Neural Network

Controlling the Lipschitz constant of a neural network is a standard way to promote robustness and stability. Most existing constraining strategies are designed for Euclidean spaces. In this work, we construct and analyze a class of 1-Lipschitz neural networks on Hadamard manifolds. Our layers are of gradient-descent type, $1$-Lipschitz, and quasi-$α$-firmly nonexpansive. The core building blocks of the proposed architecture are Busemann functions, and we exploit the properties of Busemann gradient flows to design $1$-Lipschitz geometry-preserving layers. We provide explicit constructions and examples for hyperbolic manifolds and the manifold of symmetric positive definite (SPD) matrices. We test the proposed architecture in two numerical experiments: robust classification on the Poincaré disk and masked-Wishart covariance reconstruction. On the Poincaré disk, the proposed networks yield robust classifiers under hyperbolic perturbations. On the SPD manifold, we train SPD-valued denoisers and adopt them as a Plug-and-Play prior for a masked-Wishart covariance reconstruction problem. We show improved results from the nonexpansive denoiser over static, data-only, and Log-Euclidean denoising baselines, and empirically test its convergence properties.

Associative emotional learning enables organisms to adaptively link pleasant or unpleasant outcomes to the presence of predictive stimuli. Whereas computational models such as the Rescorla-Wagner model have shed light on this important function, the limitations of these models are also known, especially when they are applied to neural data. The advent of deep neural networks has opened another avenue for modeling associative emotional learning. In this work we proposed a deep neural network model of visual valence processing, consisting of a visual module that encodes complex natural scenes and a module that recognizes their emotional significance in terms of valence, a key dimension of emotion, and tested a novel Pavlovian learning paradigm on the model. The results showed that with learning, the model reproduced several observations from human associative learning studies, including association formation and generalization, and that the neural representations of the conditioned and the unconditioned stimuli became increasingly aligned both at the single unit and at the neural population level. Comparison between the model and human experimental data provided further validation of our approach. This study thus suggests that deep neural network models, when combined with appropriate learning algorithms, can be used to model behavioral and neural signatures of associative emotion/valence learning.

Functional magnetic resonance imaging (fMRI)-based visual decoding aims to recover visual information from measured brain activity, commonly by mapping fMRI responses into latent visual features for downstream decoding tasks. Most existing methods learn mappings from fMRI responses to visual features extracted by artificial neural networks (ANNs), yet it remains unclear whether ANN-derived features provide suitable targets for brain decoding. In this study, we investigate spiking neural network (SNN)-derived visual features as alternative targets for fMRI-based visual decoding. We compare an ANN baseline with four SNN variants from the same architectural family, which differ in their spiking dynamics. To isolate the effect of the target features, all models use the same L2-regularized linear fMRI-to-feature decoder, while only the feature vectors used as regression targets are varied. Compared with the ANN baseline, SNN-derived features exhibit stronger alignment with fMRI responses and improve visual semantic decoding performance. For instance, on the GoD dataset, SNN-derived features reduce feature-prediction error from 0.7707 to 0.0282 and improve top-1 semantic decoding accuracy from 0.1800 to 0.4400. Ablation results further indicate that both spiking neural dynamics and temporal simulation steps contribute to the observed advantage. These findings support SNN-derived features as effective brain-decodable visual representations and highlight target feature design as an important component of fMRI-based visual decoding.

Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning. Yet, their deployment has proven demanding: the number of weighted hyperedges required leads to an intractable parameter explosion. However, a novel parametrization that leverages spectral attributes for neural hypergraphs has been recently proposed, that enables to recycle parameters via a weight sharing scheme and consequently yields a significant reduction of the associated computational cost. Preliminary tests carried out on spectral higher-order architectures pointed to meaningful improvements in both performance and interpretability. Building on these results, we advance the benchmarking efforts by evaluating the spectral higher order framework on N-bit parity tasks, a well-established testbed known to be particularly challenging. As we will convincingly argue, Spectral Higher-Order Neural Networks (SHONNs) possess a versatile and highly tunable hypothesis space.

Structured pruning is essential for making neural network inference feasible under homomorphic encryption (HE), yet its impact on model reliability has remained unexplored. This paper presents a systematic reliability characterization of pruned CKKS-encrypted neural networks and introduces Polynomial-Sensitivity-Aware Pruning (PSAP), a structured pruning method that is inherently reliability-aware. PSAP scores filters jointly by weight magnitude, polynomial activation sensitivity, and rotation cost, which concentrates pruning in fault-tolerant regions. Across two architectures, two datasets, two numerical representations, and five bit-error rates (40 full-model and 108 per-layer experiments), PSAP-pruned models limit catastrophic (>10 pp accuracy drop) layers to at most two versus 5--14 for magnitude-pruned baselines, reducing worst-case vulnerability by up to 29 times under int32 bit-flip injection. Direct CKKS encrypted fault injection indicates a safe operating boundary near BER~ 10^{-5}, supporting int32 injection as a conservative reliability proxy. The fault-critical structural layers account for only 1.1% of parameters, enabling selective hardening at minimal overhead. These reliability gains are obtained alongside competitive efficiency: PSAP reduces Halevi--Shoup rotations by up to 45.2% on ResNet-32, and an adaptive mixed-degree allocation scheme lowers multiplicative depth from 66 to 56 levels, enabling leveled inference without bootstrapping.

