Vitrimer epoxies, in comparison with regular thermoset epoxies, have properties that enable new opportunities, such as particle welding. This means that vitrimer epoxies can be mechanically recycled with minimal degradation and also mixed in powder form to create blends and functional gradients when the chemistries are compatible, enabling composite behavior. To achieve this, certain parameters, such as temperature, pressure, and time, must be optimized during particle reconsolidation. This can be achieved with the correct manufacturing tooling and processes.

In this work, adipic acid and malic acid epoxy vitrimers were mechanically recycled and blended. The successful recycling procedure is described in detail. Ground particle size analysis was performed through optical microscopy, and the recycled samples were characterized with DMA, DSC, Micro-CT, FTIR, and observed through a polarized film. Thermomechanical properties were compared before and after recycling, and across different blend ratios. Malic acid vitrimer displayed a change in properties after recycling due to probable hygrothermal degradation. This was investigated further to evaluate the possibility of hydrolysis during recycling.

Analysis of blended materials displays possible partial miscibility, showing two glass transition temperatures that have partially shifted. A potential application is demonstrated with a recycled sample that has a composition gradient. A scratch was made on the surface, and a healing process was conducted by raising the temperature. Different flow behaviors were observed for each composition, displaying the benefits of blending and grading these materials. ... Read more

The backpropagation (BP) algorithm, though fundamental to modern deep learning, faces severe biological, computational, and physical limitations that hinder its applicability on energy-efficient neuromorphic systems. This has motivated the search for BP-free learning paradigms, with Hebbian-based algorithms being a notable alternative. Existing approaches range from purely local, unsupervised schemes such as SoftHebb-which naturally clusters data based on structural variance-to supervised, error-modulated approaches like PEPITA, which provides task-specific feedback through a second forward pass. However, the tradeoffs between these extremes remain largely unexplored. This study systematically compares the internal representations and hardware efficiencies of three Multi-Layer Perceptrons (MLP) trained with Backpropagation, PEPITA, and SoftHebb.

Our evaluation, utilizing geometric metrics such as Centered Kernel Alignment (CKA) and Principal Component Analysis (PCA), showcases how PEPITA exhibits higher similarity to BP, but is more geometrically aligned with the unsupervised SoftHebb. Furthermore, empirical hardware profiling exposes a significant implementation paradox: despite the theoretical efficiency of BP-free methods, high-level framework bottlenecks currently make algorithms like PEPITA computationally expensive on traditional digital architectures. ... Read more

Equilibrium Propagation (EP) is a backpropagation-free learning algorithm for energy-based networks; its standard estimator computes the gradient by comparing the equilibrium states reached in a free phase and a single nudged phase, but carries a bias that limits how closely EP can match backpropagation. The centered estimator reduces this bias and improves accuracy, but adds a second nudged phase per update, raising the training cost. To balance accuracy against compute, we introduce hybrid EP, a family of estimators that mix the standard and centered updates on a per-batch basis, and show analytically that the mixing probability controls this bias, so that annealing it interpolates between the two regimes. We evaluate three hybrid schedules - a cosine anneal, its inverse, and a fixed stochastic mix - against standard and centered EP on MNIST, Fashion-MNIST, and CIFAR-10, in order of increasing complexity. On the easier tasks the hybrids match centered EP at lower compute. On CIFAR-10 standard EP collapses to near-chance accuracy, and the cosine and inverse schedules collapse with it: each concentrates its biased updates into one long stretch, whereas only the stochastic mix, which spreads the same biased updates evenly across batches, trains stably. The compute savings of hybrid EP are therefore real but task-dependent: they are realized most cleanly when standard EP is itself viable, and training stability is governed not by the number of biased updates but by their distribution over the course of training. ... Read more

The aim of this paper is to explore the potential of adapting the Mono-Forward algorithm with Zeroth-Order Optimization for backpropagation (BP) and automatic-differentiation(AD)-free image classification, assessing its feasibility in scenarios where exact gradients are unavailable. The Mono-Forward method introduces a novel approach to training neural networks without the need for backpropagation or multiple forward passes typically required in forward-forward algorithms; however it still relies on AD for local training of model layers when implemented with modern deep learning frameworks. This work proposes MF+DD, which replaces AD in Mono-Forward with zeroth-order gradient estimation via directional derivatives, resulting in a training algorithm that is free of AD and global BP. This paper also introduces a random projection based modification to adress the limitation of Mono-Forward in architectures with large intermediate activation tensors, for increased computational efficiency. Experiments on MNIST, FashionMNIST, CIFAR-10, and CIFAR-100 with both MLP and CNN architectures show that MF+DD achieves comparable accuracy to MF with AD on simpler datasets, while the accuracy gap widens on more complex benchmarks, suggesting that the noise introduced by the directional derivative estimator becomes more impactful as task difficulty increases. Results further show that increasing the number of perturbation directions P improves both accuracy and training stability with a downside of increased computational cost. ... Read more

