Uncertainty quantification is critical in safety-sensitive applications but is often omitted from off-the-shelf neural networks due to adverse effects on predictive performance. Retrofitting uncertainty estimates post-hoc typically requires access to model parameters or gradients, limiting feasibility in practice. We propose a theoretically grounded framework for post-hoc uncertainty estimation in regression tasks by fitting an auxiliary model to both original inputs and frozen model outputs. Drawing from principles of maximum likelihood estimation and sequential parameter fitting, we formalize an exact post-hoc optimization objective that recovers the canonical MLE of Gaussian parameters, without requiring sampling or approximation at inference. While prior work has used model outputs to estimate uncertainty, we explicitly characterize the conditions under which this is valid and demonstrate the extent to which structured outputs can support quasi-epistemic inference. We find that using diverse auxiliary data, such as augmented subsets of the original training data, significantly enhances OOD detection and metric performance. Our hypothesis that frozen model outputs contain generalizable latent information about model error and predictive uncertainty is tested and confirmed. Finally, we ensure that our method maintains proper estimation of input-dependent uncertainty without relying exclusively on base model forecasts. These findings are demonstrated in toy problems and adapted to both UCI and depth regression benchmarks. Code: https://github.com/biggzlar/IO-CUE.

This paper critically re-evaluates LLMs' role in causal discovery and argues against their direct involvement in determining causal relationships. We demonstrate that LLMs' autoregressive, correlation-driven modeling inherently lacks the theoretical grounding for causal reasoning and introduces unreliability when used as priors in causal discovery algorithms. Through empirical studies, we expose the limitations of existing LLM-based methods and reveal that deliberate prompt engineering (e.g., injecting ground-truth knowledge) could overstate their performance, helping to explain the consistently favorable results reported in much of the current literature. Based on these findings, we strictly confined LLMs' role to a non-decisional auxiliary capacity: LLMs should not participate in determining the existence or directionality of causal relationships, but can assist the search process for causal graphs (e.g., LLM-based heuristic search). Experiments across various settings confirm that, by strictly isolating LLMs from causal decision-making, LLM-guided heuristic search can accelerate the convergence and outperform both traditional and LLM-based methods in causal structure learning. We conclude with a call for the community to shift focus from naively applying LLMs to developing specialized models and training method that respect the core principles of causal discovery.

Machine learning models, particularly deep neural networks, are vulnerable to privacy attacks such as membership inference attacks (MIAs), which determine whether a specific data point was included in a model's training set [9, 10, 2]. These attacks exploit the tendency of models to exhibit distinct behaviors (e.g. higher confidence or lower loss) on training data compared to unseen data, potentially compromising the confidentiality of sensitive datasets, such as those containing medical or financial records. State-of-the-art MIAs typically rely on extensive knowledge of the target model. For example, shadow model-based approaches [9] train multiple models to mimic the target's behavior, while others, e.g. the likelihood ratio attack (LiRA) by Carlini et al. [2], leverage model outputs or gradients. These methods often induce significant computational costs or require access to model internals, limiting their applicability in scenarios where only model outputs are available. We propose a new MIA method that leverages Bayesian inference for post-hoc analysis of trained model and datasets. Once a ML model, e.g. a neural network, has been trained on member datasets, we pass the test data through the trained ML model, and extract resulting metrics such as accuracy, entropy, perturbation magnitude, and dataset statistics, and uses these metrics to compute posterior probabilities of membership. This approach doesn't require access to a'training' set, although known knowledge about member and non-member datasets can improve its performance. This post-hoc method is computationally efficient, interpretable, requires minimum model query and fine-tuning, making it well-suited for real-world deployment scenarios where privacy assessments are conducted after model training.

Neural network (NN)-based end-to-end (E2E) communication systems, in which each system component may consist of a portion of a neural network, have been investigated as potential tools for developing artificial intelligence (Al)-native E2E systems. In this paper, we propose an NN-based bitwise receiver that improves computational efficiency while maintaining performance comparable to baseline demappers. Building on this foundation, we introduce a novel symbol-wise autoencoder (AE)-based E2E system that jointly optimizes the transmitter and receiver at the physical layer. We evaluate the proposed NN-based receiver using bit-error rate (BER) analysis to confirm that the numerical BER achieved by NN-based receivers or transceivers is accurate. Results demonstrate that the AE-based system outperforms baseline architectures, particularly for higher-order modulation schemes. We further show that the training signal-to-noise ratio (SNR) significantly affects the performance of the systems when inference is conducted at different SNR levels.

