A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities.

Grid cells in the mammalian brain are fundamental to spatial navigation, and therefore crucial to how animals perceive and interact with their environment. Traditionally, grid cells are thought support path integration through highly symmetric hexagonal lattice firing patterns. However, recent findings show that their firing patterns become distorted in the presence of significant spatial landmarks such as rewarded locations. This introduces a novel perspective of dynamic, subjective, and action-relevant interactions between spatial representations and environmental cues. Here, we propose a practical and theoretical framework to quantify and explain these interactions.

Grid cells in the medial entorhinal cortex create remarkable periodic maps of explored space during navigation. Recent studies show that they form similar maps of abstract cognitive spaces. Examples of such abstract environments include auditory tone sequences in which the pitch is continuously varied or images in which abstract features are continuously deformed (e.g., a cartoon bird whose legs stretch and shrink).

To solve the spatial problems of mapping, localization and navigation, the mammalian lineage has developed striking spatial representations. One important spatial representation is the Nobel-prize winning grid cells: neurons that represent self-location, a local and aperiodic quantity, with seemingly bizarre non-local and spatially periodic activity patterns of a few discrete periods. Why has the mammalian lineage learnt this peculiar grid representation? Mathematical analysis suggests that this multi-periodic representation has excellent properties as an algebraic code with high capacity and intrinsic error-correction, but to date, synthesis of multi-modular grid cells in deep recurrent neural networks remains absent. In this work, we begin by identifying key insights from four families of approaches to answering the grid cell question: dynamical systems, coding theory, function optimization and supervised deep learning. We then leverage our insights to propose a new approach that elegantly combines the strengths of all four approaches. Our approach is a self-supervised learning (SSL) framework - including data, data augmentations, loss functions and a network architecture - motivated from a normative perspective, with no access to supervised position information. Without making assumptions about internal or readout representations, we show that multiple grid cell modules can emerge in networks trained on our SSL framework and that the networks generalize significantly beyond their training distribution. This work contains insights for neuroscientists interested in the origins of grid cells as well as machine learning researchers interested in novel SSL frameworks.

Research in Neuroscience, as in many scientific disciplines, is undergoing a renaissance based on deep learning. Unique to Neuroscience, deep learning models can be used not only as a tool but interpreted as models of the brain. The central claims of recent deep learning-based models of brain circuits are that they make novel predictions about neural phenomena or shed light on the fundamental functions being optimized. We show, through the case-study of grid cells in the entorhinal-hippocampal circuit, that one may get neither. We begin by reviewing the principles of grid cell mechanism and function obtained from first-principles modeling efforts, then rigorously examine the claims of deep learning models of grid cells. Using large-scale architectural and hyperparameter sweeps and theory-driven experimentation, we demonstrate that the results of such models may be more strongly driven by particular, non-fundamental, and post-hoc implementation choices than fundamental truths about neural circuits or the loss function(s) they might optimize. We discuss why these models cannot be expected to produce accurate models of the brain without the addition of substantial amounts of inductive bias, an informal No Free Lunch result for Neuroscience. Based on first principles work, we provide hypotheses for what additional loss functions will produce grid cells more robustly. In conclusion, circumspection and transparency, together with biological knowledge, are warranted in building and interpreting deep learning models in Neuroscience.

Predictions of fatalities from violent conflict on the PRIO-GRID-month (pgm) level are characterized by high levels of uncertainty, limiting their usefulness in practical applications. We discuss the two main sources of uncertainty for this prediction task, the nature of violent conflict and data limitations, embedding this in the wider literature on uncertainty quantification in machine learning. We develop a strategy to quantify uncertainty in conflict forecasting, shifting from traditional point predictions to full predictive distributions. Our approach compares and combines multiple tree-based classifiers and distributional regressors in a custom auto-ML setup, estimating distributions for each pgm individually. We also test the integration of regional models in spatial ensembles as a potential avenue to reduce uncertainty. The models are able to consistently outperform a suite of benchmarks derived from conflict history in predictions up to one year in advance, with performance driven by regions where conflict was observed. With our evaluation, we emphasize the need to understand how a metric behaves for a given prediction problem, in our case characterized by extremely high zero-inflatedness. While not resulting in better predictions, the integration of smaller models does not decrease performance for this prediction task, opening avenues to integrate data sources with less spatial coverage in the future.

Wildfires pose a threat to ecosystems, economies and public safety, particularly in Mediterranean regions such as Spain. Accurate predictive models require high-resolution spatio-temporal data to capture complex dynamics of environmental and human factors. To address the scarcity of fine-grained wildfire datasets in Spain, we introduce IberFire: a spatio-temporal dataset with 1 km x 1 km x 1-day resolution, covering mainland Spain and the Balearic Islands from December 2007 to December 2024. IberFire integrates 120 features across eight categories: auxiliary data, fire history, geography, topography, meteorology, vegetation indices, human activity and land cover. All features and processing rely on open-access data and tools, with a publicly available codebase ensuring transparency and applicability. IberFire offers enhanced spatial granularity and feature diversity compared to existing European datasets, and provides a reproducible framework. It supports advanced wildfire risk modelling via Machine Learning and Deep Learning, facilitates climate trend analysis, and informs fire prevention and land management strategies. The dataset is freely available on Zenodo to promote open research and collaboration.

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities.

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Together, grid cells' activity within a grid cell module forms a 2D torus [9, 20].