In robotic manipulation studies, grasping is often treated as a binary success or failure problem, usually defined by whether the object simply stays in the hand. For forceful tool use, however, this view is insufficient because grasp compliance becomes a critical factor governing how the hand and tool behave under load. Compliance arises from coupled kinematics, grasp configuration, passive mechanics, and contact conditions, producing nonlinear behavior in which deformation and interaction forces influence each other. Understanding this relationship is essential for predictive models of how a grasped tool and a compliant hand jointly respond to external loading. In underactuated hands, these effects are amplified: such designs offer low cost and adaptive grasping, but make compliance behavior more difficult to model and predict. Our goal is therefore to develop a predictive model for grasped tool behavior during forceful interactions. To address this challenge, we introduce an analytical model informed neural network (AMINN), a hybrid predictive model that combines an analytical mechanics layer with data driven learning to estimate grasp stability and in hand tool displacement under external loading. The model is evaluated on a three finger underactuated robotic hand and shows strong predictive capability with mechanically meaningful outputs across diverse loading conditions. Compared with a black box multilayer perceptron baseline, AMINN also achieves better energy based physical consistency. Beyond prediction accuracy alone, this framework advances physically interpretable learning for robotic manipulation and supports more reliable, safer, and more trustworthy autonomous tool use in safety critical settings during forceful interaction.

In this work, we investigate the effect of lookahead branching strategies in neural network verification. We present a general recipe to integrate lookahead into any branch-and-bound verifier and demonstrate how one of the current state-of-the-art branching heuristics, FSB, can be viewed as a special instantiation of the lookahead branching strategy. We also describe how, in addition to improving the quality of branching decisions, lookahead can generate additional lemmas that accelerate verification. We instantiate the method in two representative branch-and-bound-based verifiers (Marabou and $α$-$β$-CROWN), and demonstrate that lookahead leads to consistent speedups in verification time and up to $57\%$ more solved instances. Code is available at https://github.com/ai-ar-research/lookahead-branching.

Graph Neural Networks (GNNs) have emerged as a powerful, differentiable class of learning models for graph-structured systems. Their ability to generalize across topologies opens the prospect of a surrogate for combined structural and parametric optimization, which classical metamodels cannot offer. Supply chains are a natural target, yet the use of GNN surrogates for supply chain problems is largely unexplored. This paper lays the foundation, presents initial steps, and discusses key research directions. As a foundation, we formulate the problem and create a large public training dataset of programmatically generated supply chain graphs with input parameters and steady-state performance metrics obtained using our SupplyNetPy simulation library. As initial steps, we explore GNN architectures that work well as surrogates for node- and network-level predictions, and analyze their accuracy-compute trade-off against simulation. Most importantly, we outline the exciting directions this opens, namely gradient-based optimization over topology, fast design-space exploration, and sensitivity analysis.

The widespread adoption of high-level deep learning libraries, while accelerating model development, has increasingly abstracted away the internal mechanics of neural networks, creating a gap between practical usage and fundamental understanding. To address this, the paper presents a self-contained neural network framework implemented entirely from scratch without relying on automatic differentiation or pre-built deep learning modules. The implementation encompasses all essential components, including multi-layer architectures, diverse activation functions, regularization techniques, and state-of-the-art optimizers. Beyond serving as a pedagogical instrument that demystifies forward/backward propagation, gradient dynamics, and optimization landscapes, the framework demonstrates robust performance when applied to a multi-class classification task, successfully validating its correctness, numerical stability, and generalization across varied configurations. The extensible design and clean modularity further position it as a reliable baseline for educational purposes and future research exploration.

Oscillatory Neural Networks (ONNs) present an attractive physics-based computing paradigm rooted in the dynamics of a network of typically fully coupled oscillators aiming to minimize an underlying energy function. In this paper, we propose an ONN-based solver for one well-known constrained combinatorial optimization problem, namely a Sudoku, by formulating the problem as a Graph Coloring problem. By modifying the already existing Graph Coloring solver to a computationally cheaper version and introducing an additional term ensuring the fulfillment of the Sudoku constraints, our solver is shown to significantly outperform the existing HNN- and ONN solvers in terms of accuracy. In particular, we are able to achieve nearly flawless accuracies on $4 \times 4$ as well as rather high accuracies on $9 \times 9$ Sudoku puzzles for different numbers of unknown digits.

Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing. This work investigates hypergraph oversmoothing from a dynamical-systems perspective and develops a reaction--diffusion framework for depth-resistant hypergraph learning. By defining hypergraph gradient and divergence operators, we interpret message passing as an incidence-level diffusion process. The analysis of pure diffusion shows that its continuous semiflow exponentially contracts the null-mode-free component of node representations and drives the Dirichlet energy to zero, revealing hypergraph oversmoothing as an intrinsic transverse-energy dissipation phenomenon. Motivated by this analysis, we propose Hypergraph Neural Reaction--Diffusion (HNRD), which introduces a reaction mechanism acting on the transverse component to compensate diffusion-induced dissipation and stabilize discriminative variations. We establish global well-posedness of the proposed dynamics and prove that the null-mode-free Dirichlet energy remains bounded away from zero. A forward-Euler discretization provides a practical HNRD layer with a stability condition for deep propagation. Experiments on benchmark and synthetic heterophilic hypergraphs demonstrate that HNRD consistently improves over representative hypergraph baselines. Depth, robustness, and efficiency analyses further show that HNRD preserves stable performance and nonzero Dirichlet energy under deep propagation and perturbations. These results provide a principled dynamical framework for designing deep hypergraph architectures that maintain higher-order expressiveness without representation collapse.

Deep Neural Networks (DNNs) used in safety-critical applications are vulnerable to hardware and memory faults that corrupt network weights and degrade reliability. In this paper, we propose a Center of Gravity (CoG) guided weight correction method that restores faulty weights based on their spatial characteristics within each layer. The proposed approach detects and corrects weight faults using distance-aware correction rules, eliminating the need for retraining or architectural modification. The effectiveness of the proposed method in terms of the capability of tolerating hardware faults has been evaluated through performing fault injection at different Bit Error Rates (BERs). Experiments on safety-critical LSTM-based Networks, including StageNet for disease progression tracking and MTFNet for cardiac anomaly detection, demonstrate fault tolerance improvements of up to 230x and 6.41x, respectively, at a BER of 10^{-3}, with negligible accuracy loss. When extended to Convolutional Neural Networks (CNNs), the method achieves up to 49.55x and 20.79x improvements under comparable fault conditions on ResNet-18 and VGG-16, respectively. To the best of our knowledge, this is the first work to apply the CoG concept to neural network weight tensors for enhancing model reliability.

Physics-informed neural networks (PINNs) are unusually sensitive to interacting choices of architecture, activation, loss weighting, collocation, optimization, and constraint enforcement. Large language models (LLMs) can propose these choices, but independent recommendations do not accumulate experience from previously trained PINNs. We propose a closed-loop evolutionary algorithm that guides an LLM to generate complete, executable PINN configurations across generations, using measured training outcomes to determine subsequent search decisions. The algorithm maintains an evaluated population and lineage, applies parent-conditioned mutation and crossover, preserves elite and diverse solutions, rejects effective duplicates, and converts parent-relative successes and failures into the next-generation context supplied to the LLM. Every proposed configuration is executed directly under an exact optimizer-step budget. On a one-dimensional multiscale wave equation, two independent ten-generation runs trained 60 PINNs for 600,000 optimizer steps. In both runs, the best configuration appeared in the final generation, with best mean-squared error reduced by 2.97% and 95.38% relative to the initial population. The stronger run validated residual connections and increased depth on separate branches, combined them in a later generation, and then refined width and collocation density. It also revealed that low solution error can coexist with a high PDE residual. These results demonstrate the feasibility of evolutionary-algorithm-guided LLMs for PINN design on a controlled PDE while motivating broader, physics-aware evaluation.

We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations. We utilize structure-preserving neural networks and entropy variables to learn subgrid fluxes in coarse simulations of the Burgers' equation. In particular, we employ a decoupled neural network architecture explicitly separating the subgrid corrections into two distinct components: a conservative Flux Potential network and an Eddy Viscosity network. We demonstrate that this reduced-order framework maintains high physical fidelity, accurately reproducing the energy spectrum, spatial and temporal correlation functions, and dynamical characteristics of the full-scale system. Furthermore, we show that our approach is robust and applicable to parameters outside the training regime.

