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arxiv: 2605.05907 · v1 · submitted 2026-05-07 · 🧬 q-bio.NC

Recognition: unknown

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

Johannes Bertram, Luciano Dyballa, Savik Kinger, Steven W. Zucker, T. Anderson Keller

Pith reviewed 2026-05-08 03:26 UTC · model grok-4.3

classification 🧬 q-bio.NC
keywords neural representationsdecoding manifoldsencoding manifoldsrepresentational similarity analysisalignment metricsneurosciencedeep learning models
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The pith

Decoding similarity metrics do not imply similar neural computation because they can be shaped by tiny neuron subsets

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper shows that widely used methods for comparing neural representations, such as Representational Similarity Analysis and decoding manifolds, rest on a flawed assumption. These alignment metrics measure similarity in how stimuli are represented geometrically, yet the geometry can be produced by a small minority of neurons rather than reflecting the population as a whole. Consequently, two neural systems can display nearly identical decoding behavior while differing in the actual organization of their neurons' responses. The authors introduce encoding manifolds as a complementary approach that tracks how function is distributed across the entire population. Experiments across biological data and deep networks, including a controlled MNIST manipulation, demonstrate that decoding alignment stays unchanged even when encoding topology is altered.

Core claim

The paper establishes that similarity in decoding representations, as captured by classic alignment metrics such as RSA and DSA, does not entail similarity in function or computation. This holds because decoding geometry is often dominated by non-representative subpopulations, and these metrics remain insensitive to the topology of encoding manifolds that describe how responses are organized across neurons. A causal MNIST demonstration confirms that manipulating encoding structure via training loss leaves decoding metrics intact, while biological and model comparisons reveal that alignment can arise without matching encoding organization.

What carries the argument

Encoding manifolds, which describe the global organization of neuron responses to stimuli, contrasted with decoding manifolds that capture stimulus geometry independent of population structure.

If this is right

  • High alignment scores from RSA or DSA can occur between systems whose neurons are organized differently to encode information.
  • Encoding topology serves as a distinguishing signature across biological neural systems that decoding metrics overlook.
  • Decoding-based comparisons between brain regions or between brains and models can miss computational differences.
  • Encoding manifolds provide a direct way to characterize how a population implements its representations.
  • Causal interventions on encoding structure, such as loss function changes, can leave decoding metrics unchanged.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Comparisons between artificial networks and biological circuits may need to incorporate explicit checks on encoding organization rather than relying solely on output geometry.
  • Methods that sample or ablate neurons could test whether alignment persists after removing suspected small subpopulations.
  • This distinction may help explain cases where neural systems align in decoding yet fail to match in behavioral predictions.
  • Future work could develop metrics that jointly assess both decoding geometry and encoding topology.

Load-bearing premise

Decoding geometry reflects the properties of the full neuronal population rather than being controlled by a small subset of neurons.

What would settle it

An experiment in which two systems show identical decoding alignment scores yet differ in measured encoding manifold topology and also differ in a direct functional test, such as generalization behavior or perturbation sensitivity.

Figures

Figures reproduced from arXiv: 2605.05907 by Johannes Bertram, Luciano Dyballa, Savik Kinger, Steven W. Zucker, T. Anderson Keller.

