such as selecting neurons by their PC contribution, to ensure that the sampled units are not representative of a single functional mode. This addresses the finding that representation alignment metrics inherit this blind spot when only a small subset of neurons is used for decoding performance.

5. Enhance interpretability methods to analyze functional circuitry by quantifying Attribution entropy and overlap and Assortativity, as these metrics reveal differences in internal organization, such as showing that same-class neurons preferentially connect within class-specific pathways. This moves beyond simply observing what a population does to understanding how it is organized to do it.

RSA and CKA are standard metrics for comparing neural representations across brain regions, organisms, and deep learning models. We demonstrate a fundamental weakness: these decoding-based metrics are insensitive to encoding manifold topology---the internal functional organization of a neural population. In a controlled MNIST experiment, RSA, CKA, and Procrustes R squared remain statistically unchanged when encoding topology is causally manipulated via an auxiliary clustering loss, while the two model populations differ significantly in attribution patterns, weight-graph assortativity, and out-of-distribution robustness. Across biological systems and machine learning models, similar decoding behavior can arise from small, non-representative subpopulations, and alignment metrics are insensitive to encoding manifold topology even when it is fundamentally altered. These findings bear directly on mechanistic interpretability: standard alignment metrics cannot distinguish whether two networks share the same computational circuits or merely produce indistinguishable aggregate outputs. We propose encoding manifolds and Gromov-Wasserstein distance as complementary diagnostics for any decoding-based similarity claim, and provide a Neural Manifold Explorer tool at https://johannesbertram.github.io/FNN Manifolds/index.html for further experimentation.