Continuous-time spiking neural networks (SNNs) provide an event-driven framework for temporal computation, computational neuroscience, and neuromorphic hardware. However, training deep continuous-time SNNs is severely constrained by the memory required for exact spike-time computation, which evaluates and retains candidate firing times over intervals determined by presynaptic spike ordering. Here we introduce a memory-efficient training framework based on differentiable spike-time discretization (DSTD) for leaky integrate-and-fire neurons with general membrane and synaptic time constants. DSTD maps irregular presynaptic spikes onto differentiable weighted events at fixed time points, replacing the input-dependent candidate dimension with $M$ fixed time intervals while accurately approximating continuous-time membrane-potential dynamics. This reduces candidate-related activation memory from $O(N_{\mathrm{out}}N_{\mathrm{in}})$ to $O(N_{\mathrm{out}}M)$ in the case of time-to-first-spike (TTFS) coding, where $N_{\mathrm{in}}$ and $N_{\mathrm{out}}$ denote the numbers of presynaptic and postsynaptic neurons, respectively. We further introduce synfire-chain-inspired temporal regularization that organizes layer-wise firing windows, mitigates dead-neuron failures, and enables pipeline-like processing. In dense LIF layers, DSTD reduced peak memory consumption by up to approximately 100-fold and training time by up to approximately 20-fold compared with exact spike-time computation. Together, these methods allowed us to train 9-layer convolutional SNNs on CIFAR-10 and 20-layer convolutional SNNs on Fashion-MNIST on a single GPU.

Estimating spatially heterogeneous elastic properties from low-resolution displacement measurements is a severely ill-posed inverse elasticity problem because low resolution obscures spatial details needed to distinguish heterogeneous property variations, and small measurement perturbations or fitting errors are amplified through inverse estimation. Existing inverse methods often rely on high-fidelity observations and manually prespecified loss weights, limiting their adaptability and making them sensitive to noise and resolution degradation. We propose a Probabilistic Inverse Elasticity Physics-Informed Neural Network (PIE-PINN) framework for robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data. PIE-PINN models displacement observation, strain-discrepancy, and equilibrium residuals using Laplace distributions within a unified probabilistic model. To improve robustness, the framework combines a B-spline-guided displacement network with a hierarchical half-Cauchy model for displacement residual scales. The B-spline provides a smooth global representation of the displacement field, while the neural network correction captures local variations. The hierarchical scale model adaptively downweights severe displacement fitting errors, enabling more robust recovery of the latent mean displacement field. An alternating maximum-likelihood training strategy updates the mean through weighted residual minimization and updates the scales to adjust the loss weights. Systematic case studies across varying noise levels and observation resolutions demonstrate the robustness of PIE-PINN.

The interconnected nature of global financial systems makes them vulnerable to systemic risks, where the failure of a few institutions can trigger catastrophic cascading defaults. Traditional risk models often fail to capture the complex, non-linear dynamics of these networks. While Graph Neural Networks (GNNs) have shown promise in modeling relational data, they primarily learn correlative patterns and function as black boxes, offering little insight into the causal mechanisms of shock propagation. This limitation is critical for regulators who require explainable models to perform stress tests and devise effective interventions. We introduce CausalGraphX, a novel framework that integrates GNNs with counterfactual reasoning to provide explainable assessments of systemic risk. CausalGraphX employs a Graph Attention mechanism to learn representations of institutional vulnerability and uses an adversarial regularization technique to ensure these representations capture causal drivers rather than spurious correlations. Furthermore, we propose an optimization-based approach to generate counterfactual explanations, answering questions such as, "What minimum capital injection would have prevented Bank A's default under a specific stress scenario?" We validate CausalGraphX on large-scale synthetic financial networks. Our results demonstrate that CausalGraphX significantly outperforms traditional and deep learning baselines in predicting cascading defaults while providing sparse, plausible, and actionable counterfactual explanations.

Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE). However, PINNs have been shown to perform poorly, sometimes even converging to trivial solutions, in challenging PDE domains, or when generalizing to unseen but related PDE domains. Previously proposed solutions detail hyperparameter tuning to reduce loss imbalance between data-driven and physics guided losses, curriculum learning based training strategies, or dynamic re-sampling of hard collocation points. These methods face certain pitfalls: hyperparameter tuning is expensive, designing a training curriculum is ambiguous in multi-parameter PDE settings, and dynamic resampling still fails in complex PDE settings. Complementary to this line of thinking, we believe the initial PINN network weights also play a crucial role in the emergence of catastrophic failures during training, yet the effect of PINN weight initialization has been surprisingly under-investigated. To this end, we propose a framework for Learned Initialization via Gated Layerwise Optimization (LIGO-PINN) to overcome PINN convergence failures. Through rigorous evaluation on 1D and 2D PDE domains, including a challenging 2D fluid dynamics setting, we demonstrate that our methodology outperforms state-of-the-art methods designed to alleviate PINN failures, achieving a 91.5% average performance improvement across six baselines and 81% over the strongest baseline. We also verify that LIGO-PINN generalizes to 3D unstructured domains. Finally, we analyze training dynamics across all three PDE domains to explain both LIGO-PINN's improvement and the convergence failure of traditional PINNs. Code: https://github.com/scailab/ligo-pinn Keywords: Machine Learning, Physics-Informed Neural Networks, Deep Learning, PDE Modeling

