Detecting and Discriminating Operator Misspecification in Hybrid PDE-Parameter Learning: a Reference-Free Instrument, with Discrimination Bounded In Sample

• URL: http://arxiv.org/abs/2608.16925v1
• Date: Tue, 04 Aug 2026 21:20:44 GMT
• Title: Detecting and Discriminating Operator Misspecification in Hybrid PDE-Parameter Learning: a Reference-Free Instrument, with Discrimination Bounded In Sample
• Abstract summary: We build an instrument that reads from a single fit and with no oracle.<n>We report where the instrument is blind, a pre-registered negative where a neural estimator loses to Tikhonov-regularized inversion at recovery.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We build an instrument that reads, from a single fit and with no oracle, whether the operator a hybrid PDE-parameter estimator postulates is wrong-and separates that from a merely unidentifiable parameter. On one self-adjoint parabolic inverse problem, an information-matrix statistic with plug-in scale and per-seed parameter has median 0.19 under correct specification, rejection rate $0.033$ against a pre-registered ceiling of $0.10$, and rises to $224$ and $85$ under two misspecifications, firing in every replicate. On a correctly specified but non-identifiable design it stays mute-$0.050$ at $n=200$, Clopper-Pearson $[0.024, 0.090]$-while a rank statistic collapses to zero at a pre-registered boundary $c_5^*=2.15\times10^{-3}.$ Two readings of one fit therefore separate the two failures across the three designs a deployable test reaches. That separation is the contribution; detection alone is a crowded flank. In sample it is a bound, out of sample a direction. It is needed because the usual accuracy check is blind: the misspecified estimator's in-domain RMSE is $2.7\times 10^{-2}$, below the observation noise for $σ\geq 0.05,$ while the coefficient is wrong by $29.7\%$ at zero noise, $31.2\%$ at the loudest. Nor is the failure architectural: a one-parameter curve fit, a bare parameter and multilayer perceptrons of $49$ and $241$ parameters converge to the same pseudo-true, matched in closed form to $0.07\%,$ whereas a physics-informed network, with its composite objective, converges to a disjoint one. We report where the instrument is blind, a pre-registered negative where a neural estimator loses to Tikhonov-regularized inversion at recovery, and the hypothesis under which its guarantee holds but a trained network violates it.

