Language diffusion models aim to improve sampling speed and coherence over autoregressive LLMs. We introduce Neural Flow Diffusion Models for language generation, an extension of NFDM that enables the straightforward application of continuous diffusion models to discrete state spaces. NFDM learns a multivariate forward process from the data, ensuring that the forward process and generative trajectory are a good fit for language modeling. Our model substantially reduces the likelihood gap with autoregressive models of the same size, while achieving sample quality comparable to that of previous latent diffusion models.

We propose and analyze the problems of \textit{community goodness-of-fit and two-sample testing} for stochastic block models (SBM), where changes arise due to modification in community memberships of nodes. Motivated by practical applications, we consider the challenging sparse regime, where expected node degrees are constant, and the inter-community mean degree ($b$) scales proportionally to intra-community mean degree ($a$). Prior work has sharply characterized partial or full community recovery in terms of a ``signal-to-noise ratio'' ($\mathrm{SNR}$) based on $a$ and $b$. For both problems, we propose computationally-efficient tests that can succeed far beyond the regime where recovery of community membership is even possible. Overall, for large changes, $s \gg \sqrt{n}$, we need only $\mathrm{SNR}= O(1)$ whereas a na\ive test based on community recovery with $O(s)$ errors requires $\mathrm{SNR}= \Theta(\log n)$. Conversely, in the small change regime, $s \ll \sqrt{n}$, via an information theoretic lower bound, we show that, surprisingly, no algorithm can do better than the na\ive algorithm that first estimates the community up to $O(s)$ errors and then detects changes. We validate these phenomena numerically on SBMs and on real-world datasets as well as Markov Random Fields where we only observe node data rather than the existence of links.

The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two-layer leaky ReLU networks trained with the hinge loss on a binary classification task. We consider input data which can be decomposed into the sum of a common signal and a random noise component, which lie on subspaces orthogonal to one another. We characterize conditions on the signal to noise ratio (SNR) of the model parameters giving rise to benign versus non-benign, or harmful, overfitting: in particular, if the SNR is high then benign overfitting occurs, conversely if the SNR is low then harmful overfitting occurs. We attribute both benign and non-benign overfitting to an approximate margin maximization property and show that leaky ReLU networks trained on hinge loss with gradient descent (GD) satisfy this property. In contrast to prior work we do not require the training data to be nearly orthogonal. Notably, for input dimension $d$ and training sample size $n$, while results in prior work require $d = \Omega(n^2 \log n)$, here we require only $d = \Omega(n)$.

We study the statistical problem of estimating a rank-one sparse tensor corrupted by additive gaussian noise, a Gaussian additive model also known as sparse tensor PCA. We show that for Bernoulli and Bernoulli-Rademacher distributed signals and \emph{for all} sparsity levels which are sublinear in the dimension of the signal, the sparse tensor PCA model exhibits a phase transition called the \emph{all-or-nothing phenomenon}. This is the property that for some signal-to-noise ratio (SNR) $\mathrm{SNR_c}$ and any fixed $\epsilon> 0$, if the SNR of the model is below $\left(1-\epsilon\right)\mathrm{SNR_c}$, then it is impossible to achieve any arbitrarily small constant correlation with the hidden signal, while if the SNR is above $\left(1+\epsilon \right)\mathrm{SNR_c}$, then it is possible to achieve almost perfect correlation with the hidden signal. The all-or-nothing phenomenon was initially established in the context of sparse linear regression, and over the last year also in the context of sparse 2-tensor (matrix) PCA and Bernoulli group testing. Our results follow from a more general result showing that for any Gaussian additive model with a discrete uniform prior, the all-or-nothing phenomenon follows as a direct outcome of an appropriately defined ``near-orthogonality property of the support of the prior distribution.

Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed that, contrary to the unconditional case, no universally finite-sample valid test can ever achieve nontrivial power. While informative, this result (based on "hiding" dependence) does not seem to explain the frequent practical failures observed with popular CI tests. We investigate the Kernel-based Conditional Independence (KCI) test - of which we show the Generalized Covariance Measure underlying many recent tests is nearly a special case - and identify the major factors underlying its practical behavior. We highlight the key role of errors in the conditional mean embedding estimate for the Type-I error, while pointing out the importance of selecting an appropriate conditioning kernel (not recognized in previous work) as being necessary for good test power but also tending to inflate Type-I error.

