Cross-Architecture Representation Study
Question. Do different agent architectures, trained identically on the Zhang et al. (2025) chaser–explorer task, learn the same internal representations of the social interaction? Or does the phenomenon the paper reports — genuine shared neural dynamics between two independently trained agents — depend on the architecture?
Design. Four architectures, identical in everything except the memory mechanism: reward structure, 10×10 world, 100-step episodes, seeds 0–9, analysis dimension 256, PPO settings, evaluation protocol, and analysis pipeline. They span a memory ladder:
| architecture | memory mechanism | internal state at step t |
|---|---|---|
MLP (k=8 frame stack) |
none (finite window) | pure function of the last 8 observations |
| SSM (gated diagonal LRU) | compressed, linear dynamics | eigenvalue-controlled linear state |
| RNN (paper's ReLU RNN) | compressed, nonlinear dynamics | chaotic nonlinear recurrence |
| Transformer (2-layer causal) | none evolving; re-attends history | pre-head residual recomputed per step |
Each was trained as a full 20-pair experiment (mouse-run-run-1 for the RNN,
mouse-run-run-2-{mlp,ssm,transformer} for the rest): 20,000 PPO updates ×
40 episodes × 100 steps per pair, 20/20 units completed on the first
attempt for every architecture, zero failed/interrupted attempts.
1. Behavior: the architectures converged to different strategies
Chaser capability against a standardized random explorer (100 episodes × 100 steps), and the explorer's learned escape (collisions it suffers against a random chaser — lower is better escape):
| architecture | chaser collisions ↑ | chaser partner-in-vision | explorer collisions-suffered ↓ |
|---|---|---|---|
| RNN | 8.98 ± 5.70 | 0.61 | 0.57 |
| MLP | 26.93 ± 4.00 | 0.93 | 0.92 |
| SSM | 35.92 ± 3.56 | 0.94 | 0.45 |
| Transformer | 41.31 ± 3.29 | 0.96 | 0.28 |
All four learned role-specific social behavior (non-social controls collide 2.7–3.4× regardless). But the RNN converged to a qualitatively different strategy: a low-vision "stealth" chaser (61% partner-in-vision, 9 collisions) that tracks the explorer from memory, whereas MLP/SSM/Transformer converged to high-vision "pursuit" chasers (93–96% vision, 27–41 collisions) that stay glued to the explorer. This behavioral fork is the first sign the architectures are not learning the same thing — and it turns out to drive the representation difference.
The raw capability ranking (Transformer > SSM > MLP > RNN) is not the headline. A chaser that collides 41×/episode by never leaving the explorer's side is behaviorally strong but representationally shallow. The scientific question is about the internal representation, below.
2. Event decoding replicates across architectures (C2)
Linear-classifier balanced accuracy for social events decoded from single-agent hidden states (5-fold CV, shuffled controls ≈ 0.50 throughout):
| architecture | collision | partner escape | partner approach |
|---|---|---|---|
| RNN | 0.983 | 0.888 | 0.886 |
| MLP | 0.914 | 0.780 | 0.778 |
| SSM | 0.850 | 0.768 | 0.733 |
| Transformer | 0.847 | 0.761 | 0.759 |
Every architecture encodes collision and partner approach/escape above chance in social agents — the paper's C2 claim is architecture-robust. Decoding accuracy tracks the memory ladder (RNN > MLP ≈ SSM > Transformer), but the qualitative result (social events are linearly represented) holds for all.
3. Shared dimensions: a methodological correction, then the key result (C3)
The paper's headline is C3: social agents develop shared neural dimensions across the two independently trained networks (PLSC). Measuring this across architectures exposed a confound that the analysis had to fix.
The raw cross-agent correlation is contaminated by time-locked scaffolds.
The Transformer's top_dim_correlation was 0.957 in the non-social control
— higher than its social value, and higher than any architecture's social
score. There is no partner input in the non-social task, so this cannot be
genuine sharing. The cause: the Transformer's positional embedding makes every
timestep a deterministic function of absolute position t; both agents' networks
carry this identical positional scaffold, and it dominates the top singular
dimension. The RNN and MLP have no such clean scaffold (their "clocks" are noisy
or absent), so their raw non-social correlation stays near zero — which is
exactly why the raw statistic looked fine until the Transformer exposed it.
Fix (standard in neuroscience): remove the evoked/time-locked component. Subtract the across-episode mean at each timestep — the response identical across episodes at a given t (positional embeddings, hidden-state clocks, mean approach dynamics) — and run PLSC on the episode-specific residual, where genuine interaction lives. This removes every architecture's deterministic temporal scaffold uniformly, making the effect size comparable.
Aggregate residualized top-dim correlation (interaction-driven sharing):
| architecture | social | non-social | separation |
|---|---|---|---|
| RNN | 0.688 ± 0.23 | 0.067 | 0.62 |
| MLP (floor) | 0.679 ± 0.06 | 0.103 | 0.58 |
| SSM | 0.642 ± 0.12 | 0.315 | 0.33 |
| Transformer | 0.438 ± 0.08 | 0.356 | 0.08 |
The MLP is the common-input floor: being memoryless, any cross-agent sharing it shows is by construction reactive (both nets responding to the same visible game state). That its social sharing (0.679) nearly matches the RNN's aggregate (0.688) is the crux — the aggregate mean hides the real difference. The Transformer's social/non-social separation collapses to 0.08 once its positional scaffold is removed: its apparent sharing was mostly the scaffold.
