What are the limits of controlling language models via synthetic training data? We develop a reinforcement learning (RL) primitive, the Dataset Policy Gradient (DPG), which can precisely optimize synthetic data generators to produce a dataset of targeted examples. When used for supervised fine-tuning (SFT) of a target model, these examples cause the target model to do well on a differentiable metric of our choice. Our approach achieves this by taking exact data attribution via higher-order gradients and using those scores as policy gradient rewards. We prove that this procedure closely approximates the true, intractable gradient for the synthetic data generator. To illustrate the potential of DPG, we show that, using only SFT on generated examples, we can cause the target model's LM head weights to (1) embed a QR code, (2) embed the pattern $\texttt{67}$, and (3) have lower $\ell^2$ norm. We additionally show that we can cause the generator to (4) rephrase inputs in a new language and (5) produce a specific UUID, even though neither of these objectives is conveyed in the generator's input prompts. These findings suggest that DPG is a powerful and flexible technique for shaping model properties using only synthetic training examples.

Large language models (LLMs) can struggle to memorize factual knowledge in their parameters, often leading to hallucinations and poor performance on knowledge-intensive tasks. In this paper, we formalize fact memorization from an information-theoretic perspective and study how training data distributions affect fact accuracy. We show that fact accuracy is suboptimal (below the capacity limit) whenever the amount of information contained in the training data facts exceeds model capacity. This is further exacerbated when the fact frequency distribution is skewed (e.g. a power law). We propose data selection schemes based on the training loss alone that aim to limit the number of facts in the training data and flatten their frequency distribution. On semi-synthetic datasets containing high-entropy facts, our selection method effectively boosts fact accuracy to the capacity limit. When pretraining language models from scratch on an annotated Wikipedia corpus, our selection method enables a GPT2-Small model (110m parameters) to memorize 1.3X more entity facts compared to standard training, matching the performance of a 10X larger model (1.3B parameters) pretrained on the full dataset.

This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures. The classical estimation method, restricted maximum likelihood (REML), requires repeated inversion and factorization of large, sparse precision matrices, which makes this computation costly. To sort this problem out, we propose a variational restricted maximum likelihood (VREML) framework that approximates the intractable marginal likelihood using a Gaussian variational distribution. By constructing an evidence lower bound (ELBO) on the restricted likelihood, we derive a computationally efficient coordinate-ascent algorithm for jointly estimating the spatial random effects and variance components. In this article, we theoretically establish the monotone convergence of ELBO and mathematically exhibit that the variational family is exact under Gaussian ICAR settings, which is an indication of nullifying approximation error at the posterior level. We empirically establish the supremacy of our VREML over MLE and INLA.

In the last decades, energy-based models (EBMs) have become an important class of probabilistic models in which a component of the likelihood is intractable and therefore cannot be evaluated explicitly. Consequently, parameter estimation in EBMs is challenging for conventional inference methods. In this work, we provide a unified framework that connects noise contrastive estimation (NCE), reverse logistic regression (RLR), multiple importance sampling (MIS), and bridge sampling within the context of EBMs. We further show that these methods are equivalent under specific conditions. This unified perspective clarifies relationships among existing methods and enables the development of new estimators, with the potential to improve statistical and computational efficiency. Furthermore, this study helps elucidate the success of NCE in terms of its flexibility and robustness, while also identifying scenarios in which its performance can be further improved. Hence, rather than being a purely descriptive review, this work offers a unifying perspective and additional methodological contributions. The MATLAB code used in the numerical experiments is also made freely available to support the reproducibility of the results.

Existing support vector machines(SVM) models are sensitive to noise and lack sparsity, which limits their performance. To address these issues, we combine the elastic net loss with a robust loss framework to construct a sparse $\varepsilon$-insensitive bounded asymmetric elastic net loss, and integrate it with SVM to build $\varepsilon$ Insensitive Zone Bounded Asymmetric Elastic Net Loss-based SVM($\varepsilon$-BAEN-SVM). $\varepsilon$-BAEN-SVM is both sparse and robust. Sparsity is proven by showing that samples inside the $\varepsilon$-insensitive band are not support vectors. Robustness is theoretically guaranteed because the influence function is bounded. To solve the non-convex optimization problem, we design a half-quadratic algorithm based on clipping dual coordinate descent. It transforms the problem into a series of weighted subproblems, improving computational efficiency via the $\varepsilon$ parameter. Experiments on simulated and real datasets show that $\varepsilon$-BAEN-SVM outperforms traditional and existing robust SVMs. It balances sparsity and robustness well in noisy environments. Statistical tests confirm its superiority. Under the Gaussian kernel, it achieves better accuracy and noise insensitivity, validating its effectiveness and practical value.

