#01Jul 16, 2026
cs.LG
Learning in Infinitesimal Non-Compositional Sketches
Sridhar Mahadevan
This paper develops a categorical framework -- Learning in Infinitesimal Non-Compositional Sketches (LINCS) -- as the repair of non-compositionality: failures of diagrams to factor through quotient sketches lifted to the tangent category setting. Machine learning problems are specified as sketches: graphs with commutativity conditions $\mathcal D$, limit cones $\mathcal L$, and colimit cocones $\mathcal K$, generalizing the usual scalarization of loss functions or vector space assumptions. Non-compositionality is defined purely as failure of a universal factorization problem, not as arithmetic error between the desired and actual predictions. Given a learning sketch $\mathbb S=(S,\mathcal D,\mathcal L,\mathcal K)$, whose underlying graph is $S$, and a model $D:J \rightarrow C$, the base defect is the obstruction to factorization $\mbox{Obs}(\mbox{Fact}_{\mathbb S}(D))$. The tangent lift applies the tangent functor $T$ to obtain $TD:J \rightarrow C$, and LINCS is defined as the obstruction $\mbox{Obs}(\mbox{Fact}_{\mathbb S}(TD))$ -- asking whether infinitesimal perturbations preserve the compositionality constraints.The paper also introduces Tangent Learning Sketches, which are sketches equipped with Cockett-Cruttwell tangent structure. The paper defines the INC endofunctor, which iterates the tangent lift, producing a tower $D,TD,T^2D, \cdots$ of factorization problems. ML is thereby formulated as the search for a coalgebraic fixed point where successive tangent unfoldings stabilize ($νT_{\mbox{INC}}$). Using the Aczel--Mendler theorem, we prove existence of a final INC coalgebra whenever $T_{\mbox{INC}}$ admits a set-based class realization that creates its final carrier. A detailed experimental evaluation of LINCS is underway in a number of concrete ML settings, including deep learning, large language models, and reinforcement learning, and is described in companion papers.
#02Jul 16, 2026
cs.CV
Online Neural Space Time Memory for Dynamic Novel View Synthesis
Baback Elmieh, Lynn Tsai, Zeman Li and 8 more
Online novel view synthesis from multi-view streaming videos faces a fundamental trade-off: maintaining a persistent, long-horizon memory to reconstruct temporarily occluded regions while operating under strict real-time constraints. While Test-Time Training (TTT) offers a powerful memory mechanism, standard models mandate gradient-based memory updates at every frame to adapt to the changing motion in dynamic scenes. The computational cost of heavy memory updates precludes real-time application and can lead to instability over long contexts. Given that memory updates are more demanding than memory application and video content is largely redundant, we propose to decouple the frequencies of these two processes. Our approach performs periodic memory updates while applying the memory on a per-frame basis, using cross-view attention to manage deformations between the prior memory state and the current frame. To lock in the historical context, we introduce two critical mechanisms: an auxiliary Memory Loss that forces persistent internalization of the scene, and a Memory Caching strategy that regularizes active weights against catastrophic drift. Our method demonstrates real-time, state-of-the-art performance on scenes with dynamic human motion as well as minute-scale online memorization.