Least absolute shrinkage and selection operator (Lasso), a popular method for high-dimensional regression, is now used widely for estimating high-dimensional time series models such as the vector autoregression (VAR). Selecting its tuning parameter efficiently and accurately remains a challenge, despite the abundance of available methods for doing so. We propose $\mathsf{autotune}$, a strategy for Lasso to automatically tune itself by optimizing a penalized Gaussian log-likelihood alternately over regression coefficients and noise standard deviation. Using extensive simulation experiments on regression and VAR models, we show that $\mathsf{autotune}$ is faster, and provides better generalization and model selection than established alternatives in low signal-to-noise regimes. In the process, $\mathsf{autotune}$ provides a new estimator of noise standard deviation that can be used for high-dimensional inference, and a new visual diagnostic procedure for checking the sparsity assumption on regression coefficients. Finally, we demonstrate the utility of $\mathsf{autotune}$ on a real-world financial data set. An R package based on C++ is also made publicly available on Github.

Adaptive beam switching is essential for mission-critical military and commercial 6G networks but faces major challenges from high carrier frequencies, user mobility, and frequent blockages. While existing machine learning (ML) solutions often focus on maximizing instantaneous throughput, this can lead to unstable policies with high signaling overhead. This paper presents an online Deep Reinforcement Learning (DRL) framework designed to learn an operationally stable policy. By equipping the DRL agent with an enhanced state representation that includes blockage history, and a stability-centric reward function, we enable it to prioritize long-term link quality over transient gains. Validated in a challenging 100-user scenario using the Sionna library, our agent achieves throughput comparable to a reactive Multi-Armed Bandit (MAB) baseline. Specifically, our proposed framework improves link stability by approximately 43% compared to a vanilla DRL approach, achieving operational reliability competitive with MAB while maintaining high data rates. This work demonstrates that by reframing the optimization goal towards operational stability, DRL can deliver efficient, reliable, and real-time beam management solutions for next-generation mission-critical networks.

The widespread adoption of depth sensors has substantially lowered the barrier to point-cloud acquisition. This letter proposes a semantic wireless transmission framework for three dimension (3D) point clouds built on Deep Joint Source - Channel Coding (DeepJSCC). Instead of sending raw features, the transmitter predicts combination weights over a receiver-side semantic orthogonal feature pool, enabling compact representations and robust reconstruction. A folding-based decoder deforms a 2D grid into 3D, enforcing manifold continuity while preserving geometric fidelity. Trained with Chamfer Distance (CD) and an orthogonality regularizer, the system is evaluated on ModelNet40 across varying Signal-to-Noise Ratios (SNRs) and bandwidths. Results show performance on par with SEmantic Point cloud Transmission (SEPT) at high bandwidth and clear gains in bandwidth-constrained regimes, with consistent improvements in both Peak Signal-to-Noise Ratio (PSNR) and CD. Ablation experiments confirm the benefits of orthogonalization and the folding prior.

We extend the moduli-theoretic framework of psychometric batteries to the domain of dynamical systems. While previous work established the AAI capability score as a static functional on the space of agent representations, this paper formalizes the agent as a flow $ν_r$ parameterized by computational resource $r$, governed by a recursive Generator-Verifier-Updater (GVU) operator. We prove that this operator generates a vector field on the parameter manifold $Θ$, and we identify the coefficient of self-improvement $κ$ as the Lie derivative of the capability functional along this flow. The central contribution of this work is the derivation of the Variance Inequality, a spectral condition that is sufficient (under mild regularity) for the stability of self-improvement. We show that a sufficient condition for $κ> 0$ is that, up to curvature and step-size effects, the combined noise of generation and verification must be small enough. We then apply this formalism to unify the recent literature on Language Self-Play (LSP), Self-Correction, and Synthetic Data bootstrapping. We demonstrate that architectures such as STaR, SPIN, Reflexion, GANs and AlphaZero are specific topological realizations of the GVU operator that satisfy the Variance Inequality through filtration, adversarial discrimination, or grounding in formal systems.