#01Oct 21, 2026
math.ST
Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance
Shayan Hundrieser, Tudor Manole
We analyze the problem of estimating univariate Gaussian mixture densities using the nonparametric maximum likelihood estimator (NPMLE) based on $n$ independent and identically distributed samples. We show that the unconstrained NPMLE achieves the minimax optimal rate $\log(n)/n$ in squared Hellinger distance, when the true mixing measure is sub-Gaussian. In addition, we show that when the true mixing measure has compact support, the NMPLE constrained to a compact interval also achieves the minimax optimal rate, which is slightly faster and of order $\log(n)/(n \log \log n)$. Our proof consists of sharply characterizing the local Hellinger bracketing entropy of the class of finite Gaussian mixtures. One of our key technical innovations is to sharply bound the $L^2$ bracketing entropy of balls of bounded-degree polynomials, which may be of independent interest. As an application, we establish the regret-optimality of $g$-modeling procedures based on the NPMLE in the Gaussian Empirical Bayes problem with bounded priors.
#02Oct 21, 2026
cs.LG
Differentially Private Sparse Reward Estimation with Preference Feedback
Meng Ding, Mingxi Lei, Jie Zhang and 2 more
Reinforcement Learning with Human Feedback (RLHF) has become a central paradigm for aligning Large Language Models with human values. However, the reliance on sensitive preference data necessitates rigorous differential privacy (DP) guarantees to prevent user information leakage. Existing private alignment methods typically assume dense reward parameterizations, resulting in estimation error bounds that scale polynomially with the ambient {model size $d$}. Such dependence is prohibitive in modern {overparameterized models} where $d$ is vast. In this work, we study \emph{Private Sparse RLHF} problem to address this limitation, assuming that human preferences (reward model) are governed by a subset of $s^* \ll d$ relevant features. We provide the first comprehensive theoretical framework for differentially private sparse reward estimation from pairwise preference feedback under the Bradley-Terry-Luce model, and introduce efficient algorithms for both Sample-DP and Label-DP settings. Theoretically, under the squared $\ell_2$ parameter estimation error, we establish upper bounds of $\widetilde{O}(s^*/n + {s^*}^2/n^2\varepsilon^2)$ for $(\varepsilon,δ)$-Sample-DP and $\widetilde{O}(s^*/n + s^*/n\varepsilon^2)$ for $\varepsilon$-Label-DP based on randomized response, where $n$ is the training data size. For the lower bounds, we show that the Sample-DP rate is nearly optimal, and that the guarantee for our Label-DP method cannot be further improved within the randomized-response framework. We also provide a general lower bound for the problem with Label-DP. Empirically, our framework demonstrates superior efficacy over dense baselines across sentiment generation and safety alignment benchmarks, offering a significantly more favorable privacy-utility trade-off.
#03Oct 21, 2026
cs.CR
VX-One: Typed, Calibrated Decision Heads for Real-Time Perimeter Triage - An empirical study of unknown-attack honesty, cascade gray zones, and calibration under drift
Juan S. Santillana
Perimeter triage faces a latency/semantics trade-off: signature engines are fast and format-safe but blind to unseen attacks, while generative models are semantic but slow and produce unparseable output. In late 2026 a class of commercial System One decision models (TypeSafe Jev; Microsoft-Decision-1) began selling typed decision primitives - binary gates, closed-set choices, ordinal scores - as product APIs, with no academic treatment. We present VX-One: a small multi-head network (100K-10M parameters) whose outputs are these primitives - a calibrated gate, a choice over a closed candidate set that always includes an explicit unknown option, and an ordinal score, trained multi-task, temperature-calibrated per head (~0.7-1.7 ms p50 on CPU). We evaluate it on UNSW-NB15, CIC-IDS2017, EMBER2024 against calibrated XGBoost, Random-Forest, MLP, Kitsune, and measure a two-phase cascade (Suricata with 52,674 Emerging-Threats rules -> VX-One) over five days of CIC-IDS2017. Findings: (i) VX-One wins detection (AUROC/FPR@95%TPR) on UNSW-NB15 and under temporal drift on CIC-IDS2017 (0.711 vs 0.637), but XGBoost wins multi-class attribution on all three benchmarks; (ii) leave-one-family-out gate detects never-seen families on 9/9 UNSW folds yet drops below chance on CIC recon family, and abstention threshold transfers poorly across benchmarks; (iii) on payload-less reconstructions signature engines resolve ~0.1% of flows - gray zone ~99.9% of traffic, recovered by Phase 2 (combined recall >=0.978); (iv) calibration collapses under temporal drift (ECE 0.04->0.40) for every method while ranking partially survives. We provide a measured account of where typed calibrated decisions help perimeter triage, and where they fail.
#04Oct 21, 2026
cs.CL
GoiBERT: Compact Vietnamese Language Models via Two-Stage Knowledge Distillation
Quang Anh Kiet Tran, Nam Anh Tran, Manh Hung Trinh and 3 more
Vietnamese pre-trained encoders have improved rapidly, but the strongest ones are large, multilingual-vocabulary models or depend on external word segmentation, which makes them costly to deploy. We present GoiBERT, a family of two compact Vietnamese encoders with 26M and 49M parameters that operate directly on raw text. GoiBERT learns from two complementary teachers. A same-tokenizer Vietnamese encoder first teaches general-purpose representations. A much larger teacher then provides task-level guidance through soft labels that are generated without ever labeling its own training data. Across eight benchmarks covering text classification, aspect-based sentiment analysis, natural language inference, and named entity recognition, GoiBERT-large achieves the highest average score among non-teacher models. It does so with fewer than half the parameters of the strongest compact baseline and twice its throughput. GoiBERT-base retains 99% of that baseline's performance at a quarter of its size. Our analysis shows that compression is nearly lossless for sentiment and classification tasks but remains costly for inference and entity recognition, which points to clear directions for future work. Our code and models are available at: https://github.com/Nhantran65/GoiBERT.git
#05Oct 21, 2026
cs.LG
Orbitol: Crystal Generation on Wyckoff Orbits
Ivan Žugec, Joshua Rosenthal, Ivor Lončarić and 2 more
Generative models propose crystalline materials by learning composition and geometry, but unconditional sampling gives no direct control over the space group, which constrains whether responses such as piezoelectricity are symmetry-allowed. We present Orbitol, a crystal generator built on the Crystalite diffusion Transformer that replaces atom tokens with Wyckoff-orbit tokens. Given a space group and a collection of occupied Wyckoff positions, Orbitol generates the atom type and free coordinates of each orbit together with a compatible lattice, so every valid structure is invariant under the operations of the requested group. It generates structures two to three orders of magnitude faster than the symmetry-aware baselines at the evaluated settings. On MP-20, 13.8% of Orbitol's attempts yielded stable or metastable, unique and novel structures that retained the requested space group after relaxation, compared with 10.8% for SGFM, the next best model. We also introduce SPARC, a score that combines retention of the raw detected space group with agreement between the retained-group and training distributions. Finally, we used Orbitol to generate candidates in piezoelectric crystal classes. Of the structures selected by internal screening, 89% passed our density functional theory checks, and 79% also matched no Materials Project or Alexandria entry with the same space group. Their median figure of merit was nine times that of the piezoelectric materials computed in the Materials Project, and 24% of the new candidates ranked in that set's top 10%.