#01Oct 27, 2026
math.ST
Regression Functions as Fields on Covariate Space: Evolution Equations, the Hessian, and Identification
Nobuaki Tanaka
For each time $t$, the regression function $m_t(x)=E[Y_t\mid X_t=x]$ of an outcome on contemporaneous covariates can be regarded as a field on covariate space. We study how this field evolves when the covariates of individual units move as a diffusion and the outcome attached to each unit changes according to its own dynamics. Under mild regularity we show that $m_t$ satisfies a second-order evolution equation whose diffusion term is $\frac12\mathrm{tr}(Σ\nabla^2 m_t)$, the trace of the Hessian of the regression function weighted by the instantaneous covariance $Σ$ of the covariate increments, whose transport term is the drift of the time-reversed covariate process, and whose source term is the conditional mean rate of change of the outcome. The equation is a regression-theoretic reading of a classical transport law, and it yields a Feynman-Kac representation of $m_t$ along reversed covariate paths. We connect the Hessian appearing in the equation to the Hessian estimated by quadratic regression (under Gaussian design the best quadratic approximation has Hessian $E[\nabla^2 m(X)]$ exactly) and to the leading bias of kernel smoothers. For binary outcomes governed by bistable replicator dynamics with imitation among units with similar covariates, the closed equation is of Nagumo type, its planar travelling fronts are exactly logistic in $(x,t)$, and a single logistic regression of the outcome on covariates and time identifies the ratio of diffusion to reaction and the direction of invasion. We discuss identification under panel versus repeated cross-sectional designs and a two-stage estimation strategy, and we illustrate the results with simulations.
#02Oct 27, 2026
stat.ML
Graph Representation Learning via Adaptive Expectile Aggregation
Tianyi Zhu, Wei Lan
Graph neural networks (GNNs) rely critically on neighborhood aggregation, yet conventional mean aggregation may fail to capture class-relevant distributional information, particularly in heterophilic graphs. We propose ExpectileGCN, an adaptive graph aggregation framework that introduces a learnable expectile level to capture neighborhood information beyond the mean. The proposed operator continuously adjusts aggregation between minimum- and maximum-type behaviors, with mean aggregation as a special case. A differentiable approximation based on sigmoid smoothing and fixed-point iterations enables end-to-end optimization. Theoretically, we establish stability properties and transductive generalization guarantees for ExpectileGCN. We further investigate its classification risk under heterophilic neighborhood models. For informative neighborhoods, we show that expectile aggregation can exploit class-dependent scale differences to achieve a classification advantage over mean aggregation. Under a local asymptotic regime with diminishing per-neighbor label informativeness, we establish that this advantage can persist in terms of limiting classification risk. Experiments on homophilic and heterophilic benchmark graphs demonstrate strong predictive performance and improved robustness under feature corruption and structural perturbations.
#03Oct 27, 2026
stat.ML
QD-PINN:A Physics-Informed Neural Network Approach to Bayesian Quickest Detection in High-Dimensional Diffusions
Hang Ye, Yi Liu, Haipeng Xing
Quickest detection problems (QDPs) arise in a wide range of applications. However, the complementarity structure of the associated variational inequalities poses substantial challenges for traditional numerical methods, particularly in high-dimensional settings. We propose a PINN-based framework for estimating the optimal stopping boundary in QDPs with high-dimensional diffusion processes and spatial dependence, while overcoming the curse of dimensionality. Theoretically, we establish a novel equivalence between the free-boundary PDE and an infinite-dimensional stochastic optimization problem, rigorously justifying the use of finite-dimensional neural networks to approximate the true solution. Furthermore, we assess the robustness of the proposed framework by quantifying uncertainty in the learned stopping boundaries using deep ensembles and Monte Carlo dropout. The results show low variability across independent training runs and stochastic forward passes, indicating stable and consistent boundary estimates. We also compare our PINN results with reference numerical solutions where available and find close agreement.
#04Oct 27, 2026
cs.NI
Keeping Inference in the Radio: Design and Measurement of a Spiking Accelerator for mmWave ISAC Activity Recognition
Anthony Sánchez, Rafael Ruiz, José A. Belloch and 2 more
Integrated sensing and communication allows wireless networks to recognize human activity from the channel estimates that the receiver computes anyway. The inference, however, runs on the general-purpose processors of the base station, access point or handset, which are the first components a device switches off to save energy. Always-on sensing therefore requires a classifier that is small enough to remain powered while the rest of the system sleeps. We investigate whether Spiking Neural Networks (SNNs) can provide such a classifier. To this end, we generate SNN accelerators for micro-Doppler activity recognition on the public DISC dataset (IEEE 802.11ay at 60 GHz) with the open-source Spiker+ framework, and implement them together with a spike encoder on a ZCU208 RFSoC, so that the complete chain from micro-Doppler frame to activity label runs in programmable logic. A fully connected SNN with 132 neurons achieves 94.7 % accuracy (90.7 % macro-F1) on unseen subjects and performs an inference in 206 microseconds. Compared to conventional networks of the same topology on the same device, it requires an eighth of the logic and 3.4X less dynamic energy per decision than a network fed the same binary spikes, at comparable accuracy, and 7.6X less than a network fed the 16-bit spectrogram, at 1.2 points lower accuracy. Quantization-aware training reduces its weights to 3 bits within half a percentage point of the 6-bit network at the same encoder threshold
#05Oct 27, 2026
cs.LG
An Input Skip Can Reparameterize a VAE Without Improving the Generator
Kevin Lee
An input skip can reduce reconstruction error while leaving a model's distribution of new samples unchanged. For a Gaussian variational autoencoder (VAE) with constant input skip $0\leqα<1$, a model without a skip can be written in skip form by multiplying its decoder output by $b=1-α$ and its noise variance by $b^2$. The distribution of observations and latent variables and its exact generative scores stay the same, while reconstruction mean squared error (MSE) is multiplied by $b^2$. Separate training can produce different generators because optimization depends on the parameter coordinates. In a Gaussian experiment with known density, changing skip and observation variance together reduces MSE but worsens energy score and the estimate of negative log density from importance sampling. On seven annual Deep-ocean Assessment and Reporting of Tsunamis (DART) records, energy score differences at the same observation variance have both signs on four original records and favor the skip on three records from 2018. Probabilistic principal component analysis (PPCA) has lower mean energy scores than every neural DART fit. With the encoder and decoder kept the same, estimating observation variance from training reconstruction error can also worsen energy score. Assessing generation requires more than reconstruction error.