We study linear TD(0) under Markovian sampling, where data are generated along a single trajectory. We provide high-probability guarantees for a plain \emph{unprojected} TD(0) algorithm with Polyak–Ruppert (PR) averaging, using a \emph{single} stepsize schedule $\eta_t \propto 1/(\tau_{\mathrm{mix}}\log(t)\,\sqrt{t})$ that depends on mixing time but requires \emph{no prior knowledge of the curvature parameter $\omega$}. Our first result shows that such a choice of the stepsize guarantees that the TD(0) iterates are automatically and uniformly bounded \emph{with high probability}, without projections and without any stability argument based on $\omega$. Building on this result, we establish a simultaneous high-probability convergence guarantee for the PR average: the same stepsize yields both a robust curvature-free $\widetilde{\mathcal O}(\tau_{\mathrm{mix}}/\sqrt{T})$ rate and a fast curvature-dependent $\widetilde{\mathcal O}(\tau_{\mathrm{mix}}^2/(\omega T))$ rate, with the bound taking the minimum of the two. The core technical ingredient is a Poisson-equation toolkit for geometrically mixing Markov chains, which decomposes Markov noise into a martingale term plus a controlled remainder and enables a new self-bounding inductive argument for pathwise stability.

We study fundamental limits of first\hyp order stochastic optimization in a range of non\hyp convex settings, including $L$-smooth functions satisfying Quasar\hyp Convexity ({QC}), Quadratic Growth ({QG}), and Restricted Secant Inequalities ({RSI}). While the convergence properties of standard algorithms are well understood in deterministic regimes, significantly fewer results address the stochastic case, where only unbiased and noisy gradients are available. We establish new lower bounds on the number of noisy gradient queries to minimize these classes of functions, also showing that they are tight (up to a logarithmic factor) in all the relevant quantities characterizing each class. Our approach reformulates the optimization task as a function identification problem, leveraging \textit{divergence decomposition} arguments to construct a challenging subclass that leads to sharp lower bounds. Furthermore, we present a specialized algorithm in the one\hyp dimensional setting that achieves faster rates, suggesting that certain dimensional thresholds are intrinsic to the complexity of non\hyp convex stochastic optimization.

Physics-guided Neural Networks (PGNNs) represent an emerging class of neural networks that are trained using physics-guided (PG) loss functions (capturing violations in network outputs with known physics), along with the supervision contained in data. Existing work in PGNNs has demonstrated the efficacy of adding single PG loss functions in the neural network objectives, using constant tradeoff parameters, to ensure better generalizability. However, in the presence of multiple PG functions with competing gradient directions, there is a need to adaptively tune the contribution of different PG loss functions during the course of training to arrive at generalizable solutions. We demonstrate the presence of competing PG losses in the generic neural network problem of solving for the lowest (or highest) eigenvector of a physics-based eigenvalue equation, which is commonly encountered in many scientific problems. We present a novel approach to handle competing PG losses and demonstrate its efficacy in learning generalizable solutions in two motivating applications of quantum mechanics and electromagnetic propagation. All the code and data used in this work are available at https://github.com/jayroxis/Cophy-PGNN.

This paper presents a detailed description of NCTU's proposal for learning-based image compression, in response to the JPEG AI Call for Evidence Challenge. The proposed compression system features a VVC intra codec as the base layer and a learning-based residual codec as the enhancement layer. The latter aims to refine the quality of the base layer via sending a latent residual signal. In particular, a base-layer-guided attention module is employed to focus the residual extraction on critical high-frequency areas. To reconstruct the image, this latent residual signal is combined with the base-layer output in a non-linear fashion by a neural-network-based synthesizer. The proposed method shows comparable rate-distortion performance to single-layer VVC intra in terms of common objective metrics, but presents better subjective quality particularly at high compression ratios in some cases. It consistently outperforms HEVC intra, JPEG 2000, and JPEG. The proposed system incurs 18M network parameters in 16-bit floating-point format. On average, the encoding of an image on Intel Xeon Gold 6154 takes about 13.5 minutes, with the VVC base layer dominating the encoding runtime. On the contrary, the decoding is dominated by the residual decoder and the synthesizer, requiring 31 seconds per image.

We consider a generalization of mixed regression where the response is an additive combination of several mixture components. Standard mixed regression is a special case where each response is generated from exactly one component. Typical approaches to the mixture regression problem employ local search methods such as Expectation Maximization (EM) that are prone to spurious local optima. On the other hand, a number of recent theoretically-motivated \emph{Tensor-based methods} either have high sample complexity, or require the knowledge of the input distribution, which is not available in most of practical situations. In this work, we study a novel convex estimator \emph{MixLasso} for the estimation of generalized mixed regression, based on an atomic norm specifically constructed to regularize the number of mixture components. Our algorithm gives a risk bound that trades off between prediction accuracy and model sparsity without imposing stringent assumptions on the input/output distribution, and can be easily adapted to the case of non-linear functions. In our numerical experiments on mixtures of linear as well as nonlinear regressions, the proposed method yields high-quality solutions in a wider range of settings than existing approaches.

The latent feature model (LFM), proposed in (Griffiths \& Ghahramani, 2005), but possibly with earlier origins, is a generalization of a mixture model, where each instance is generated not from a single latent class but from a combination of latent features. Thus, each instance has an associated latent binary feature incidence vector indicating the presence or absence of a feature. Due to its combinatorial nature, inference of LFMs is considerably intractable, and accordingly, most of the attention has focused on nonparametric LFMs, with priors such as the Indian Buffet Process (IBP) on infinite binary matrices. Recent efforts to tackle this complexity either still have computational complexity that is exponential, or sample complexity that is high-order polynomial w.r.t. the number of latent features. In this paper, we address this outstanding problem of tractable estimation of LFMs via a novel atomic-norm regularization, which gives an algorithm with polynomial run-time and sample complexity without impractical assumptions on the data distribution.