Figure 1
Figure 1. Figure 1: Encoding and decoding manifolds provide complementary views of neural systems. (A) A neural network as an input-output map. The same behavior – categorization – can be achieved with different maps. (B) Stimuli can be represented in neural coordinates (decoding manifold, right, colors represent different stimuli) or neurons can be represented in stimulus coordinates (encoding manifold, left, colors represen… view at source ↗
Figure 2
Figure 2. Figure 2: Population-size sweep across Retina, V1 (flows, gratings, natural) for six decoding metrics view at source ↗
Figure 3
Figure 3. Figure 3: Encoding manifold coverage and decoding scores for 5% subpopulations selected by view at source ↗
Figure 4
Figure 4. Figure 4: FPS-based subpopulations with continuous (top row, dark red) vs. clustered (bottom view at source ↗
Figure 5
Figure 5. Figure 5: MNIST experiment: continuous (A) vs. clustered (B) encoding manifold colored by view at source ↗
Figure 6
Figure 6. Figure 6: Fraction sweep for kNN accuracy and normalized DSA z scores. view at source ↗
Figure 7
Figure 7. Figure 7: Size-matched encoding manifold region sampling for Retina, V1 and VISp (gratings and view at source ↗
Figure 8
Figure 8. Figure 8: Size-matched encoding manifold region sampling for Retina, V1 and VISp (gratings and view at source ↗
Figure 9
Figure 9. Figure 9: Encoding manifold pipeline stability across sample size (columns), tensor decomposition factors (rows) and datasets (Blue: V1, Red: Retina). Encoding topology is stable, showing continuous manifolds in V1 and clustered ones in retina. GW distance groups the two datasets together (bottom). 17 view at source ↗
Figure 10
Figure 10. Figure 10: GW intuition based on simple synthetic datasets. The ring and torus being topologically equivalent are grouped together. Similarly, the sphere and ball are close in GW space. The line is furthest from all other datasets, not allowing for circular matching of points. 18 view at source ↗
Figure 11
Figure 11. Figure 11: Retina — FPS subpopulation showcase. Each row shows the 3-D encoding manifold (left), 3-D decoding manifold (center), and stimulus trajectories (right) for the full population (top), FPS continuous subpopulation (n=50 seeds, m=1 neighbor, ≈100 neurons; middle), and FPS clustered subpopulation (n=10 seeds, m=9 neighbors, ≈100 neurons; bottom). The bottom bar chart reports all eight decoding metrics relativ… view at source ↗
Figure 12
Figure 12. Figure 12: V1 — FPS subpopulation showcase. Layout as in view at source ↗
Figure 13
Figure 13. Figure 13: Allen VISp (drifting gratings) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 14
Figure 14. Figure 14: Allen VISrl (drifting gratings) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 15
Figure 15. Figure 15: Allen VISam (drifting gratings) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 16
Figure 16. Figure 16: Allen VISpm (drifting gratings) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 17
Figure 17. Figure 17: Allen VISl (drifting gratings) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 18
Figure 18. Figure 18: Allen VISp (natural movie, 156 scenes) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 19
Figure 19. Figure 19: Allen VISrl (natural movie) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 20
Figure 20. Figure 20: Allen VISam (natural movie) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 21
Figure 21. Figure 21: Allen VISpm (natural movie) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 22
Figure 22. Figure 22: Allen VISl (natural movie) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 23
Figure 23. Figure 23: FNN output layer — FPS subpopulation showcase. Layout as in view at source ↗
Figure 24
Figure 24. Figure 24: Flyvision (T, Tm cells) — FPS subpopulation showcase. Layout as in view at source ↗
Figure 25
Figure 25. Figure 25: R(2+1)D layer 4 — FPS subpopulation showcase. Layout as in view at source ↗
Figure 26
Figure 26. Figure 26: ViT Layer 11 — FPS subpopulation showcase. Layout as in view at source ↗
Figure 27
Figure 27. Figure 27: Raptor — FPS subpopulation showcase. Layout as in view at source ↗
read the original abstract

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. Popular methods include decoding (perceptual) manifolds and alignment metrics such as Representational Similarity Analysis (RSA) and Dynamic Similarity Analysis (DSA), where similarity in decoding representations is interpreted as evidence for similar computation. This 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. 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, motivating the use of encoding manifolds as a complementary tool for comparing neural systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that decoding-based alignment metrics such as RSA and DSA, widely used to compare representations across neural systems, can produce high similarity scores even when the underlying encoding manifolds differ in how function is distributed across neurons. This occurs because decoding geometry can be dominated by small, non-representative subpopulations. The authors support this via experiments in biological systems, deep learning models, and a causal MNIST manipulation where training loss alters encoding topology without changing decoding alignment scores, concluding that decoding similarity does not imply similar computation and motivating encoding manifolds as a complementary tool.

