Venn-Abers predictors are probabilistic predictors that enjoy appealing properties of validity, but their major limitation is that they have been applicable only to binary classification, apart from a recent extension to bounded regression. We generalize them to the case of unbounded regression, which requires adding an element of conformal prediction. In our simulation and empirical studies we investigate the predictive efficiency of point regressors derived from Venn-Abers regressors and argue that they somewhat improve the predictive efficiency of standard regressors for larger training sets.
Bayesian Optimization is an iterative method, tailored to optimizing expensive black box objective functions. Surrogate models like Gaussian Processes, which are the gold standard in Bayesian Optimization, can be inefficient for inputs with permutation symmetries, as the most common kernels employed are better suited for vector inputs rather than unordered sets of items. Motivated by this issue, we turn to permutation invariant Bayesian Optimization for well placement in Carbon Capture and Storage projects. The high fidelity black box simulator is instructed to operate wells under group control, giving rise to permutation symmetries within injector and producer groups that cannot be exploited with standard GP kernels. In this work, our main contribution is a novel Gaussian Process kernel (GP-Perm) that encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations, and can be combined with standard kernels for additional vector-valued inputs. As a learned invariant baseline, we also consider a Deep Kernel Learning model (DKL-DS) using the Deep Sets architecture to learn a permutation-invariant embedding. We evaluate the proposed methodology across 8 use cases, comprising seven synthetic benchmarks and one realistic CCS case study (Johansen formation)
Relocation of compact sets in an $n$-dimensional manifold by self-diffeomorphism is of its own interest as well as significant potential applications to data classification in data science. This paper presents a theory for relocating a finite number of compact sets in $\mathbb{R}^n$ to be relocated to arbitrary target domains in $\mathbb{R}^n$ by diffeomorphisms of $\mathbb{R}^n$. Furthermore, we prove that for any such collection, there exists a differentiable embedding into $\mathbb{R}^{n+1}$ such that their images become linearly separable.
As applications of the established theory, we show that a finite number of compact datasets in $\mathbb{R}^n$ can be made linearly separable by width-$n$ deep neural networks (DNNs) with Leaky-ReLU, ELU, or SELU activation functions, under a mild condition. In addition, we show that any finite number of mutually disjoint compact datasets in $\mathbb{R}^n$ can be made linearly separable in $\mathbb{R}^{n+1}$ by a width-$(n+1)$ DNN.
Decision-makers rely on weather forecasts to plant crops, manage wildfires, allocate water and energy, and prepare for weather extremes. Today, such forecasts enjoy unprecedented accuracy out to two weeks thanks to steady advances in physics-based dynamical models and data-driven artificial intelligence (AI) models. However, model skill drops precipitously at subseasonal timescales (2 - 6 weeks ahead), due to compounding errors, systemic model biases, and the chaotic nature of the atmosphere. To counter this degradation, we introduce probabilistic bias correction (PBC), a machine learning framework that substantially reduces systematic error by learning to correct historical probabilistic forecasts. When applied to the leading dynamical and AI models from the European Centre for Medium-Range Weather Forecasts (ECMWF), PBC doubles the modest subseasonal skill of the AI Forecasting System and improves the skill of the operationally-debiased dynamical model for 91% of pressure, 92% of temperature, and 98% of precipitation targets. We designed PBC for operational deployment, and, in ECMWF's 2025 real-time forecasting competition, its global forecasts placed first for all weather variables and lead times, outperforming the dynamical models from six operational forecasting centers, an international dynamical multi-model ensemble, ECMWF's AI Forecasting System, and the forecasting systems of 34 teams worldwide. These probabilistic skill gains translate into more accurate prediction of extreme events and have the potential to improve agricultural planning, energy management, and disaster preparedness in vulnerable communities.
Hannah Guan, Soukayna Mouatadid, Paulo Orenstein et al.· 0 citations
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We study polynomial group convolutional neural networks (PGCNNs) for an arbitrary finite group $G$. In particular, we introduce a new mathematical framework for PGCNNs using the language of graded group algebras. This framework yields two natural parametrizations of the architecture, based on Hadamard and Kronecker products, related by a linear map. We compute the dimension of the associated neuromanifold, verifying that it depends only on the number of layers and the size of the group. We also describe the general fiber of the Kronecker parametrization up to the regular group action and rescaling, and conjecture the analogous description for the Hadamard parametrization. Our conjecture is supported by explicit computations for small groups and shallow networks.
