#01Jul 20, 2026
cs.LG
A Continual Validation, Updating, and Decision-Making Framework for Self-Adaptive Digital Twins via Robust Model Predictive Control: A Case Study in Additive Manufacturing
Yi-Ping Chen, Ying-Kuan Tsai, Vispi Karkaria and 3 more
Digital Twins rely on surrogate models to mirror physical systems in real time, yet these models can degrade as operating conditions evolve, a phenomenon known as concept drift. Maintaining surrogate fidelity under drift, particularly when models must also capture aleatoric uncertainty, remains an open challenge. Existing adaptive frameworks lack principled mechanisms for detecting when updates are needed, for efficiently adapting models from limited streaming data, and for certifying that updates genuinely improve predictive performance. Here we present an adaptive Digital Twin framework that integrates a Fisher score--based multivariate drift detector, Low-Rank Adaptation (LoRA) for parameter-efficient continual learning, and a Mann--Whitney $U$ test for online statistical validation. The framework monitors surrogate-model confidence via Fisher score vectors, triggers targeted fine-tuning of fewer than 1% of model parameters upon drift detection, and statistically certifies predictive improvement before deploying the updated surrogate. Applied to a stochastic linear system and a directed energy deposition additive manufacturing process as case studies, the framework successfully detects distributional shifts with short delays and restores both predictive accuracy and uncertainty quantification under abrupt and incremental drift. These results establish a statistically rigorous and computationally tractable pathway for sustaining the trustworthiness of neural-network--based Digital Twins throughout their operational life cycle.
#02Jul 20, 2026
cs.LG
The Calibration Channel Determines the Bayes-Error Proxy: An Exact Law for Temperature-Induced Distortion
Shreyas Pradeepkumar Khandale
The soft-label Bayes-error estimator beta(z) = E[min(z, 1-z)] of Ishida et al. estimates the irreducible error of a binary task directly from probability-valued labels. Recent work by Ushio et al. showed that this estimator is fragile when the probabilities are not the true posterior: even perfectly calibrated soft labels can yield a substantially inaccurate estimate, and they propose isotonic calibration as a consistent remedy. We complement that line of work by characterizing exactly how the most widely used post-hoc calibration map -- temperature scaling -- distorts the proxy. We prove an exact, model-free identity reducing the temperature-scaled proxy to the classifier's margin distribution, from which we obtain (i) strict monotonicity in the temperature and (ii) a continuous bijection from the temperature axis onto the open interval (0, 1/2), so that a fixed classifier -- with fixed decisions and fixed 0-1 error -- can be made to report any proxy value whatsoever. Under a Gaussian model of the logits we further derive a two-parameter closed form for the entire proxy-versus-temperature curve. Across CIFAR-10, Fashion-MNIST, and SVHN (eight binary tasks), the proxy varies by 56x to 980x at constant test error, the closed form reproduces the empirical curve to within 0.018, and the calibration temperature that minimizes the expected calibration error does not coincide with any stable proxy value. Our results give a precise, predictive account of the distortion whose existence motivates calibration-based remedies, and they reinforce the practical recommendation that a proxy value is meaningful only together with the mechanism that produced its probabilities.
#03Jul 20, 2026
cs.CL
How Does Alignment Tuning Shape Representations of Sycophancy and Related Cue-Induced Biases in LLMs?
Prakhar Gupta, Terry Jingchen Zhang, Florent Draye and 2 more
Modern LLMs are alarmingly susceptible to surprisingly simple immaterial changes of input prompts: a casual hint, an incorrectly labeled few-shot example, or a fake prior assistant turn often flips an originally correct answer. We study where this susceptibility, spanning sycophancy and related cue-induced biases, lives inside the model. Across five model families and seven BCT bias types, we extract a per-bias direction from hidden states and triangulate it through three measures: probing, leave-one-dataset-out transfer, and causal intervention. The susceptibility is largely installed by alignment tuning rather than pretraining: pretrained base models barely cave to these biases, and their activations carry no cue-specific signal beyond question content. Within aligned models, each bias becomes a single coherent direction that we can both decode and steer along, recovering the unbiased answer across every family we test. The biases stay representationally distinct, however: cross-bias entanglement is model-specific rather than a property of the bias category, and even behaviorally similar biases occupy different directions. The same intervention also serves as a modest debiasing tool, recovering a meaningful share of bias-induced errors while preserving most correct answers across all instruct families. Cue-induced bias is therefore best understood not as a single flaw in LLMs but as a family of distinct, causally active directions that alignment tuning installs.
#04Jul 20, 2026
cs.LG
Totally Positive Matrices and the Highest-Order Coefficients of the Characteristic Polynomial
Tiago Closs, Leandro Farina
We investigate the extent to which totally positive matrices can be distinguished through the highest-order coefficients of their characteristic polynomials. To identify the most informative coefficients, we also employed neural-network classifiers together with feature-attribution methods. Using datasets built from several structured totally positive families, including products of positive bidiagonal matrices, Vandermonde matrices, and Cauchy matrices, we find that the coefficients (a_{n-1}, a_{n-2}, a_{n-3}) already contain strong discriminatory information for separating totally positive from non-totally positive matrices in dimensions 5, 10, and 30. The resulting separation is markedly nonlinear and admits a natural geometric description in the corresponding three-dimensional coefficient space by means of Mahalanobis ellipsoids. These ellipsoids enclose the totally positive samples while excluding most non-totally positive ones. Moreover, different structured totally positive families exhibit distinct ellipsoidal signatures, and the separation between these signatures increases with the dimension. These observations lead us to formulate a conjecture on the geometric separation of structured totally positive families in the space determined by the three highest-order characteristic coefficients.
#05Jul 20, 2026
econ.EM
Vector Search As Nearest Neighbor Matching: RAG-based Policy Learning in Causal Inference
Masahiro Kato, Taka Kato
We propose one-step and two-step methods for policy learning with retrieval-augmented generation (RAG). We formulate RAG-based action selection under the potential outcome framework. In the two-step method, vector search retrieves action-specific neighboring evidence in an embedding space, the generator estimates conditional expected outcomes or their contrasts, and a plug-in rule selects an action. This formulation connects action-specific vector search with nearest-neighbor matching in causal inference. We decompose the regret of the two-step method into candidate-generation regret and within-candidate choice regret, and we bound the latter using prediction-error guarantees for nearest-neighbor estimators and transformers. We evaluate the one-step method directly as a policy because its intermediate computation is unobserved.