Go to TMLR homepageThe Fake Mirror Effect: Foreign Feedback Disrupts Self-Correction in Minimal Recurrent Networks
Abstract: When a recurrent network iteratively refines its predictions, is the performance gain driven primarily by generic temporal integration, or does it depend on the specific geometry of the model's own prior output? To resolve this, we dissect a minimal 35-neuron recurrent network with controlled feedback interventions. Recurrent-specific gain is isolated by two contrasts that do not depend on the convergence-sensitive variable-noise residual: static repeated input, where any deterministic stateless aggregator yields zero gain by construction, and a 120k-parameter MNIST extension where the recurrent loop retains a small but reliable residual. Under variable noise a loop−ensemble residual is additionally present at low-to-moderate noise but is convergence-dependent (reported descriptively), with the no-feedback within-network ensemble matching or nominally exceeding the loop at high noise.
Testing feedback-source dependence directly, we replace self-generated feedback with structurally valid output from an independently trained clone. This consistently degrades performance relative to self-feedback at all tested scales. At the minimal scale, clone feedback drops accuracy below the no-feedback baseline — a scale-bounded fake-mirror inversion (robust under static input; marginal under variable noise). This absolute-harm penalty is scale-dependent in both regimes: under variable noise it transitions to a net-positive but still suboptimal signal at the largest tested width and on MNIST, while under static input it attenuates toward near-neutral at the largest widths; coordinate-shuffled feedback by contrast is harmful at every tested scale.
Progressively stronger static aligners recover the clone-feedback loss essentially fully under static input but plateau near ~85% under variable noise, indicating that static open-loop mapping does not fully restore closed-loop compatibility under variable noise across the aligner capacities we evaluated. A relative condition-number analysis does not separate the evaluated feedback-source conditions. Together, these results characterise feedback-geometry compatibility: an empirical relation between a recurrent receiver and the geometry of its self-generated feedback that is not captured by generic temporal integration alone.
Submission Type: Long submission (more than 12 pages of main content)
Changes Since Last Submission: We have uploaded a revised manuscript addressing the three reviewer reports. The revision adds or changes five main components.
First, in response especially to Reviewer 2HZg's concerns about claim scope and load-bearing analogies, we clarified the framing and terminology around self-feedback, closed-loop feedback, evidence accumulation, co-adaptation, and feedback-geometry compatibility. The claim hierarchy and multiplicity structure are stated explicitly, with a "Descriptive analyses and anchoring" statement identifying which results are descriptive. To bound the chain-of-thought motivation against overreach, §1.5 now includes an explicit one-to-one structural-mapping table with a "Limits of analogy" column scoping the analogy to fixed-step classification and the 35-neuron-to-MNIST range.
Second, we added a no-feedback within-network ensemble control (§3.6) to decompose the variable-noise gain into temporal integration and a recurrent-loop residual. We report its noise-dependent structure descriptively and anchor the recurrent-specific claim on two contrasts that do not depend on this convergence-sensitive comparison: the static-input contrast, where any deterministic stateless aggregator yields zero gain by construction, and the MNIST-scale loop−ensemble residual.
Third, we added quantitative local diagnostics requested by Reviewer 2HZg, including feedback-Jacobian condition-number analysis, norm-matched clone feedback, and additional cosine-divergence measurements. A donor-capability control (§3.3) and an agreement-stratified C2 analysis confirm that the clone is capability-matched (donor vs target t3 paired Wilcoxon p=0.53) and that C2 harm survives on the t1-agreement subset, so the penalty is neither a capability deficit nor reducible to class-level disagreement. As these local diagnostics do not pairwise dissociate the feedback conditions, the mechanistic interpretation remains grounded in the trajectory-level analyses.
Fourth, in response to Reviewer fAhq's scale-honesty concern, we revised the scale claims throughout the paper. Coordinate-shuffled feedback (C1) remains harmful at every tested scale, whereas clone-feedback absolute harm (C2 below no-feedback) is scale- and regime-dependent: under variable noise it transitions to a net-positive but still suboptimal signal at the largest tested width and on MNIST, while under static input it attenuates toward near-neutral at the largest widths. The abstract, §3.9, §4.2, limitations, and conclusion now state this scope explicitly.
Fifth, we added a task-supervised closed-loop BPTT alignment ablation (Appendix G) in response to the concern that static open-loop alignment may be too narrow. This complementary ablation shows that a supervised closed-loop adapter can close the performance gap while using donor information, but it does so by driving the receiver into a saturated feedback regime outside the receiver's native self-feedback distribution. We therefore scope the ~85% static-alignment ceiling to label-free static open-loop alignment rather than treating it as an absolute limit.
We also revised readability throughout in response to Reviewer HJE3: a redesigned decision-space figure (Figure 4), an architecture-and-feedback schematic, first-use definitions of previously undefined terms (variable noise, cosine divergence, same-class resampled feedback, decoupled knockouts), explicit notation, and a plain-language explanation of the Wilcoxon procedure.
During revision we also standardized the training protocol. The submitted 35-neuron pipeline used a time-weighted loss as a weighted sum, which coupled the sum of the weights into the effective learning rate. The revised pipeline uses a weighted average and trains all primary 35-neuron configurations to 1000 epochs. Under this standardized rerun, the main qualitative conclusions remain: the static-input recurrent gain remains positive, the minimal-scale foreign-feedback pattern remains as reported (C1 robustly negative; C2 below no-feedback robustly under static input and marginally under variable noise), the uniform-weight emergence result remains 40/40, and the MNIST-scale residual remains positive. Appendix J decomposes the submitted-protocol versus revised-protocol changes, including a low-band sign flip in the convergence-sensitive §3.6 noise sweep.
Assigned Action Editor: ~Pin-Yu_Chen1
Submission Number: 8010
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