#03Jul 16, 2026
cs.NE
NeuronSoup: Evolving Asynchronous, Shared-Neuron Temporal Graphs without Backpropagation
Subodh Kalia
We present NeuronSoup, a neural computation architecture that replaces synchronous layer-by-layer processing with asynchronous, delay-mediated signal propagation through a pool of shared neurons. Each path in the network routes a continuous-valued signal from one input neuron to one output neuron through a variable number of intermediate hidden neurons. Hidden neurons are physically shared across paths: when two paths pass through the same neuron, the second arrival encounters the accumulated state left by the first, producing constructive or destructive interference that depends on signal polarity and arrival timing. The entire architecture -- topology, weights, delays, and connectivity -- is co-evolved by a genetic algorithm operating on a flat real-valued genome of 14,602 genes. On 10-class MNIST digit classification using frozen ResNet18 features as input, the system evolves a network of 204 active paths through 266 hidden neurons (156 shared across multiple paths, with one neuron participating in 11 distinct paths) and achieves 85.9\% test accuracy after 10,000 generations. The trained model occupies 115 KB. We argue that this architecture addresses fundamental limitations of current deep learning: it requires no differentiable computation graph, adapts its computation depth per-sample, and discovers lateral interactions between processing pathways that current architectures must engineer explicitly. We discuss why genetic algorithms are the correct optimization tool for this problem class, why CMA-ES fails at this scale, and how the architecture generalizes to arbitrary domains by substituting the encoder and output structure.
#04Jul 16, 2026
cs.LG
An Introduction to Sparse Identification of Nonlinear Dynamics for Engineering Applications
Yao Cheng Li, Ana Larrañaga, Steven L. Brunton and 1 more
Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known. Surrogate modeling techniques such as neural networks can capture the behavior of these systems, but they typically demand large training datasets that are difficult to obtain in engineering contexts and yield models with limited physical interpretability. The Sparse Identification of Nonlinear Dynamics (SINDy) method addresses both limitations by performing sparse regression over libraries of candidate nonlinear terms, recovering interpretable governing equations from comparatively small datasets. Although SINDy has been demonstrated extensively on canonical benchmark systems, its application to practical engineering problems is less widely documented. This tutorial introduces the SINDy method and progressively builds toward its main extensions, from noise-robust weak-form and ensembling-based variants to constrained and parametrizable formulations. The paper and the accompanying tutorial (available at https://github.com/paullililili/SINDy4Engineers) is organized in three parts: the first introduces the standard SINDy algorithm and progressively extends it, inviting readers without prior knowledge to follow each step and adapt the methods to their own problems; the remaining two parts present detailed case studies on (1) the system identification of an unmanned aerial vehicle and (2) a chaotic thermosyphon heat exchanger. Through these examples, we aim to demonstrate that SINDy is simple to implement yet flexible enough to serve as a valuable identification tool for advanced engineering applications.
#05Jul 16, 2026
cs.AI
Concept-Guided Spatial Regularization for World Models in Atari Pong
Yukuan Lu, Zaishuo Xia, Weyl Lu and 1 more
World models are usually evaluated as components of model-based reinforcement learning (MBRL) systems, while the world models themselves are rarely studied in isolation. We examine five representative visual world-model agents in Atari Pong: DreamerV3, DIAMOND, TWISTER, Simulus, and STORM. After reproducing their training pipelines and matching the reported agent performance, we freeze the learned world models and evaluate them with a closed-loop rollout diagnostic: a policy trained separately from the corresponding MBRL agent interacts with each frozen model, and the generated video trajectories are inspected for visual and dynamical errors. Across all five models, the rollouts contain clear failures, including ball disappearance, incorrect ball motion, and invalid ball-paddle interactions. Beyond visual trajectories, we further evaluate them with pixel-space zero-shot MBRL, where a new policy is trained entirely inside a frozen world model and then evaluated in the real environment. Across all five models, the resulting policies substantially underperform those produced by the corresponding original MBRL training pipelines. The gap is particularly large for DreamerV3, whose mean return drops from -5.5 to -20.9, near the minimum Pong return of -21. We hypothesize that insufficient modeling of task-critical concepts, such as the ball in Pong, may contribute to these failures. We therefore propose Concept-Guided Spatial Regularization (CGSReg), an auxiliary pixel reconstruction loss applied to segmented concept regions. Experiments show that CGSReg improves both closed-loop rollouts and pixel-space zero-shot MBRL in DreamerV3, DIAMOND, and TWISTER. Its effects vary across the remaining models and evaluation metrics, indicating that CGSReg alone does not address all world-model bottlenecks.