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We study mean estimation of a random vector $X$ in a distributed parameter-server-worker setup. Worker $i$ observes samples of $a_i^\top X$, where $a_i^\top$ is the $i$th row of a known sensing matrix $A$. The key challenges are adversarial measurements and asynchrony: a fixed subset of workers may transmit corrupted measurements, and workers are activated asynchronously--only one is active at any time. In our previous work, we proposed a two-timescale $\ell_1$-minimization algorithm and established asymptotic recovery under a null-space-property-like condition on $A$. In this work, we establish tight non-asymptotic convergence rates under the same null-space-property-like condition. We also identify relaxed conditions on $A$ under which exact recovery may fail but recovery of a projected component of $\mathbb{E}[X]$ remains possible. Overall, our results provide a unified finite-time characterization of robustness, identifiability, and statistical efficiency in distributed linear estimation with adversarial workers, with implications for network tomography and related distributed sensing problems.

We derive generalization error bounds for the training of two-layer neural networks without assuming boundedness of the loss function, using Wasserstein distance estimates on the discrepancy between a probability distribution and its associated empirical measure, together with moment bounds for the associated stochastic gradient method. In the case of independent test data, we obtain a dimension-free rate of order $O(n^{-1/2} )$ on the $n$-sample generalization error, whereas without independence assumption, we derive a bound of order $O(n^{-1 / ( d_{\rm in}+d_{\rm out} )} )$, where $d_{\rm in}$, $d_{\rm out}$ denote input and output dimensions. Our bounds and their coefficients can be explicitly computed prior to the training of the model, and are confirmed by numerical simulations.

Spiking reservoir computing provides an energy-efficient approach to temporal processing, but reliably tuning reservoirs to operate at the edge-of-chaos is challenging due to experimental uncertainty. This work bridges abstract notions of criticality and practical stability by introducing and exploiting the robustness interval, an operational measure of the hyperparameter range over which a reservoir maintains performance above task-dependent thresholds. Through systematic evaluations of Leaky Integrate-and-Fire (LIF) architectures on both static (MNIST) and temporal (synthetic Ball Trajectories) tasks, we identify consistent monotonic trends in the robustness interval across a broad spectrum of network configurations: the robustness-interval width decreases with presynaptic connection density $β$ (i.e., directly with sparsity) and directly with the firing threshold $θ$. We further identify specific $(β, θ)$ pairs that preserve the analytical mean-field critical point $w_{\text{crit}}$, revealing iso-performance manifolds in the hyperparameter space. Control experiments on Erdős-Rényi graphs show the phenomena persist beyond small-world topologies. Finally, our results show that $w_{\text{crit}}$ consistently falls within empirical high-performance regions, validating $w_{\text{crit}}$ as a robust starting coordinate for parameter search and fine-tuning. To ensure reproducibility, the full Python code is publicly available.

We propose a new conformal prediction method for time-series data with a guaranteed asymptotic conditional coverage rate, Sequential Conformalized Density Regions (SCDR), which is flexible enough to produce both prediction intervals and disconnected prediction sets, signifying the emergence of bifurcations. Our approach uses existing estimated conditional highest density predictive regions to form initial predictive regions. We then use a quantile random forest conformal adjustment to provide guaranteed coverage while adaptively changing to take the non-exchangeable nature of time-series data into account. We show that the proposed method achieves the guaranteed coverage rate asymptotically under certain regularity conditions. In particular, the method is doubly robust -- it works if the predictive density model is correctly specified and/or if the scores follow a nonlinear autoregressive model with the correct order specified. Simulations reveal that the proposed method outperforms existing methods in terms of empirical coverage rates and set sizes. We illustrate the method using two real datasets, the Old Faithful geyser dataset and the Australian electricity usage dataset. Prediction sets formed using SCDR for the geyser eruption durations include both single intervals and unions of two intervals, whereas existing methods produce wider, less informative, single-interval prediction sets.