Konrad Paul Kording

Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For example, when programming a neural network, conditionals and iteration cannot be used everywhere; they can break the derivatives necessary for gradient-based learning to work. This limits the class of differentiable algorithms we can directly express, imposing restraints on how we build neural networks and differentiable programs more generally. However, these restraints are not fundamental. Recent work shows conditionals can be first-class, by compiling them into differentiable form as linear neurons. Similarly, this work shows iteration can be first-class---by compiling to linear recurrent neurons. We present a minimal typed, higher-order and linear programming language with iteration called Cajal(N). We prove its programs compile correctly to recurrent neurons, allowing discrete algorithms to be expressed in a differentiable form compatible with gradient-based learning. With our implementation, we conduct two experiments where we link these recurrent neurons against a neural network solving an iterative image transformation task. This determines part of its function prior to learning. As a result, the network learns faster and with greater data-efficiency relative to a neural network programmed without first-class iteration. A key lesson is that recurrent neurons enable a rich interplay between learning and the discrete structures of ordinary programming.

Machine learning is accelerating biomedical research. Cross-validation is widely used to compare predictive performance — not only to benchmark algorithms, but also to inform scientific applications, such as ranking biomarkers. However, prediction performance estimates across cross-validation folds are not independent. Standard tests for comparing prediction performance (e.g., paired t-test) assume independence and can therefore inflate false positive rates. In a PRISMA-guided meta-analysis of 210 studies (impact factor ≥15, 1 June 2020 – 1 June 2025), we find that 97% ignored fold dependence when comparing prediction performance. This problem is ubiquitous across scientific fields and unaffected by impact factor, rigor-promoting policies, or open science practices. Simulations across 420 scenarios spanning four diverse datasets show that ignoring fold dependence leads to invalid false positive control in most settings. Repeated cross-validation further compounds this problem, with false positive rates rising toward 100% as the number of repetitions grows. Existing fold-dependence-aware tests rely on strong assumptions because the variance of fold-level statistics and the between-fold correlation cannot be disentangled under standard cross-validation. We therefore propose the SHARP (Split-HAlf RePeated) test, a simple modification to standard cross-validation that enables direct estimation of variance and correlation. Benchmarked against 12 tests, SHARP provides the best overall balance of false-positive control, statistical power, and confidence-interval calibration across simulation schemes. We conclude by providing best practices and reporting guidelines for valid model comparison inference in biomedical machine learning and beyond.

Neurons interact at synapses, but they also communicate through physical contact and proximity, including diffusion, glia-mediated interactions, and ephaptic coupling. Standard connectomes map synapses, but cannot capture the full set of cell-cell contacts that can support these pathways. Here we extract contactomes from two large mouse visual cortex volumes at nanoscale resolution and quantify every cell-cell contact, the shared surface area of each contact, and the relationship between contact and synaptic connectivity. We find that contactomes are 5 to 10 times denser than synaptic graphs, revealing that neurons physically contact a much larger set of potential neighbors than they synaptically connect to. We further find that most nearby potential neighbors are already in physical contact, indicating that local structural change would add few new candidate synaptic partners. Finally, we find that astrocytes form a single large syncytium-like network that spans the tissue and directly contacts nearly all neurons, and that glial processes lie within a micron or two of almost every synapse, indicating that synapses reside within a pervasive glia-shaped microenvironment. Together, these results show that physical contact forms a distinct layer of brain architecture that extends far beyond the synaptic connectome

Attention is a cornerstone of cognition and neural computation, enabling the brain to select relevant information, bind features into coherent objects, and guide behavior. However, we currently lack a unifying computational model that connects the diverse phenomena of attention, from spatial and feature-based selection to object-based binding, within a single, neurally plausible computational framework. Here, we propose a bidirectional recurrent gating mechanism integrated into a principled architecture of the ventral visual stream. In this architecture, feedforward pathways extract visual features, while top-down and lateral connections transmit context- and task-dependent modulatory signals that control information flow. We demonstrate that our model, trained on recognition and segmentation problems, successfully performs the canonical attention tasks of orienting, filtering, and visual search on complex scenes. It replicates key psychophysical phenomena, such as perceptual load and inattentional blindness, while its internal units develop neural properties consistent with primate physiology, including multiplicative gain modulation and border-ownership coding. Our work provides evidence that this diverse set of attentional and binding phenomena can emerge from error-backpropagation combined with architectural constraints upon information flow, offering a powerful tool for neuroscience and a compelling, bio-inspired alternative to standard AI architectures.

Cerebral palsy (CP), affecting approximately 1 in 500 children due to abnormal brain development, impacts movement control. Early risk assessment via the general movements assessment (GMA) at 3–4 months is highly predictive for CP but relies on trained clinicians. Machine-learning-based approaches for predicting GMA score from video have shown considerable promise, but typically rely on dataset-specific preprocessing, custom feature sets, and manually designed model pipelines, which make external benchmarking more difficult. This, combined with strict privacy constraints on sharing data, makes it challenging to train and evaluate models across datasets, which is important for assessing clinical utility. There is therefore a need to develop approaches that will work across different datasets to enable multi-site dataset aggregation and model training. To address this gap, we developed an end-to-end pipeline that uses off-the-shelf pose estimation, general-purpose feature extraction, and automated machine learning—none of which are tuned to a specific dataset. We applied this approach to a newly generated large dataset of 1053 infants (with approximately 10–12% positive class for adverse GMA outcome, drawn from a high-risk clinical cohort) within a preregistered study design. Model performance was evaluated on a strict “lock-box” test set, which remained untouched during any phase of model development or preprocessing optimization, and only used for evaluation once the final model and pipeline had been preregistered. The developed model achieved moderate predictive accuracy for clinician-assessed GMA scores (area under the receiver operating characteristic curve, ROC-AUC = 0.77; area under the precision-recall curve, PR-AUC = 0.41). The moderate accuracy is noteworthy given the 10–12% positive class prevalence, and power-law scaling of ROC-AUC as a function of increasing dataset size. By releasing de-identified feature data and open-source code, and simplifying the training pipeline using AutoML, our work establishes essential groundwork for future robust, globally relevant CP screening tools suitable for low-resource settings.