We investigate conditional invertible neural networks (cINNs) as probabilistic inverse-dynamics models for multirotor control. For a planar X8 coaxial multicopter, we learn $p(u \mid s_t, c_t)$ from an incremental nonlinear dynamic inversion (INDI) teacher using rational-quadratic spline coupling and invertible linear mixing. Open-loop reproduction reaches $R^2 = 0.944$, mean CRPS 0.0915, and log-probability-error correlation $ρ= -0.60$. Over 15 closed-loop scenarios, position RMSE matches INDI (9.7 vs. 9.5 m), with 47 percent tracking acceptably; failures separate into attitude divergence under aggressive steps and phase lag under high-frequency references, isolating command bandwidth and data coverage as dominant failure mechanisms.

Interfacing with Biological Neural Networks (BNNs) requires encoding information into stimulation patterns that can be effectively processed and that enable the underlying system to adapt. Nevertheless, the role of stimulation encoding remains poorly understood. In this work, we compare multiple encoding strategies, including rate-based, phase-based, burst-based, and time-to-first-spike temporal encodings, in a closed-loop neural classification task using cultured BNNs. We encode visual inputs as spatiotemporal stimulation patterns delivered via a Multi-Electrode Array (MEA) and evaluate classification performance for each encoding scheme. We find that burst-based temporal encoding yields the highest observed performance, achieving up to 95.6 % accuracy in a binary classification task, compared to substantially lower performance from rate- and phase-based approaches. We further show that performance is highly sensitive to the spatial distribution of stimulation, with suboptimal electrode selection significantly degrading accuracy. These findings indicate that effective interfacing with biological neural systems requires the joint optimization of temporal and spatial encoding strategies, and highlight temporal encoding as a key design dimension for bio-digital computing.

The Hessian matrix is an important quantity of interest when it comes to studying the loss landscape and optimization dynamics in deep learning, as well as designing measures of generalization, second-order learning algorithms, etc. Prior works have focused on empirical results or pursued a theoretical treatment under overly simplified settings. In this work, we derive the eigenvalues of the Hessian of linear networks with arbitrary widths and depths, and datasets with an arbitrary number of samples, features, and labels. Importantly, for classification tasks with MSE loss, we identify that the sharpness of the solution is directly related to the maximum proportion of samples belonging to any class. We empirically validate our predictions and systematically analyze the effects of shedding the impractical assumptions one at a time, as well as incorporating nonlinearities. We observe that our predictions are considerably robust in most cases, allowing us to extend our conclusions to more practical learning setups.

Centroid neural network (CentNN) is an unsupervised competitive learning algorithm in which centroid splitting is triggered only after strict local stabilization, often leading to prolonged low-movement training phases before model expansion. This report proposes FastCentNN, an accelerated variant that addresses this inefficiency by introducing an early splitting strategy based on the total centroid movement per epoch, which serves as a training entropy proxy. As a result, FastCentNN reduces unnecessary reassignment epochs while preserving the original winner-loser learning dynamics. FastCentNN supports both absolute and stage-relative movement thresholds, allowing the splitting criterion to remain either fixed or adaptive throughout training. Experiments on some benchmark datasets show that FastCentNN consistently achieves clustering quality comparable to CentNN while reducing runtime by up to 16% on synthetic 2D datasets and about 5% on high-dimensional datasets. FastCentNN therefore provides a practical and efficient drop-in replacement for CentNN, retaining its online adaptive learning behavior while offering a simple and interpretable speed-stability trade-off through configurable splitting thresholds.

We develop a convergent scheme to train neural networks involving analytic activation functions based on gradient flows. Convergence properties are guaranteed by Lojasiewicz theory. The main advantage of this approach is its simplicity of implementation. The coefficients of the network are approximated by solving a system of ordinary differential equations. We test the method by constructing residual neural network approximations of solutions of parametric problems. The dependence of the solutions of simple ordinary differential equations on a few parameters is correctly reproduced. The solutions of inverse problems involving wave constraints which depend on a few parameters can be reasonably approximated, even in regions in which the problem is severely ill posed.

For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy. For middle-dimensional problems ($4 \leq d \lesssim 10$), spectral methods remain feasible through specific techniques such as sparse grids or hyperbolic cross. However, for high-dimensional problems ($d\gg 10$), spectral methods suffer frome the curse of dimensionality. Physics-informed neural networks (PINNs) have emerged as a promising approach to overcome this challenge, offering scalability to high dimensions, but often suffer from limited accuracy and efficiency. Recently proposed spectral-informed neural networks (SINNs) combine spectral methods with PINNs, operating directly in the spectral domain to avoid spatial derivative computations and to reduce memory consumption. In this work, we introduce Modified SINNs, which integrate coefficient decay scaling and basis embeddings motivated by harmonic analysis to enhance accuracy in high-dimensional problems and enable accurate approximation of unknown spectral coefficients. Numerical experiments on steady and time-dependent partial differential equations demonstrate that Modified SINNs outperform sparse grid spectral methods on middle-dimensional problems with incomplete spectral information and achieve superior accuracy compared to PINNs on high-dimensional problems.