Significance. If the central claim holds, the work has clear significance for computational neuroscience and ML interpretability by identifying a systematic limitation in popular alignment methods that assume representational geometry reflects the full population. The causal MNIST experiment is a particular strength, as it directly tests insensitivity to encoding topology changes rather than relying on correlational counterexamples. This could shift practice toward hybrid decoding-encoding analyses when comparing systems.

major comments (2)
  1. [Abstract / Results] The abstract and introduction state that experiments demonstrate claims (i) and (ii), but the manuscript provides no methods section details on datasets, model architectures, neuron selection criteria, statistical tests, or data availability. Without these, the quantitative support for high alignment arising from small subpopulations cannot be evaluated (e.g., what fraction of neurons drives the RSA/DSA scores, and what are the effect sizes?).
  2. [MNIST experiment] § on the MNIST causal experiment: while the manipulation via training loss is described as leaving decoding metrics unchanged, the specific loss terms, the resulting changes in encoding manifold topology (e.g., via some distance or clustering metric), and the invariance of alignment scores need explicit quantification and controls to confirm causality rather than incidental invariance.
minor comments (2)
  1. [Introduction] Notation for 'encoding manifold' and 'decoding manifold' should be defined more precisely early on, including how they are computed from population responses, to avoid ambiguity with standard manifold learning terms.
  2. [Results] The paper would benefit from a table or figure summarizing alignment scores (RSA/DSA values) across the biological, DL, and MNIST cases before/after manipulations for direct comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the work's significance and for highlighting the strength of the causal MNIST experiment. We agree that additional methodological transparency and quantification are needed to fully support the claims. Below we respond point-by-point to the major comments and commit to a revised manuscript that incorporates the requested details.

read point-by-point responses

  1. Referee: [Abstract / Results] The abstract and introduction state that experiments demonstrate claims (i) and (ii), but the manuscript provides no methods section details on datasets, model architectures, neuron selection criteria, statistical tests, or data availability. Without these, the quantitative support for high alignment arising from small subpopulations cannot be evaluated (e.g., what fraction of neurons drives the RSA/DSA scores, and what are the effect sizes?).

    Authors: We agree that the current version lacks a dedicated Methods section with the requested details. In the revision we will add a comprehensive Methods section specifying: (1) all datasets (biological recordings with sources, DL model architectures and training procedures), (2) neuron selection criteria and subpopulation identification methods, (3) exact statistical tests and effect-size calculations, and (4) data and code availability. We will also include new supplementary figures/tables that quantify the fraction of neurons driving RSA/DSA scores and report effect sizes for the reported alignment values. These additions will make the quantitative support for claims (i) and (ii) directly evaluable. revision: yes

  2. Referee: [MNIST experiment] § on the MNIST causal experiment: while the manipulation via training loss is described as leaving decoding metrics unchanged, the specific loss terms, the resulting changes in encoding manifold topology (e.g., via some distance or clustering metric), and the invariance of alignment scores need explicit quantification and controls to confirm causality rather than incidental invariance.

    Authors: We accept that the current description of the MNIST experiment requires more explicit quantification. In the revised manuscript we will: (1) state the precise loss terms and hyperparameters used for the causal manipulation, (2) report quantitative changes in encoding manifold topology using explicit metrics (e.g., clustering coefficients, pairwise distance distributions, or manifold dimensionality estimates), (3) provide statistical tests confirming invariance of RSA/DSA scores across conditions, and (4) add control analyses (e.g., varying manipulation strength and showing that topology changes occur without corresponding decoding shifts). These additions will strengthen the causal interpretation. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's argument is advanced entirely through empirical counterexamples and a controlled causal manipulation (MNIST training-loss intervention that redistributes function across neurons while leaving decoding metrics unchanged). No equations, fitted parameters, or self-referential definitions appear in the provided text; the central claim that high RSA/DSA scores can arise from non-representative subpopulations is demonstrated directly by the reported experiments rather than derived from prior self-citations or ansatzes. The derivation chain is therefore self-contained against external benchmarks and contains no load-bearing steps that reduce to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on challenging a common domain assumption in neuroscience about what decoding metrics capture, without introducing new parameters or entities.

axioms (1)
  • domain assumption Representational geometry from decoding is assumed to be representative of the entire neuronal population
    This is the assumption the paper critiques as misleading when shaped by small subsets of neurons.

pith-pipeline@v0.9.0 · 5581 in / 1311 out tokens · 65946 ms · 2026-05-08T03:26:39.964602+00:00 · methodology

discussion (0)

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