The discriminating view: sharing vs behavioral coupling (vision). The MLP
can only share when both agents see each other. So the question is whether an
architecture achieves shared representation at low mutual vision — which
requires genuine internal (memory/prediction) coupling, not common input.
Residualized social top_r, split by chaser partner-in-vision:
| architecture | low vision (<40%) | high vision (≥40%) |
|---|---|---|
| RNN | 0.652 (n=7) | 0.947 (n=1) |
| MLP | — (0 units) | 0.679 (n=10) |
| SSM | — (0 units) | 0.642 (n=9) |
| Transformer | — (0 units) | 0.438 (n=10) |
This is the result. Only the RNN develops shared representation without the agents seeing each other — 7 of its 8 analyzable social units sit below 40% mutual vision yet reach 0.65 residualized correlation. Every social unit of the other three architectures lives at high vision; their sharing is vision-gated, i.e. common-input-like. MLP cannot do otherwise (no memory). SSM and Transformer have memory mechanisms but did not use them to build low-vision coordination — they converged to the reactive, high-vision solution.
4. Representational geometry: the RNN is the outlier (CKA)
Feeding the same game-state observation stream through every architecture's social chaser and comparing representations with linear CKA (rotation/scaling invariant):
| RNN | MLP | SSM | Transformer | |
|---|---|---|---|---|
| RNN | 1.00 | 0.68 | 0.64 | 0.67 |
| MLP | 0.68 | 1.00 | 0.71 | 0.78 |
| SSM | 0.64 | 0.71 | 1.00 | 0.76 |
| Transformer | 0.67 | 0.78 | 0.76 | 1.00 |
The RNN is the representational outlier (0.64–0.68 with everything else), while MLP/SSM/Transformer cluster together (0.71–0.78). A third independent method agrees with behavior and PLSC: the RNN encodes the task differently; the other three converge to a more mutually similar (reactive) geometry.
5. Degeneracy is itself an architecture property
The paper excludes "degenerate" episodes where agents get stuck. The SSM is markedly more prone to this: 1/10 social and 2/10 non-social units were fully degenerate (too few valid episodes to analyze), and several more had only 3–8 of 25 episodes valid — versus zero fully-degenerate units for RNN, MLP, and Transformer. The linear recurrence appears to collapse toward fixed-point / stuck behavior more readily — a concrete failure mode of the linear-dynamics inductive bias on this task.
Answer to the question
Different architectures do not learn the same internal representations. Three independent methods converge:
- Behavior — the RNN alone converges to a low-vision, memory-based stealth strategy; the others to high-vision reactive pursuit.
- Shared dimensions (residualized, vision-conditioned) — the RNN alone develops genuine interaction-driven sharing when the agents cannot see each other; the others' sharing is vision-gated and, for the Transformer, mostly a positional scaffold once corrected.
- CKA — the RNN is the representational outlier; the other three cluster.
The paper's hallmark phenomenon — genuine internal shared dynamics between independently trained agents — is not architecture-universal. It emerged cleanly only in the vanilla RNN. The memoryless MLP cannot produce it (its sharing is the common-input floor). The SSM and Transformer, despite having the capacity for memory, did not: their inductive biases steered them to a reactive, high-vision solution whose apparent sharing is largely explained by behavioral and input coupling, plus (Transformer) a deterministic temporal scaffold.
Honest confounds and limitations
- Strategy mediates representation. The architectures converged to different behavioral strategies, so the representation difference is partly mediated by strategy, not a direct architecture→representation effect. But that is itself a finding: the architecture's inductive bias shapes which solution is found, and only the RNN's solution has genuine internal shared dynamics. Isolating a direct effect would require conditioning on matched behavior (e.g. training all architectures to the same vision regime), which these runs do not do.
- Not parameter-matched. RNN 119k, SSM 382k, MLP 477k, Transformer 1.24M params (analysis dim held at 256). The RNN's distinctness is not a capacity-advantage artifact — it is the smallest model.
- Time-mean subtraction removes any genuinely time-locked coordination along with the scaffold; for random-initial-position episodes the interaction timing is episode-specific, so this should be conservative, but it is an assumption.
- PLSC significant-dimension counts saturate at these sample sizes (MLP hits 256/256 in both conditions); the effect size (residualized top correlation), not the count, is the discriminating statistic and is what this report uses.
- The perturbation (C5) and neural-action-space (C4) analyses are not yet run across architectures; C5 in particular (does removing shared dimensions impair social behavior) would test causality of the RNN's shared dimensions.
Artifacts
- Per-experiment behavior/eval/rollouts/reports:
runs/{experiment}/,runs/reports/{experiment}/. - Neural analyses:
runs/analyses/{experiment}/neural_summary.json. - Cross-architecture:
runs/analyses/cross_arch_plsc_residualized.json,cross_arch_perunit.json,cross_arch_cka.json. - Figures:
runs/analyses/figures/{sharing_vs_vision,cross_arch_cka}.png. - Analysis code:
mouse_run_run/analysis.py,scripts/analysis/neural_analyses.py.