发表机构
Independent Researcher（独立研究者）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在两个推理任务中具有学习初始化的端口哈密顿深度平衡模型，发现隐式计算存在问题，求解平衡常等于起始点，迭代次数与难度无关，模型未超两层MLP，追溯机制到梯度饥饿，提炼四测试诊断协议。
AI 中文摘要
深度平衡模型有望实现输入自适应隐式计算：更难的问题应需要更多求解器迭代，且求解出的平衡应编码真实迭代推理的结果。我们对一个具有学习初始化的端口哈密顿深度平衡模型在两个推理任务上进行了警示性研究，这两个任务分别是对冻结的DeBERTa嵌入进行ProofWriter蕴含推理以及一个经广度优先搜索验证的图可达性基准测试，其中隐式计算是一个无声无操作。在各个任务、种子和受控消融分支中，求解出的平衡在数值精度上等于求解器的起始点，并且在19次训练运行中的18次中，完全绕过求解器对测试准确率的改变为+0.00个百分点。受控干预证伪了诱人的解释：去除锚定项重现了所有结果，并且用噪声解耦的起始点重新训练得到一个收敛到噪声起始点的求解器，而解码器学会忽略它。唯一的一次逃逸运行发散了（$\|h^{*}-z_0\|=171$），产生了一个协同适应的噪声通道，去除该通道可提高准确率。迭代次数与真实难度不相关（$r=0.009$），并且整个模型在这两个任务上都从未超过两层多层感知器。我们将机制追溯到沿两条不同路径的梯度饥饿，表明标准归零消融被混淆，给出的答案严重依赖种子，而正确的替代测试给出稳定的零值，并且提炼出一个用于审核声称的隐式计算的四测试诊断协议。所有实验都在单个免费的Colab GPU上运行；代码、原始日志和分析脚本已发布。
英文摘要
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.
Comments14 pages, 5 figures. Code, raw logs, and analysis scripts: https://github.com/joyjeet-singh/lazy-identity-deq