Many large enterprises that operate highly governed and complex ICT environments have no efficient and effective way to support their Data and AI teams in rapidly spinning up and tearing down self-service data and compute infrastructure, to experiment with new data analytic tools, and deploy data products into operational use. This paper proposes a key piece of the solution to the overall problem, in the form of an on-demand self-service data-platform infrastructure to empower de-centralised data teams to build data products on top of centralised templates, policies and governance. The core innovation is an efficient method to leverage immutable container operating systems and infrastructure-as-code methodologies for creating, from scratch, vendor-neutral and short-lived Kubernetes clusters on-premises and in any cloud environment. Our proposed approach can serve as a repeatable, portable and cost-efficient alternative or complement to commercial Platform-as-a-Service (PaaS) offerings, and this is particularly important in supporting interoperability in complex data mesh environments with a mix of modern and legacy compute infrastructure.

It's one paper, cite it as one paper.

The paper shows that profile maximum likelihood, an idea from the distribution estimation literature from a couple of years ago, enjoys optimality properties for a large class of property estimation tasks. The class of tasks includes a number of popular problems studied in the distribution learning literature. All reviewers liked the paper and advocate acceptance. Please do go over the reviews and incorporate any feedback for the camera ready.

Deep neural networks are renowned for their ability to generalise well across diverse tasks, even when heavily overparameterized. Existing works offer only partial explanations (for example, the NTK-based task-model alignment explanation neglects feature learning). Here, we provide an end-to-end, analytically tractable case study that links a network's inductive prior, its training dynamics including feature learning, and its eventual generalisation. Specifically, we exploit the one-to-one correspondence between depth-2 discrete fully connected networks and disjunctive normal form (DNF) formulas by training on Boolean functions. Under a Monte Carlo learning algorithm, our model exhibits predictable training dynamics and the emergence of interpretable features. This framework allows us to trace, in detail, how inductive bias and feature formation drive generalisation.

Kernel method-based intensity estimators, formulated within reproducing kernel Hilbert spaces (RKHSs), and classical kernel intensity estimators (KIEs) have been among the most easy-to-implement and feasible methods for estimating the intensity functions of inhomogeneous Poisson processes. While both approaches share the term "kernel", they are founded on distinct theoretical principles, each with its own strengths and limitations. In this paper, we propose a novel regularized kernel method for Poisson processes based on the least squares loss and show that the resulting intensity estimator involves a specialized variant of the representer theorem: it has the dual coefficient of unity and coincides with classical KIEs. This result provides new theoretical insights into the connection between classical KIEs and kernel method-based intensity estimators, while enabling us to develop an efficient KIE by leveraging advanced techniques from RKHS theory. We refer to the proposed model as the kernel method-based kernel intensity estimator (K$^2$IE). Through experiments on synthetic datasets, we show that K$^2$IE achieves comparable predictive performance while significantly surpassing the state-of-the-art kernel method-based estimator in computational efficiency.

Multimodal contrastive learning is a methodology for linking different data modalities; the canonical example is linking image and text data. The methodology is typically framed as the identification of a set of encoders, one for each modality, that align representations within a common latent space. In this work, we focus on the bimodal setting and interpret contrastive learning as the optimization of (parameterized) encoders that define conditional probability distributions, for each modality conditioned on the other, consistent with the available data. This provides a framework for multimodal algorithms such as crossmodal retrieval, which identifies the mode of one of these conditional distributions, and crossmodal classification, which is similar to retrieval but includes a fine-tuning step to make it task specific. The framework we adopt also gives rise to crossmodal generative models. This probabilistic perspective suggests two natural generalizations of contrastive learning: the introduction of novel probabilistic loss functions, and the use of alternative metrics for measuring alignment in the common latent space. We study these generalizations of the classical approach in the multivariate Gaussian setting. In this context we view the latent space identification as a low-rank matrix approximation problem. This allows us to characterize the capabilities of loss functions and alignment metrics to approximate natural statistics, such as conditional means and covariances; doing so yields novel variants on contrastive learning algorithms for specific mode-seeking and for generative tasks. The framework we introduce is also studied through numerical experiments on multivariate Gaussians, the labeled MNIST dataset, and on a data assimilation application arising in oceanography.