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"claims": [
"Theorem 3.7 proves an upper bound on excess risk of B_p* * B_X * M/sqrt(D) under an M-coverage condition on depth-D DAGs, extending networked information aggregation from squared loss to Binary Cross-Entropy-based binary classification (Theorem 3.7).",
"Theorem 4.5 proves a matching lower bound showing instances with excess loss of at least Omega(k/D), where k is feature dimension and D is path depth, establishing network depth as a necessary bottleneck (Theorem 4.5).",
"Lemma 3.1 establishes an orthogonality property of Binary Cross-Entropy residuals, E[x(p*(x)-y)] = 0, replacing the variance-decomposition tools used in prior squared-loss analyses (Lemma 3.1).",
"Lemma 3.3 provides a KL/Bregman-type loss decomposition L(q) = L(p*) + D(p*||q), used with Pinsker-style bounds to connect BCE progress to prediction error (Lemma 3.3).",
"The protocol models a sequential DAG in which each agent observes only a subset of features, receives parent logits (not probabilities), and locally minimizes Binary Cross-Entropy before passing its own logits downstream (Section 2)."
],
"formula_summary": {
"all_positive": true,
"cells": 72,
"depth_exponent_minus_one_half": true
},
"gates": {
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"all_m_coverage": true,
"all_pinsker_certificates": true,
"all_upper_bound_certificates": true,
"bce_kl_decomposition_exact": true,
"five_exact_claims_present": true,
"formula_bounds_positive": true,
"formula_panel_complete": true,
"lower_bound_coefficients_valid": true,
"lower_bound_excess_positive": true,
"lower_bound_panel_complete": true,
"lower_bound_scaled_constant_positive": true,
"nonoptimal_reference_control_fails": true,
"orthogonality_panel_complete": true,
"orthogonality_residual_small": true,
"positive_probability_control_gap": true,
"probability_passing_control_worse": true,
"protocol_panel_complete": true,
"source_archive_pin": true,
"source_pdf_pin": true,
"source_scope_rows_complete": true,
"upper_depth_exponent_minus_one_half": true
},
"lower_bound_summary": {
"all_coefficients_in_open_unit_interval": true,
"all_excess_positive": true,
"cells": 56,
"maximum_scaled_excess_D_over_k": 0.099745574981,
"minimum_scaled_excess_D_over_k": 0.049078635566
},
"orthogonality_summary": {
"all_pinsker_certificates": true,
"cells": 24,
"maximum_absolute_decomposition_gap": 0.0,
"maximum_orthogonality_residual": 0.0,
"nonoptimal_reference_counterexamples": 24
},
"paper": {
"arxiv": "2605.01082v1",
"openreview_id": "mrtg4NmvAe",
"title": "Networked Information Aggregation for Binary Classification"
},
"passed": true,
"protocol_summary": {
"all_logit_losses_nonincreasing": true,
"all_m_coverage": true,
"all_upper_bound_certificates": true,
"cells": 48,
"mean_probability_control_excess_gap": 0.00618226885,
"probability_control_worse_cells": 48
},
"scientific_scope": {
"decomposition": "The BCE/KL identity requires the optimal same-feature-space logistic reference.",
"matching": "The source uses matching for the depth bottleneck; upper and lower exponents are not identical.",
"protocol": "The source transmits logits rather than probabilities."
},
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}
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