Yacoub Hendi, Daniel Persson, Magdalena Larfors· 0 citations
Message passing is a core mechanism in Graph Neural Networks (GNNs), enabling the iterative update of node embeddings by aggregating information from neighboring nodes. Graph Convolutional Networks (GCNs) exemplify this approach by adapting convolutional operations for graph structures, allowing features from adjacent nodes to be combined effectively. However, GCNs encounter challenges with complex or dynamic data. Capturing long-range dependencies often requires deeper layers, which not only increase computational costs but also lead to over-smoothing, where node embeddings become indistinguishable. To overcome these challenges, reservoir computing has been integrated into GNNs, leveraging iterative message-passing dynamics for stable information propagation without extensive parameter tuning. Despite its promise, existing reservoir-based models lack structured convolutional mechanisms, limiting their ability to accurately aggregate multi-hop neighborhood information. To address these limitations, we propose RGC-Net (\emph{Reservoir-based Graph Convolutional Network}), which integrates reservoir dynamics with structured graph convolution. Key contributions include: (i) a reimagined convolutional framework with fixed-random reservoir weights and a leaky integrator to enhance feature retention; (ii) a robust, adaptable model for graph classification; and (iii) an RGC-Net-powered transformer for graph generation with application to dynamic brain connectivity. Extensive experiments show RGC-Net achieves state-of-the-art performance in classification and generative tasks, including brain graph evolution, with faster convergence and mitigated over-smoothing. Our source code is available at https://github.com/basiralab/RGC-Net.
Mayssa Soussia, Gita Ayu Salsabila, Mohamed Ali Mahjoub et al.· 0 citations
Brain foundation models (BFMs) are advancing neurotechnology by learning transferable representations from neural signals, with broad potential in clinical diagnosis and neuroscience research. Their development relies on large-scale pretraining corpora of electrical brain signals, including scalp electroencephalography (EEG) and intracranial EEG (iEEG). However, existing BFM benchmarks primarily focus on EEG, cover only a limited subset of models, and provide limited analysis beyond downstream performance. We introduce Brain4FMs, the first unified benchmark, to our knowledge, for jointly evaluating BFMs on EEG and iEEG. It integrates 17 representative models and 21 public datasets across clinical diagnosis, sleep staging, communication, and affective computing. Brain4FMs is open and plug-and-play, with dataset-aware preprocessing, cross-subject evaluation, heterogeneous multichannel handling, and standardized downstream adaptation workflows. The benchmark reveals performance variation across tasks, signal modalities, and adaptation protocols, with no single BFM consistently dominating all evaluation scenarios. % To better understand these heterogeneous transfer behaviors, we further conduct exploratory analyses of model-specific properties. To better understand these behaviors, we further conduct exploratory analyses of model-specific properties of spatial, spectral, and discrete representations. The code is available at https://github.com/wajtsq/Brain4FMs.
Fanqi Shen, Enhong Yang, Jiahe Li et al.· 0 citations
Many strong decoding methods for text generation follow a sample-and-rerank paradigm: they draw multiple candidates, score each under a utility (reward) function using consensus across samples, and return the best one. Although effective, these methods incur high computational costs during inference due to repeated sampling and scoring. Prior attempts to amortize inference-time computation typically rely on gold references, teacher labels, or curated preference data, increasing dataset construction effort and the demand for high-fidelity reward models. We propose Consensus Group Relative Policy Optimization (C-GRPO), which distills Minimum Bayes Risk (MBR) decoding into training by formulating the consensus utility as a group-relative objective within GRPO. C-GRPO requires only a utility function and policy samples, without gold references or explicit preference labels. Under ideal conditions, we show that the objective function of C-GRPO is directionally aligned with the gradient of the expected-utility objective underlying MBR decoding, leading to a convergence guarantee. Experiments on machine translation (WMT 2024) and text summarization (XSum) demonstrate that C-GRPO successfully achieves performance comparable to MBR decoding without the associated inference-time overhead, while outperforming reference-free baseline methods.
Yuki Ichihara, Yuu Jinnai, Kaito Ariu et al.· 0 citations
Standard weather forecast evaluations focus on the forecaster's perspective and on a statistical assessment comparing forecasts and observations. In practice, however, forecasts are used to make decisions, so it seems natural to take the decision-maker's perspective and quantify the value of a forecast by its ability to improve decision-making. Decision calibration provides a novel framework for evaluating probabilistic forecast performance at the decision level rather than the forecast level. We evaluate decision calibration to compare a Machine Learning and a classical numerical weather prediction model on various weather-dependent decision tasks, though the framework is applicable to any set of forecast models. We find that model performance at the forecast level does not reliably translate to performance in downstream decision-making: some performance differences only become apparent at the decision level, and even among seemingly similar decision tasks, model rankings can change. Our results confirm that typical forecast evaluations are insufficient for selecting the optimal forecast model for a specific decision task.
