Coşku Can Horuz

Coşku Can Horuz, Matthias Karlbauer, Timothy Praditia et al.

Spatiotemporal partial differential equations (PDEs) find extensive application across various scientific and engineering fields. While numerous models have emerged from both physics and machine learning (ML) communities, there is a growing trend towards integrating these approaches to develop hybrid architectures known as physics-aware machine learning models. Among these, the finite volume neural network (FINN) has emerged as a recent addition. FINN has proven to be particularly efficient in uncovering latent structures in data. In this study, we explore the capabilities of FINN in tackling the shallow-water equations, which simulates wave dynamics in coastal regions. Specifically, we investigate FINN's efficacy to reconstruct underwater topography based on these particular wave equations. Our findings reveal that FINN exhibits a remarkable capacity to infer topography solely from wave dynamics, distinguishing itself from both conventional ML and physics-aware ML models. Our results underscore the potential of FINN in advancing our understanding of spatiotemporal phenomena and enhancing parametrization capabilities in related domains.

Coşku Can Horuz, Andrea Ceni, Claudio Gallicchio et al.

Memristive devices present a promising foundation for next-generation information processing by combining memory and computation within a single physical substrate. This unique characteristic enables efficient, fast, and adaptive computing, particularly well suited for deep learning applications. Among recent developments, the memristive-friendly echo state network (MF-ESN) has emerged as a promising approach that combines memristive-inspired dynamics with the training simplicity of reservoir computing, where only the readout layer is learned. Building on this framework, we propose memristive-friendly parallelized reservoirs (MARS), a simplified yet more effective architecture that enables efficient scalable parallel computation and deeper model composition through novel subtractive skip connections. This design yields two key advantages: substantial training speedups of up to 21x over the inherently lightweight echo state network baseline and significantly improved predictive performance. Moreover, MARS demonstrates what is possible with parallel memristive-friendly reservoir computing: on several long sequence benchmarks our compact gradient-free models substantially outperform strong gradient-based sequence models such as LRU, S5, and Mamba, while reducing full training time from minutes or hours down seconds or even only a few hundred milliseconds. Our work positions parallel memristive-friendly computing as a promising route towards scalable neuromorphic learning systems that combine high predictive capability with radically improved computational efficiency, while providing a clear pathway to energy-efficient, low-latency implementations on emerging memristive and in-memory hardware.

Coşku Can Horuz, Geoffrey Kasenbacher, Saya Higuchi et al.

Modeling sophisticated activation functions within deep learning architectures has evolved into a distinct research direction. Functions such as GELU, SELU, and SiLU offer smooth gradients and improved convergence properties, making them popular choices in state-of-the-art models. Despite this trend, the classical ReLU remains appealing due to its simplicity, inherent sparsity, and other advantageous topological characteristics. However, ReLU units are prone to becoming irreversibly inactive - a phenomenon known as the dying ReLU problem - which limits their overall effectiveness. In this work, we introduce surrogate gradient learning for ReLU (SUGAR) as a novel, plug-and-play regularizer for deep architectures. SUGAR preserves the standard ReLU function during the forward pass but replaces its derivative in the backward pass with a smooth surrogate that avoids zeroing out gradients. We demonstrate that SUGAR, when paired with a well-chosen surrogate function, substantially enhances generalization performance over convolutional network architectures such as VGG-16 and ResNet-18, providing sparser activations while effectively resurrecting dead ReLUs. Moreover, we show that even in modern architectures like Conv2NeXt and Swin Transformer - which typically employ GELU - substituting these with SUGAR yields competitive and even slightly superior performance. These findings challenge the prevailing notion that advanced activation functions are necessary for optimal performance. Instead, they suggest that the conventional ReLU, particularly with appropriate gradient handling, can serve as a strong, versatile revived classic across a broad range of deep learning vision models.

Coşku Can Horuz, Sebastian Otte, Martin V. Butz et al.

We introduce MinConvLSTM and MinConvGRU, two novel spatiotemporal models that combine the spatial inductive biases of convolutional recurrent networks with the training efficiency of minimal, parallelizable RNNs. Our approach extends the log-domain prefix-sum formulation of MinLSTM and MinGRU to convolutional architectures, enabling fully parallel training while retaining localized spatial modeling. This eliminates the need for sequential hidden state updates during teacher forcing - a major bottleneck in conventional ConvRNN models. In addition, we incorporate an exponential gating mechanism inspired by the xLSTM architecture into the MinConvLSTM, which further simplifies the log-domain computation. Our models are structurally minimal and computationally efficient, with reduced parameter count and improved scalability. We evaluate our models on two spatiotemporal forecasting tasks: Navier-Stokes dynamics and real-world geopotential data. In terms of training speed, our architectures significantly outperform standard ConvLSTMs and ConvGRUs. Moreover, our models also achieve lower prediction errors in both domains, even in closed-loop autoregressive mode. These findings demonstrate that minimal recurrent structures, when combined with convolutional input aggregation, offer a compelling and efficient alternative for spatiotemporal sequence modeling, bridging the gap between recurrent simplicity and spatial complexity.