发现物理结构化深度平衡模型实际未进行迭代推理，初始值即为最终解。
The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning
- 通过控制实验揭示模型收敛至初始值，迭代过程形同虚设。
- 18/19训练中跳过求解器对准确率无影响，说明隐式计算未发挥作用。
- 提出四步诊断法，可检测模型是否真正执行了迭代推理。
深度平衡模型承诺输入自适应的隐式计算：难题应需更多求解迭代，且平衡点应反映真实迭代推断结果。我们对一个基于端口-哈密顿的DEQ模型在两个推理任务上进行了警示性研究——基于冻结DeBERTa嵌入的ProofWriter蕴含判断，以及经广度优先搜索验证的图可达性基准测试。结果显示，隐式计算实质是无声的空操作：所有任务、随机种子和受控消融中，求解后的平衡点与求解起始点数值精度一致；完全跳过求解器后，测试准确率变化为+0.00个百分点（19次训练中18次）。受控干预否定了常见解释：移除锚定项后重现所有结果；用噪声解耦起始点重训练，求解器收敛至噪声起始点，而解码器学会忽略它。唯一发散的训练运行偏差达‖h*−z₀‖=171，产生共适应的噪声通道，其移除反而提升准确率。迭代次数与真实难度完全无关（r=0.009），整个系统在任一任务上均不及两层MLP表现。我们追溯机制源于梯度饥饿的两条路径，证明标准零化消融存在混淆，正确替代测试才给出稳定零结果，并提炼出四步诊断协议以审计声称的隐式计算。所有实验仅用单个免费Colab GPU完成；代码、原始日志与分析脚本均已公开。
原文摘要 · Abstract (English)
Deep equilibrium models promise input-adaptive implicit computation: harder problems should demand more solver iterations, and the solved equilibrium should encode the result of genuine iterative inference. We report a cautionary study of a port-Hamiltonian DEQ with a learned initialization on two reasoning tasks -- ProofWriter entailment over frozen DeBERTa embeddings and a BFS-verified graph-reachability benchmark -- in which the implicit computation is a silent no-op. Across tasks, seeds, and controlled ablation arms, the solved equilibrium equals the solver's start point to numerical precision, and bypassing the solver entirely changes test accuracy by +0.00 percentage points in 18 of 19 training runs. Controlled interventions falsify the tempting explanation: removing the anchoring term reproduces every result, and retraining with noise-decoupled starts yields a solver that converges to the noisy start while the decoder learns to ignore it. The single escaping run diverges instead ($\|h^{*}-z_0\|=171$), producing a co-adapted noise channel whose removal improves accuracy. Iteration counts are uncorrelated with ground-truth difficulty ($r=0.009$), and the full apparatus never outperforms a two-layer MLP on either task. We trace the mechanism to gradient starvation along two distinct routes, show that the standard zeroing ablation is confounded and gives wildly seed-dependent answers where the correct substitution test gives a stable zero, and distill a four-test diagnostic protocol for auditing claimed implicit computation. All experiments run on a single free Colab GPU; code, raw logs, and analysis scripts are released.
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