Contemporary reservoir computing relies heavily on globally Lipschitz, well-behaved activation functions, limiting applications in defense, disaster response, and pharmaceutical modeling where robust operation under extreme conditions is critical. We systematically investigate non-smooth activation functions, including chaotic, stochastic, and fractal variants, in echo state networks. Through parameter sweeps across 36,610 reservoir configurations, we demonstrate that several non-smooth functions not only maintain behavior consistent with the Echo State Property (ESP) but outperform traditional smooth activations in convergence speed and spectral radius tolerance.
Notably, the Cantor function (continuous everywhere, zero derivative almost everywhere) maintains ESP-consistent behavior up to spectral radii of rho = 10, an order of magnitude beyond typical bounds for traditional functions, while achieving 2.6x faster convergence than tanh and ReLU. We introduce a theoretical framework for quantized activation functions, defining a Degenerate Echo State Property (d-ESP) capturing stability for discrete-output functions, and prove that d-ESP implies traditional ESP.
We conjecture a critical crowding ratio Q=N/k (reservoir size / quantization levels) predicting failure thresholds for discrete activations. Our analysis reveals that preprocessing topology, rather than continuity, determines stability: monotone, compressive preprocessing maintains ESP across scales, while dispersive or discontinuous preprocessing triggers sharp failures. Our findings challenge assumptions about activation function design in reservoir computing; the exceptional performance of certain fractal functions is only partially explained by the effective-gain analysis presented here, suggesting fundamental gaps in our understanding of how geometric properties of activation functions influence reservoir dynamics.
Time series are ubiquitous in many applications that involve forecasting, classification and causal inference tasks, such as healthcare, finance, audio signal processing and climate sciences. Still, large, high-quality time series datasets remain scarce. Synthetic generation can address this limitation; however, current models confined either to the time or frequency domains struggle to reproduce the inherently multi-scaled structure of real-world time series. We introduce WaveletDiff, a new framework that trains diffusion models directly on wavelet coefficients to exploit the inherent multi-resolution structure of time series data. The model combines dedicated transformers for each decomposition level with cross-level attention mechanisms that enable selective information exchange between temporal and frequency scales through adaptive gating. It is also informed by level-specific energy constraints based on Parseval's theorem which preserve time-frequency properties throughout the diffusion process. Comprehensive tests across six real-world datasets from energy, finance, and neuroscience domains demonstrate that WaveletDiff outperforms the diffusion baselines FourierDiffusion, Diffusion-TS, and SigDiffusions on the majority of metrics, with the smallest margin over FourierDiffusion, while still achieving roughly 3x lower discriminative and Context-FID scores. Against the VAE/transformer-based MSDformer, the results are mostly comparable, with WaveletDiff using fewer parameters and less training time on most datasets. The most revealing finding is the significant performance gap on fMRI data (in favor of MSDformer) and EEG (in favor of WaveletDiff). This finding is explained via a careful testing/examination of the properties of wavelet coefficients for generative, as opposed to analyses/decomposition tasks. Our code is available at https://github.com/GarlicWang/WaveletDiff.
Nanopore-based single-molecule sensing is a promising route to fast, low-cost disease diagnosis and protein sequencing: as an analyte such as a peptide or protein traverses a nanoscale pore, it modulates the ionic current, producing a resistive pulse whose signature is determined by the analyte's structure and its interactions with the pore. Translating these signatures into reliable molecular identities, however, is an open problem well suited for machine learning, as the signals are noisy, suffer from variations due to experimental conditions, and are difficult to featurize, which has so far limited classification accuracy. Here we translate the peptide identification problem into an image-classification task by transforming each resistive pulse into a scaleogram via the continuous wavelet transform, a representation that jointly encodes amplitude, frequency, and time in a form well suited for deep convolutional models. On a dataset of 42 peptides, recorded as six separate peptide ladders, this approach reaches a macro-averaged classification accuracy of $82\,\%$ on held-out events, an improvement of $8.6$ percentage points over the descriptor-based approach previously reported for the same dataset. We further show that the trained models tolerate substantial compression, retaining their accuracy with half of their weights set to zero and under 8-bit quantization, a prerequisite for deploying trained classifiers on embedded sensing hardware. Our results demonstrate how physically motivated signal representations can make complex single-molecule data tractable for modern learning algorithms, a step on the path towards point-of-care peptide and protein diagnostics.
Julian Ho{\ss}bach, Samuel Tovey, Sandro Kuppel et al.· 0 citations
Professor Sherry Turkle’s new book, “Artificial Intimacy,” offers a withering critique of chatbots and the antisocial dynamics she believes they encourage.
MIT News · Artificial Intelligence· news.mit.eduSep 25, 2026
A weeklong summer workshop brought higher education faculty to campus to explore how AI and machine learning materials can be adapted for their classrooms.
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