In this work, we introduce CoCo, a loss function aimed at learning normalized and well-structured representations. The proposed loss encourages intra-class collapse and inter-class contrast while preserving sufficient flexibility for neural networks to approximate geometrically optimal embeddings with large angular separation between classes. We provide a theoretical analysis positioning CoCo with respect to related objectives such as dot regression and cross-entropy, showing that the new proposed loss benefits from closer initialization to the optimal configuration, more informative gradients, and stronger incentives for class-wise representation collapse. Extensive experiments on diverse tabular datasets from the OpenML-CC18 benchmark show that CoCo achieves competitive performance with state-of-the-art methods, including kernel SVM, Random Forest, dot regression, and cross-entropy-based neural networks. In addition, both theoretical arguments and empirical analyses demonstrate that the proposal promotes tighter class clustering and faster convergence. These results highlight CoCo loss as an effective objective for learning discriminative representations while maintaining competitive predictive performance.

This paper proposes a Gaussian-Based Shift-Variant filtered backprojection (FBP) neural network, which is designed for the efficient reconstruction of non-circular trajectory cone beam computed tomography. The traditional differentiable shift-variant FBP model consists of a filtering component and a backprojection process. The filtering component includes operations such as weightings, differentiations, a 2D Radon transform, and a 2D backprojection. The proposed methods build on this framework by introducing a trainable 2D Gaussian model to represent the trajectory-related part in the filtering process, achieving a substantial reduction in the number of trainable parameters. Experimental results demonstrate that the proposed model reduces the parameter count by 99%, while only sacrificing a slight amount of reconstruction quality. Furthermore, the training time for each trajectory is reduced to one-fourth of the original, significantly accelerating convergence. These enhancements demonstrate a considerable augmentation in the model's practicality and effectiveness, making it a valuable asset for real-world applications.

We introduce a straightforward yet effective method to empirically study memorization in deep neural networks for classification tasks. Our approach augments each training sample with auxiliary random labels, which are then predicted by a random label prediction head (RLP-head). RLP-heads can be attached at arbitrary depths of a network, predicting random labels from the corresponding intermediate representation and thereby enabling analysis of how memorization capacity evolves across layers. By interpreting the RLP-head performance as an empirical estimate of Rademacher complexity, we obtain a direct measure of both sample-level memorization and model capacity. We leverage this random label accuracy metric to analyze generalization and overfitting in different models and datasets. Building on this approach, we further propose a novel regularization technique based on the output of the RLP-head, which demonstrably reduces memorization. Interestingly, our experiments reveal that reducing memorization can either improve or impair generalization, depending on the dataset and training setup. These findings challenge the traditional assumption that overfitting is equivalent to memorization and suggest new hypotheses to reconcile these seemingly contradictory results. The source code is available at https://github.com/MarlonBecker/RandomLabelHeads

In this paper, we propose TECO, a multi-dimensional pruning framework to collaboratively prune the three dimensions (depth, width, and resolution) of convolutional neural networks (CNNs) for better execution efficiency on embedded hardware. In TECO, we first introduce a two-stage importance evaluation framework, which efficiently and comprehensively evaluates each pruning unit according to both the local importance inside each dimension and the global importance across different dimensions. Based on the evaluation framework, we present a heuristic pruning algorithm to progressively prune the three dimensions of CNNs towards the optimal trade-off between accuracy and efficiency. Experiments on multiple benchmarks validate the advantages of TECO over existing state-of-the-art (SOTA) approaches. The code and pre-trained models are available at https://github.com/ntuliuteam/Teco.

Neural networks increasingly guide decisions in high-stakes domains such as medical diagnosis, credit approval, and energy bidding. Audit in these settings requires case-level evidence: which training cases support an action and what outcomes they carried. Case-based decision theory (CBDT) formalizes this reasoning by aggregating outcome support from remembered cases. We show that an OLS action readout fitted on a fixed neural representation admits an exact case-based decomposition. Each action score is a weighted sum of training-case returns, with coefficients determined by empirical Gram geometry. We identify a sufficient regime for CBDT similarity semantics; outside it, the coefficients should generally be treated as signed Gram-geometric influence. The decomposition yields audit signals that trace scores to training cases, measure action coherence, and identify weak support. Across synthetic CBDT, PJM, Adult Income, and Default Credit tasks, the method recovers case-level preference structure and achieves the highest mean Top-30 consistency among compared attribution baselines, while remaining competitive on support reconstruction. The audit requires only fitting an OLS top-layer probe, without retraining the representation or accessing the original optimization trajectory; probe fidelity is measured by score reconstruction.

