发表机构
University of Illinois Chicago（伊利诺伊大学芝加哥分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出“挑战下的训练”可执行证书框架，定义资源索引的挑战能力模，通过实验验证其在ResNet-18蒸馏问题中可有效区分解码器欠使用与表征不足，实现对神经网络训练状态的诊断与重新认证。
AI 中文摘要
平坦的训练曲线无法揭示神经网络是否已达到全局最优、陷入局部最优、受表征限制或与训练器不匹配。我们提出“挑战下的训练”这一可执行证书框架，其中预先声明的、架构有效的过程在同一认证类别中构建完整替代方案，并重新评估同一目标。任何值更低的候选都是可复现的见证，其下界为检查点的经验全局最优间隙。通过有限套件仅为套件相对的；全局间隙结论需要单独证明的覆盖机制。我们定义资源索引的挑战能力模，其表征与通过兼容的最大间隙。对于平方损失，当前的块递减算子使覆盖可检验，并产生一致和实现残差界。我们证明了逆前沿：无覆盖时，一阶ReLU训练器可达到无限多个精确条件头最优，同时收敛到非全局点。在具有已知最优的通道门控ResNet-18蒸馏问题中，8个内部挑战覆盖所有240个审计输出方向，实现残差界在真实间隙的1.74至3.02倍范围内。配对预测证书区分解码器欠使用与表征不足，而量化去噪研究展示了诊断、修复和当前状态的重新认证。
英文摘要
A flat training curve does not reveal whether a neural network has reached a global optimum, is locally trapped, is representation-limited, or is mismatched to its trainer. We introduce Training Under Challenge, an executable-certificate framework in which predeclared, architecture-valid procedures construct complete alternatives in the same certified class and reevaluate the same objective. Any lower-valued candidate is a replayable witness that lower-bounds the checkpoint's empirical global-optimality gap. Passing a finite suite is only suite-relative; global-gap conclusions require a separately justified coverage mechanism. We define a resource-indexed challenge-power modulus that characterizes the largest gap compatible with passage. For squared loss, current block-decrease operators make coverage checkable and yield uniform and realized-residual bounds. We prove the converse frontier: without coverage, a first-order ReLU trainer can reach infinitely many exact conditional head optima while converging to a non-global point. On a channel-gated ResNet-18 distillation problem with known optimum, eight internal challenges cover all 240 audited output directions, and realized-residual bounds lie within factors of 1.74--3.02 of the true gap. Paired predictive certificates separate decoder under-use from representation insufficiency, while quantized-denoising studies demonstrate diagnosis, repair, and current-state recertification.
Comments82 pages, 24 figures, 10 tables. Ancillary reproducibility materials included
