| { |
| "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": { |
| "all_logit_losses_nonincreasing": true, |
| "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." |
| }, |
| "source_checks": { |
| "pdf_sha256": "ca7263e8fd591b27cbd3f869d93ffe1818af27baaa439f278a27a5248ddd92b7", |
| "source_sha256": "d17612d6f31795fe581812dd7e20bf00ce5fabc7408e61411b439232b9917417" |
| } |
| } |
|
|
