Related papers: Scale-Consistent State-Space Dynamics via Fractal …

This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…

Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely…

Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the dataset and the training algorithm must be taken into account…

Robots deployed at orders of magnitude different size scales, and that retain the same desired behavior at any of those scales, would greatly expand the environments in which the robots could operate. However it is currently not known…

Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…

Tabular learning transforms raw features into optimized spaces for downstream tasks, but its effectiveness deteriorates under distribution shifts between training and testing data. We formalize this challenge as the Distribution Shift…

Effective sequence modeling fundamentally requires balancing the retention of unbounded history with the high-resolution detection of abrupt short-term variations common in real-world phenomena. However, existing state space models (SSMs)…

In the realm of fractal geometry, intricate structures emerge from simple iterative processes that partition parameter spaces into regions of stability and instability. Likewise, training large language models involves iteratively applying…

Scaling deep reinforcement learning networks is challenging and often results in degraded performance, yet the root causes of this failure mode remain poorly understood. Several recent works have proposed mechanisms to address this, but…

Estimating a fractal dimension from a finite stochastic trajectory is a finite-size scaling problem: the apparent box-counting exponent is shaped by an occupancy crossover between the resolved range of scales and the finite number of…

Recent deep reinforcement learning (DRL) successes rely on end-to-end learning from fixed-size observational inputs (e.g. image, state-variables). However, many challenging and interesting problems in decision making involve observations or…

This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II…

The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…

Semantic Image Segmentation facilitates a multitude of real-world applications ranging from autonomous driving over industrial process supervision to vision aids for human beings. These models are usually trained in a supervised fashion…

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

Fine-tuning adapts pretrained networks to new objectives. Whether the resulting depth profile of representational change reflects an intrinsic property of the model or the magnitude of gradient flow has not been tested directly. We measure…

A state-space model is a statistical framework for inferring latent states from observed time-series data. However, inference with nonlinear and high-dimensional state-space models remains challenging. To this end, an approach based on…

Continual learning seeks to maintain stable adaptation under non-stationary environments, yet this problem becomes particularly challenging in object detection, where most existing methods implicitly assume relatively balanced visual…

Token representations in high-dimensional latent spaces often exhibit redundancy, limiting computational efficiency and reducing structural coherence across model layers. Hierarchical latent space folding introduces a structured…