Implicit neural controllers (INCs) are static feedback laws that are evaluated through an algebraic fixed point {equation}; they include as special cases neural network controllers. We propose a so-called implicit representation of neural networks as a key enabling device that exposes the controller as a trainable linear interconnection closed through a known static activation map, thereby making well-posedness and Lyapunov/IQC analysis mathematically easy to handle. For finite-dimensional LTI plants, we first develop a rigorous analysis theory for a given INC, including Perron--Frobenius and norm conditions for well posedness, LMI/IQC certificates for exponential stability, and LMIs for discounted infinite-horizon quadratic performance. We then formulate synthesis as a certification-compatible heuristic search: training is carried out under explicit well-posedness constraints, implicit-differentiation formulas provide gradients, and the resulting controller is accepted only after independent post-training LMIs or regional admissibility checks are feasible. Finally, we establish constrained-control separation results: for a specific scalar unstable plant with hard actuator bounds, an INC achieves a strictly smaller discounted infinite-horizon cost than any admissible finite-order dynamic linear controller. Additional results cover quadratic state-input costs, comparison with linear static output feedback, and computable upper/lower-bound certificates. Numerical examples illustrate the mechanism and the resulting certified performance.

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs); however, their synchronous optimization treats residuals of different regions and constraints equally, which is inconsistent with the progressive "from source to response" physical information propagation path, degrading training stability and accuracy. Existing causal training methods focus mainly on the temporal dimension, lacking a unified characterization of spatial and boundary dimensions. To address this, we define a unified class of training priorities according to the physical information propagation path: premise regions should be learned before dependent regions; temporal, spatial, and boundary priorities are instances of this principle. Using neural tangent kernel (NTK) dynamics, we theoretically analyze why standard PINNs do not obey this priority: their residual convergence order is governed by the NTK spectrum and is independent of the propagation path. Accordingly, we propose a unified multi-dimensional priority-constraint framework that partitions the domain along the propagation path and constructs negative-exponential residual weights, converting the physical propagation order into a training priority. For cases with coexisting priorities, we introduce a directional compatibility coefficient to clarify that "orthogonal directions can be coupled multiplicatively in synergy, whereas coaxial opposite directions cannot." Benchmark cases show that this method consistently improves the convergence behavior and prediction accuracy of PINNs on problems with clear propagation paths or constraint-dominated structures, without modifying the network architecture and with controllable additional computational cost.

Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity. These low-dimensional representations have improved the interpretability of population-level coding. Yet whether such low-dimensional representations are biologically relevant and confer functional advantages in learning systems, or merely reflect neuron-level activity, remains contested in neuroscience. We show that an explicit information bottleneck forcing a recurrent neural network to learn a low-dimensional representation is necessary for rotational and out-of-distribution generalisation in a time-series prediction task. Using information-theoretic measures of causal emergence, we characterise the dynamics of this representation across the memorisation-to-generalisation transition, finding a non-monotonic trajectory which shows an initial decrease, a minimum, and a subsequent rise to a maximum, even as prediction loss falls monotonically. This trajectory scales with task complexity, and the magnitude of emergent structure reliably predicts generalisation performance. Analysis of CA1 hippocampal activity in mice learning an alternating maze task reveals analogous non-monotonic emergence dynamics that track behavioural performance. Together, these findings indicate that the ability of neural networks to learn compact, distributed and emergent representations confers a functional advantage for generalisation, supporting a causal role for learned representations in cognition.

We show how an adversarial model trainer can plant backdoors in a large class of deep, feedforward neural networks. These backdoors are statistically undetectable in the white-box setting, meaning that the backdoored and honestly trained models are close in total variation distance, even given the full descriptions of the models (e.g., all of the weights). The backdoor provides access to invariance-based adversarial examples for every input, mapping distant inputs to unusually close outputs. However, without the backdoor, it is provably impossible (under standard cryptographic assumptions) to generate any such adversarial examples in polynomial time. Our theoretical and preliminary empirical findings demonstrate a fundamental power asymmetry between model trainers and model users.

Over the last few years, there has been an increased interest in making machine learning models more interpretable. Although a great deal of effort goes into developing techniques for interpreting the interactions learned by a given model, fewer studies focus on assessing the quality of such explanations. Even fewer focus on how to adjust the model to produce explanations faithful to prior knowledge, a process known as explanation-guided learning. Furthermore, most approaches in this area focus on classification problems and usually assume prior knowledge about which input features or regions are most important. In this work, we introduce a new approach to steering neural networks based on partial dependence, such that their average response to certain features aligns with specific functional domain knowledge about the problem. We empirically demonstrate on a range of regression problems, including dynamical systems forecasting, that models whose training has been controlled using our method perform better than unconstrained models and are more data-efficient. Moreover, we highlight that interpretations obtained from the former actually align with the user-provided knowledge, whereas those obtained from the latter do not.

