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
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
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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
The recent developments in data-driven methods have paved the way to new methodologies to provide accurate state reconstruction of engineering systems; nuclear reactors represent particularly challenging applications for this task due to the complexity of the strongly coupled physics involved and the extremely harsh and hostile environments, especially for new technologies such as Generation-IV reactors. Data-driven techniques can combine different sources of information, including computational proxy models and local noisy measurements on the system, to robustly estimate the state. This work leverages the novel Shallow Recurrent Decoder architecture to infer the entire state vector (including neutron fluxes, precursors concentrations, temperature, pressure and velocity) of a reactor from three out-of-core time-series neutron flux measurements alone. In particular, this work extends the standard architecture to treat parametric time-series data, ensuring the possibility of investigating different accidental scenarios and showing the capabilities of this approach to provide an accurate state estimation in various operating conditions. This paper considers as a test case the Molten Salt Fast Reactor (MSFR), a Generation-IV reactor concept, characterised by strong coupling between the neutronics and the thermal hydraulics due to the liquid nature of the fuel. The promising results of this work are further strengthened by the possibility of quantifying the uncertainty associated with the state estimation, due to the considerably low training cost. The accurate reconstruction of every characteristic field in real-time makes this approach suitable for monitoring and control purposes in the framework of a reactor digital twin.
Stefano Riva, Carolina Introini, J. Nathan Kutz et al.· 0 citations
Trajectory similarity is fundamental to many spatio-temporal data mining applications. Recent studies propose deep learning models to approximate conventional trajectory similarity measures, exploiting their fast inference time once trained. Although efficient inference has been reported, challenges remain in similarity approximation accuracy due to difficulties in trajectory granularity modeling and in exploiting similarity signals in training data. To fill this gap, we propose TSMini, a highly effective trajectory similarity model with a sub-view modeling mechanism and a k nearest neighbor-based loss. The former enables learning multi-granularity trajectory patterns, while the latter guides TSMini to learn not only absolute similarity values between trajectories but also their relative similarity ranks. Together, these innovations enable highly accurate trajectory similarity approximation. Experiments show that TSMini outperforms the state-of-the-art models by 15% on average when learning widely used trajectory similarity measures.
Yanchuan Chang, Dingyang Lyu, Xu Cai et al.· 0 citations
A weeklong summer workshop brought higher education faculty to campus to explore how AI and machine learning materials can be adapted for their classrooms.
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