We don’t program neural networks directly. Instead, we rely on an indirect style where learning algorithms, like gradient descent, determine a neural network’s function by learning from data. This indirect style is often a virtue; it empowers us to solve problems that were previously impossible. But it lacks discrete structure. We can’t compile most algorithms into a neural network—even if these algorithms could help the network learn. This limitation occurs because discrete algorithms are not obviously differentiable, making them incompatible with the gradient-based learning algorithms that determine a neural network’s function. To address this, we introduce Cajal: a typed, higher-order and linear programming language intended to be a minimal vehicle for exploring a direct style of programming neural networks. We prove Cajal programs compile to linear neurons, allowing discrete algorithms to be expressed in a differentiable form compatible with gradient-based learning. With our implementation of Cajal, we conduct several experiments where we link these linear neurons against other neural networks to determine part of their function prior to learning. Linking with these neurons allows networks to learn faster, with greater data-efficiency, and in a way that’s easier to debug. A key lesson is that linear programming languages provide a path towards directly programming neural networks, enabling a rich interplay between learning and the discrete structures of ordinary programming.

Recent advances in machine learning have dramatically improved our ability to model language, vision, and other high-dimensional data, yet they continue to struggle with one of the most fundamental aspects of biological systems: movement. Across neuroscience, medicine, robotics, and ethology, movement is essential for interpreting behavior, predicting intent, and enabling interaction. Despite its core significance in our intelligence, movement is often treated as an afterthought rather than as a rich and structured modality in its own right. This reflects a deeper fragmentation in how movement data is collected and modeled, often constrained by task-specific goals and domain-specific assumptions. But movement is not domain-bound. It reflects shared physical constraints, conserved morphological structures, and purposeful dynamics that cut across species and settings. We argue that movement should be treated as a primary modeling target for AI. It is inherently structured and grounded in embodiment and physics. This structure, often allowing for compact, lower-dimensional representations (e.g., pose), makes it more interpretable and computationally tractable to model than raw, high-dimensional sensory inputs. Developing models that can learn from and generalize across diverse movement data will not only advance core capabilities in generative modeling and control, but also create a shared foundation for understanding behavior across biological and artificial systems. Movement is not just an outcome, it is a window into how intelligent systems engage with the world.

Computed tomography has revolutionised the study of the internal three-dimensional structure of fossils. Historically, fossils typically spent years in preparation to be freed from the enclosing rock. Now, X-ray and synchrotron tomography reveal structures that are otherwise invisible, and data acquisition can be fast. However, manual segmentation of these 3D volumes can still take months to years. This is especially challenging for resource-poor teams, as scanning may be free, but the computing power and (AI-assisted) segmentation software required to handle the resulting large data sets are complex to use and expensive. Here we present a free, browser-based segmentation tool that reduces computational overhead by splitting volumes into small chunks, allowing processing on low-memory, inexpensive hardware. Our tool also speeds up collaborative ground-truth generation and 3D visualisation, all in-browser. We developed and evaluated our pipeline on various open-data scans of differing contrast, resolution, textural complexity, and size. Our tool successfully isolated the Thrinaxodon and Broomistega pair from an Early Triassic burrow. It isolated cranial bones from the Cretaceous acipenseriform Parapsephurus willybemisi on both 45.53 µm and 13.67 µm resolution (voxel size) scanning data. We also isolated bones of the Middle Triassic sauropterygian Nothosaurus and a challenging scan of a squamate embryo inside an egg dating back to the Early Cretaceous. Our tool reliably reproduces expert-supervised segmentation at a fraction of the time and cost, offering greater accessibility than existing tools. Beyond the online tool, all our code is open source, enabling contributions from the palaeontology community to further this emerging machine-learning ecosystem.

Computed tomography has revolutionised the study of the internal three-dimensional structure of fossils. Historically, fossils typically spent years in preparation to be freed from the enclosing rock. Now, X-ray and synchrotron tomography reveal structures that are otherwise invisible, and data acquisition can be fast. However, manual segmentation of these 3D volumes can still take months to years. This is especially challenging for resource-poor teams, as scanning may be free, but the computing power and (AI-assisted) segmentation software required to handle the resulting large data sets are complex to use and expensive. Here we present a free, browser-based segmentation tool that reduces computational overhead by splitting volumes into small chunks, allowing processing on low-memory, inexpensive hardware. Our tool also speeds up collaborative ground-truth generation and 3D visualisation, all in-browser. We developed and evaluated our pipeline on various open-data scans of differing contrast, resolution, textural complexity, and size. Our tool successfully isolated the Thrinaxodon and Broomistega pair from an Early Triassic burrow. It isolated cranial bones from the Cretaceous acipenseriform Parapsephurus willybemisi on both 45.53 µm and 13.67 µm resolution (voxel size) scanning data. We also isolated bones of the Middle Triassic sauropterygian Nothosaurus and a challenging scan of a squamate embryo inside an egg dating back to the Early Cretaceous. Our tool reliably reproduces expert-supervised segmentation at a fraction of the time and cost, offering greater accessibility than existing tools. Beyond the online tool, all our code is open source, enabling contributions from the palaeontology community to further this emerging machine-learning ecosystem.