Related papers

• The exact price of local realism in CHSH experiments: a measurement-dependence-detection trade-off surface, a moiré phase-locking mechanism that saturates it, and an unmeasured fringe in the fourfold coincidence sum [0.0]
  I solve the unique detection profile $D(m)=sqrtm,h(m)$ under which a deterministic sign model reproduces the singlet exactly.<n>Surviving local accounts trade off measurement dependence against a $cos 4(a-b)$ modulation of the fourfold coincidence sum.<n>I exhibit a local mechanism -- moire phase locking -- with deterministic phase evolution and all randomness quenched in frozen offsets and flight times.
  arXiv  Detail & Related papers  (2026-08-19T13:14:52Z)
• Round-Trip Consistency: Bidirectional Diffusion Models Can Predict Their Own Rollout Errors [51.56484100374058]
  Autoregressive models accumulate error over long rollouts, yet at deployment there is no ground truth to measure it against.<n>We train a single conditional latent diffusion model that steps a dynamical system forward or backward in time via a direction flag.<n>We show that this bidirectionality supplies a measurement-free test-time error signal.
  arXiv  Detail & Related papers  (2026-08-01T13:49:46Z)
• Saturation Makes Quantization Error Additive: A Coverage Model with a Certificate [0.0]
  Mixed-precision quantization must decide which parts of a model to keep at higher precision.<n>We show that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation.<n>We propose the coverage model $f(S)=cbigl (1-prod_iin S (1-a_i)bigr)$, which reproduces the measured variance profile of $f$ to within a few percent from its $L$ fitted break-rates.
  arXiv  Detail & Related papers  (2026-07-14T02:08:33Z)
• A Spectral Phase Diagram for Binary Few-Shot Classification: Intrinsic Dimensionality, Geometric Saturation, and Representational Diagnosis [0.0]
  The saturation index $S(K) = operatornameerank(widehat_W(K)) / K$ measures the ratio of the effective rank of the pooled within-class sample covariance to the shot count.<n>The index is computable in $O(d3)$ time from support features alone, requiring no test labels or trained classifier.
  arXiv  Detail & Related papers  (2026-06-12T16:46:24Z)
• Hidden-State Privacy Has an Empty Middle [51.56484100374058]
  We prove a complementary Fisher-ball lower bound: every full-rank Gaussian release at $O(1)$ Fisher utility admits a direction whose Mahalanobis signal grows linearly in hidden width.<n>A split-memory transformer trained from scratch reaches $G_mathrmMah in [20, 33]$ at 90M and maintains a $6$--$24times$ advantage over same-budget GPT baselines from 30M to 1B at a fixed-token language loss penalty.
  arXiv  Detail & Related papers  (2026-05-21T20:12:09Z)
• The Geometry of Forgetting: Temporal Knowledge Drift as an Independent Axis in LLM Representations [50.43168858368539]
  Large language models confidently produce outdated answers, and no existing method can detect them.<n>We show this is not an engineering failure but a structural one: temporal drift is encoded as a direction in the residual stream geometrically to both correctness and uncertainty.
  arXiv  Detail & Related papers  (2026-05-09T22:27:31Z)
• MEMSAD: Gradient-Coupled Anomaly Detection for Memory Poisoning in Retrieval-Augmented Agents [0.0]
  We formalize memory poisoning attacks on retrieval-augmented agents as a Stackelberg game with a unified evaluation framework.<n>We show faithful evaluation increases measured attack success by $4times$ (ASR-R: 0.25 to 1.00$)<n>Our primary contribution is MEMSAD, a calibration-based defense grounded in a gradient coupling.
  arXiv  Detail & Related papers  (2026-05-05T08:15:41Z)
• Hardware Validation of DAGI via a Modular "Ridge" Signature and High-Order Synergistic Information [0.0]
  DAGI (Directed Acyclic Graph Information) framework on IBM Quantum hardware.<n>Small, controlled experiment whose ideal output distribution is constrained to a low-dimensional modular manifold (a "ridge)<n>Key recovery exceeds chance: per-shot accuracy 0.1689 (chance 0.125, 95% Wilson CI [0.1610, 0.1772])<n>These results support the claim that DAGI detects and quantifies non-trivial, hardware-resilient information structure.
  arXiv  Detail & Related papers  (2026-04-16T14:16:59Z)
• Tight Convergence Rates for Online Distributed Linear Estimation with Adversarial Measurements [66.94250413799232]
  We study mean estimation of a random vector $X$ in a distributed parameter-server-worker setup.<n>Key challenges are adversarial measurements and asynchrony.<n>Results provide a unified finite-time characterization of robustness, identifiability, and statistical efficiency in distributed linear estimation with adversarial workers.
  arXiv  Detail & Related papers  (2026-04-07T11:45:55Z)
• Optimal Unconstrained Self-Distillation in Ridge Regression: Strict Improvements, Precise Asymptotics, and One-Shot Tuning [61.07540493350384]
  Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth and the teacher's own predictions.<n>We show that for any prediction risk, the optimally mixed student improves upon the ridge teacher for every regularization level.<n>We propose a consistent one-shot tuning method to estimate $star$ without grid search, sample splitting, or refitting.
  arXiv  Detail & Related papers  (2026-02-19T17:21:15Z)
• The Sample Complexity of Robust Covariance Testing [56.98280399449707]
  We are given i.i.d. samples from a distribution of the form $Z = (1-epsilon) X + epsilon B$, where $X$ is a zero-mean and unknown covariance Gaussian $mathcalN(0, Sigma)$. In the absence of contamination, prior work gave a simple tester for this hypothesis testing task that uses $O(d)$ samples. We prove a sample complexity lower bound of $Omega(d2)$ for $epsilon$ an arbitrarily small constant and $gamma
  arXiv  Detail & Related papers  (2020-12-31T18:24:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.