| _version_ | 1866901126931021824 |
|---|---|
| author | Liu, Xiaoming |
| author_facet | Liu, Xiaoming |
| contents | <p>We present a controlled benchmark-design test of whether standard neural</p> <p>networks exhibit RG-like advantages on a local block-spin task. The benchmark is the</p> <p>2D Ising majority-vote coarse-graining map, whose target is well approximated by a</p> <p><span>linear-threshold rule. Our primary evidence is a unified 10-seed same-scale benchmark</span></p> <p><span>regenerated with Wolff cluster sampling. At the critical point </span><span>β</span><span>c </span><span>and lattice size</span></p> <p><span>L</span><span>= 16, the MLP achieves test MSE 0</span><span>.</span><span>226 </span><span>±</span><span>0</span><span>.</span><span>011, while a single linear layer achieves</span></p> <p><span>0</span><span>.</span><span>108 </span><span>±</span><span>0</span><span>.</span><span>010; this ordering is statistically unambiguous (Welch </span><span>p </span><span>= 1</span><span>.</span><span>4 </span><span>×</span><span>10</span><span>−15</span><span>,</span></p> <p><span>Mann-Whitney </span><span>p</span><span>= 1</span><span>.</span><span>8 </span><span>×</span><span>10</span><span>−4</span><span>, Cohen </span><span>d</span><span>=</span><span>−</span><span>11</span><span>.</span><span>46). Off-critical same-scale settings</span></p> <p><span>show the same qualitative pattern. The resulting negative claim is deliberately scoped:</span></p> <p><span>once critical slowing down is removed as the dominant caveat, extra fully connected</span></p> <p>nonlinearity still does not yield an RG-like advantage on this local majority-vote task.</p> <p><span>A reduced-budget whole-lattice tiled transfer diagnostic remains protocol-sensitive</span></p> <p><span>and does not produce a stable monotone scale-degradation law, so cross-scale claims</span></p> <p><span>remain unresolved. Appendix-level diagnostics clarify, but do not overturn, this</span></p> <p><span>picture: an XY-model circular-mean pilot shows that linear baselines cease to dominate</span></p> <p><span>uniformly once the target is genuinely nonlinear, while batch Jacobian summaries show</span></p> <p><span>architecture-dependent local sensitivities but no simple one-number proxy for RG-like</span></p> <p><span>behavior. We therefore argue that credible RG-like claims require matched budgets,</span></p> <p><span>autocorrelation-aware sampling, explicit linear baselines, and transfer protocols that</span></p> <p><span>truly test the stated scale hypothesis.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19395840 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Do Standard Neural Networks Show RG-like Advantages on Local Block-Spin Maps? Liu, Xiaoming <p>We present a controlled benchmark-design test of whether standard neural</p> <p>networks exhibit RG-like advantages on a local block-spin task. The benchmark is the</p> <p>2D Ising majority-vote coarse-graining map, whose target is well approximated by a</p> <p><span>linear-threshold rule. Our primary evidence is a unified 10-seed same-scale benchmark</span></p> <p><span>regenerated with Wolff cluster sampling. At the critical point </span><span>β</span><span>c </span><span>and lattice size</span></p> <p><span>L</span><span>= 16, the MLP achieves test MSE 0</span><span>.</span><span>226 </span><span>±</span><span>0</span><span>.</span><span>011, while a single linear layer achieves</span></p> <p><span>0</span><span>.</span><span>108 </span><span>±</span><span>0</span><span>.</span><span>010; this ordering is statistically unambiguous (Welch </span><span>p </span><span>= 1</span><span>.</span><span>4 </span><span>×</span><span>10</span><span>−15</span><span>,</span></p> <p><span>Mann-Whitney </span><span>p</span><span>= 1</span><span>.</span><span>8 </span><span>×</span><span>10</span><span>−4</span><span>, Cohen </span><span>d</span><span>=</span><span>−</span><span>11</span><span>.</span><span>46). Off-critical same-scale settings</span></p> <p><span>show the same qualitative pattern. The resulting negative claim is deliberately scoped:</span></p> <p><span>once critical slowing down is removed as the dominant caveat, extra fully connected</span></p> <p>nonlinearity still does not yield an RG-like advantage on this local majority-vote task.</p> <p><span>A reduced-budget whole-lattice tiled transfer diagnostic remains protocol-sensitive</span></p> <p><span>and does not produce a stable monotone scale-degradation law, so cross-scale claims</span></p> <p><span>remain unresolved. Appendix-level diagnostics clarify, but do not overturn, this</span></p> <p><span>picture: an XY-model circular-mean pilot shows that linear baselines cease to dominate</span></p> <p><span>uniformly once the target is genuinely nonlinear, while batch Jacobian summaries show</span></p> <p><span>architecture-dependent local sensitivities but no simple one-number proxy for RG-like</span></p> <p><span>behavior. We therefore argue that credible RG-like claims require matched budgets,</span></p> <p><span>autocorrelation-aware sampling, explicit linear baselines, and transfer protocols that</span></p> <p><span>truly test the stated scale hypothesis.</span></p> |
| title | Do Standard Neural Networks Show RG-like Advantages on Local Block-Spin Maps? |
| url | https://doi.org/10.5281/zenodo.19395840 |