Backpropagation-free learning rules depict an affinity towards neuromorphic and energy constrained hardware, yet the final representations that they learn remain not well understood. We dive deep on two local Hebbian rules that appear to compute distinct objectives: (i) Oja’s rule computes the first principal component; (ii) SoftHebb extends it to a soft winner-take-all network whose fixed points are normalized component means. In the batch setting, Ding and He (2004) have shown that K-means and PCA are strongly related, that is, the subspace spanned by the cluster centroids coincides with the span of the first K − 1 principal directions of the data covariance. We analyze if the same correspondence survives sample by sample in a streaming setting, where updates are noisy and the weight vectors are renormalized. As such, we first provide a self contained fixed-point analysis, which we are going to use it as the common lens for both rules. Second, on controlled two dimensional Gaussian data, we assess some geometric conditions under the rules agree or disagree, yielding an actionable criterion for predicting, on a given dataset, whether the rules converge to the same representation. Third, we show the disagreement is not as the naive picture suggests, that is, an expected divergence does not hold and is replaced with a quantitative account depicted by a ratio of the cluster width to the inter cluster offset. ... Read more

Recent interest in biologically plausible alternatives to backpropagation has renewed attention on Spiking Neural Networks and the Forward-Forward algorithm, where learning is driven by local layer-wise goodness functions rather than global error gradients. In most Forward-Forward learning implementations of Spiking Neural Networks, goodness is defined as spike-count activity, leaving temporal properties of neural activity unused. This work investigates whether temporal spike stability, measured using the inter-spike interval coefficient of variation (ISI-CV), can improve Forward-Forward learning in fully connected leaky integrate-and-fire spiking neural networks. Using MNIST as a benchmark, we evaluate several ISI-CV-based extensions, including direct temporal penalties, contrastive gap losses, plasticity based approaches, and candidate scoring. Directly optimizing for temporal regularity conflicts with the Forward-Forward goodness margin and destabilizes training. The use of ISI-CV as a plasticity control signal, that reduces updates to temporally stable neurons, can be used to fine-tune the model. ISI-CV-based candidate scoring performs above chance, indicating that spike timing contains class-related information, but remains weaker than standard goodness-based classification. ... Read more

Accurate constitutive modeling of hyperelastic materials remains a challenging task due to their inherently nonlinear and complex stress–strain behavior. Traditional phenomenological models often fall short in capturing this complexity, particularly in modern engineering materials with rich mechanical responses. In recent decades, data-driven modeling approaches have emerged as promising alternatives, offering flexibility in learning material behavior directly from data. Multi-Layer Perceptrons (MLPs), in particular, have become widely adopted due to their universal approximation capabilities. Despite their benefits, MLP-based approaches face significant limitations. Their "blackbox" nature limits interpretability and restricts insights into underlying material mechanics. Furthermore, although MLPs with fixed activation functions can approximate hyperelastic behavior in theory, their limited smoothness, such as in the case of ReLU, can restrict accurate representation of derivatives essential for modeling material responses. These shortcomings highlight the need for alternative frameworks that can represent material behavior more accurately and transparently. An emerging alternative is the Kolmogorov-Arnold Network (KAN), which offers improved interpretability and greater flexibility due to its architecture. By leveraging the Kolmogorov-Arnold representation theorem, KANs decompose complex functions into simpler, easy-to-understand components. WhileKANs have shown promise in various applications, including material modeling, their use in hyperelasticity remains limited due to challenges in ensuring physically consistent predictions. Current KAN-based frameworks cannot guarantee physically valid hyperelastic modeling. To address these challenges, this work introduces a novel Input-Convex Kolmogorov-Arnold Network (ICKAN) architecture tailored for hyperelastic constitutive modeling. The ICKAN model employs spline-based, learnable activation functions to capture material nonlinearities and explicitly incorporates convexity and monotonicity constraints to ensure adherence to physical principles. Validation using benchmark datasets demonstrates that ICKAN accurately predicts hyperelastic stress–strain behavior across a range of loading conditions. By enhancing interpretability and ensuring physically consistent predictions, the proposed ICKAN framework provides a robust and transparent solution, underscoring the broader potential of KANs in data-driven constitutive modeling. ... Read more