Once closed-form expressions for these Jacobians are derived, it remains to substitute those expressions into (16). The following identity (often termed the "vec" rule) will To depict the spatial topographies of the latent components measured on the EEG and fMRI analyses, the "forward-model" [ The results of the comparison are shown in Fig S1, where it is clear that the signal fidelity of the GCs (right panel) significantly exceeds those yielded by PCA (left) and ICA (middle). GCA is only able to recover sources with temporal dependencies (i.e., s Both the single electrodes and Granger components exhibit two pronounced peaks in the spectra: one near 2 Hz ("delta" Fig S3 shows the corresponding result for the left motor imagery condition. EEG motor imagery dataset described in the main text. For each technique, the first 6 components are presented.

Here the concept of Granger causality is employed to propose a new criterion for unsupervised learning that is appropriate in the case of temporally-dependent source signals. The basic idea is to identify two projections of a multivariate time series such that the Granger causality among the resulting pair of components is maximized.

We prepare 1K real-world wildfire scenarios for testing the AI models. We also propose a deep transformer, S2R-FireTr, which excels in considering the multi-modal environmental information for forecasting and backtracking the wildfire.

We introduce SpLIIF to generate implicit neural representations and enable arbitrary downscaling of weather variables. We train a model from sparse weather stations and topography over Japan and evaluate in- and out-of-distribution accuracy predicting temperature and wind, comparing it to both an interpolation baseline and CorrDiff. We find the model to be up to 50% better than both CorrDiff and the baseline at downscaling temperature, and around 10-20% better for wind.

Spatial functional organization is a hallmark of biological brains: neurons are arranged topographically according to their response properties, at multiple scales. In contrast, representations within most machine learning models lack spatial biases, instead manifesting as disorganized vector spaces that are difficult to visualize and interpret. Here, we propose a novel form of self-attention that turns Transformers into "Topoformers" with topographic organization. We introduce spatial querying - where keys and queries are arranged on 2D grids, and local pools of queries are associated with a given key - and spatial reweighting, where we convert the standard fully connected layer of self-attention into a locally connected layer. We first demonstrate the feasibility of our approach by training a 1-layer Topoformer on a sentiment classification task. Training with spatial querying encourages topographic organization in the queries and keys, and spatial reweighting separately encourages topographic organization in the values and self-attention outputs. We then apply the Topoformer motifs at scale, training a BERT architecture with a masked language modeling objective. We find that the topographic variant performs on par with a non-topographic control model on NLP benchmarks, yet produces interpretable topographic organization as evaluated via eight linguistic test suites. Finally, analyzing an fMRI dataset of human brain responses to a large set of naturalistic sentences, we demonstrate alignment between low-dimensional topographic variability in the Topoformer model and human brain language network. Scaling up Topoformers further holds promise for greater interpretability in NLP research, and for more accurate models of the organization of linguistic information in the human brain.

Once closed-form expressions for these Jacobians are derived, it remains to substitute those expressions into (16). The following identity (often termed the "vec" rule) will To depict the spatial topographies of the latent components measured on the EEG and fMRI analyses, the "forward-model" [ The results of the comparison are shown in Fig S1, where it is clear that the signal fidelity of the GCs (right panel) significantly exceeds those yielded by PCA (left) and ICA (middle). GCA is only able to recover sources with temporal dependencies (i.e., s Both the single electrodes and Granger components exhibit two pronounced peaks in the spectra: one near 2 Hz ("delta" Fig S3 shows the corresponding result for the left motor imagery condition. EEG motor imagery dataset described in the main text. For each technique, the first 6 components are presented.

The human auditory cortex is topographically organized. Neurons with similar response properties are spatially clustered, forming smooth maps for acoustic features such as frequency in early auditory areas, and modular regions selective for music and speech in higher-order cortex. Yet, evaluations for current computational models of auditory perception do not measure whether such topographic structure is present in a candidate model. Here, we show that cortical topography is not present in the previous best-performing models at predicting human auditory fMRI responses. To encourage the emergence of topographic organization, we adapt a cortical wiring-constraint loss originally designed for visual perception. The new class of topographic auditory models, TopoAudio, are trained to classify speech, and environmental sounds from cochleagram inputs, with an added constraint that nearby units on a 2D cortical sheet develop similar tuning. Despite these additional constraints, TopoAudio achieves high accuracy on benchmark tasks comparable to the unconstrained non-topographic baseline models. Further, TopoAudio predicts the fMRI responses in the brain as well as standard models, but unlike standard models, TopoAudio develops smooth, topographic maps for tonotopy and amplitude modulation (common properties of early auditory representation, as well as clustered response modules for music and speech (higher-order selectivity observed in the human auditory cortex). TopoAudio is the first end-to-end biologically grounded auditory model to exhibit emergent topography, and our results emphasize that a wiring-length constraint can serve as a general-purpose regularization tool to achieve biologically aligned representations.

Dementia (DEM) is a growing global health challenge, underscoring the need for early and accurate diagnosis. Electroencephalography (EEG) provides a non-invasive window into brain activity, but conventional methods struggle to capture its transient complexity. We present the \textbf{EEG Microstate Analysis Framework (EEG-MSAF)}, an end-to-end pipeline that leverages EEG microstates discrete, quasi-stable topographies to identify DEM-related biomarkers and distinguish DEM, mild cognitive impairment (MCI), and normal cognition (NC). EEG-MSAF comprises three stages: (1) automated microstate feature extraction, (2) classification with machine learning (ML), and (3) feature ranking using Shapley Additive Explanations (SHAP) to highlight key biomarkers. We evaluate on two EEG datasets: the public Chung-Ang University EEG (CAUEEG) dataset and a clinical cohort from Thessaloniki Hospital. Our framework demonstrates strong performance and generalizability. On CAUEEG, EEG-MSAF-SVM achieves \textbf{89\% $\pm$ 0.01 accuracy}, surpassing the deep learning baseline CEEDNET by \textbf{19.3\%}. On the Thessaloniki dataset, it reaches \textbf{95\% $\pm$ 0.01 accuracy}, comparable to EEGConvNeXt. SHAP analysis identifies mean correlation and occurrence as the most informative metrics: disruption of microstate C (salience/attention network) dominates DEM prediction, while microstate F, a novel default-mode pattern, emerges as a key early biomarker for both MCI and DEM. By combining accuracy, generalizability, and interpretability, EEG-MSAF advances EEG-based dementia diagnosis and sheds light on brain dynamics across the cognitive spectrum.

Neurons in the brain are organized such that nearby cells tend to share similar functions. AI models lack this organization, and past efforts to introduce topography have often led to trade-offs between topography and task performance. In this work, we present TopoLoss, a new loss function that promotes spatially organized topographic representations in AI models without significantly sacrificing task performance. TopoLoss is highly adaptable and can be seamlessly integrated into the training of leading model architectures. We validate our method on both vision (ResNet-18, ResNet-50, ViT) and language models (GPT-Neo-125M, NanoGPT), collectively TopoNets. TopoNets are the highest-performing supervised topographic models to date, exhibiting brain-like properties such as localized feature processing, lower dimensionality, and increased efficiency. TopoNets also predict responses in the brain and replicate the key topographic signatures observed in the brain's visual and language cortices. Together, this work establishes a robust and generalizable framework for integrating topography into leading model architectures, advancing the development of high-performing models that more closely emulate the computational strategies of the human brain.