A series of results from the NeuroAI over the past fifteen years have raised core questions both about how to compare Deep Neural Network (DNN) models to the brain, and about how much convergent evolution to expect between artificial networks and real brain networks. Here, we show that for any two minimal DNN solutions to a sufficiently hard task: (i) "weak" alignment of network representations based on affine mappings guarantees "strong" alignment of privileged axes, and (ii) alignment "zippers" up the network hierarchy, causing the emergence of privileged axes from end-to-end task optimization. These results formalize the notion of contravariance from Cao and Yamins [2024], and illustrate important consequences for the theory of NeuroAI: with sufficiently strong tasks, choice of metric for inter-network comparison is not all that sensitive, and that convergent evolution is probably inevitable.

Backpropagation (BP) dominates deep learning training, but its reliance on gradients brings inherent troubles -- vanishing and exploding gradients. The pursuit of gradient-free methods has long been a goal in the field of artificial intelligence. This paper shows that indeed the simplest Monte Carlo algorithm implemented on a single GPU -- randomly mutate a parameter, keep it if the loss decreases, otherwise retry -- can practically train deep networks. This gradient-free method does not even need common techniques such as batch normalization or residual connections to directly train sufficiently deep networks. More remarkably, its flexibility extends to several nontrivial scenarios: it enables pure pruning training, supports discrete weights, accommodates unconventional transfer functions such as Gaussian, and reveals the substantial redundancy of deep networks. We have demonstrated its feasibility on deep networks with more than 20 layers, single-hidden-layer wide networks with up to 16,384 hidden neurons, and even a simple Transformer architecture trained on both image classification (MNIST) and character-level language modeling (Tiny Shakespeare). This simple gradient-free method may offer a complementary perspective for understanding the self-organization and learning mechanisms of neural networks, and also provides an alternative route for building physically inspired deep learning systems.

We derive bounds for the volume of tubular neighbourhoods of smooth Pfaffian hypersurfaces, generalising known results for algebraic varieties. The bounds are given in terms of the Pfaffian format of the defining functions. As an application, we obtain tail bounds on the probability distribution of a condition number measuring the robustness of neural network classifiers with Pfaffian activation functions, in both the uniform and Gaussian settings. In the special case of single-hidden-layer sigmoid networks with rational weights, we derive polynomial-in-width bounds for tubular neighbourhoods of the decision boundary.

For seemless control of advanced hand prostheses and augmented reality, accurate and immediate hand gestures recognition is essential. Surface electromyography (sEMG) signals obtained from the forearm are commonly employed for this purpose. In this paper, we present a novel approach for sEMG representation that utilizes graph networks which contain information about muscle activation patterns in the forearm. Based on these graph networks, we have developed a machine learning algorithm capable of real-time hand gesture recognition using a graph neural network. The algorithm's performance was evaluated using sEMG signals acquired from myoband, which has 8 electrodes placed around the forearm, involving 8 healthy subjects. The proposed method demonstrated an average classification accuracy of 99%, surpassing the performance of state-of-the-art techniques. The average time for both graph construction and prediction stood at 48ms utilizing a M1 pro CPU, rendering the approach well-suited for real-time applications.

The Hessian of the training loss governs the local geometry of the loss landscape, yet despite existing explanations for its largest eigenvalues, the origin of the vast multitude of vanishingly small eigenvalues remains elusive. We argue that the bulk consists of the weakly lifted pseudo-Goldstone modes of the continuous symmetries of the network parametrization. In deep linear networks these symmetries are exact: they generate flat directions and hence exact zero modes, whose eigenvectors we construct explicitly. Introducing a ReLU nonlinearity as a perturbation, we show that it breaks these symmetries weakly and explicitly. Resolving the spectrum at the level of eigenvectors, we find that the high-curvature directions are orthogonal to the symmetry subspace, while the bulk lies almost entirely within it. We demonstrate the mechanism in a two-layer ReLU student--teacher model and in a network trained on CIFAR-10. A convolutional example demonstrates that the same diagnostic extends beyond fully connected layers. Together, these results link the Hessian bulk to weakly broken symmetries and clarify the origin of near-zero modes.

Bubeck, Li and Nagaraj conjectured that, for generic data, any two-layer neural network with $m$ neurons that fits $n$ noisy labels must have Lipschitz constant at least of order $\sqrt{n/m}$, with no restriction on the size of the weights. Bubeck and Sellke proved a universal version of this law for Lipschitz-parameterized classes, but under a polynomial bound on the parameters; at depth three that boundedness hypothesis is genuinely necessary. The two-layer unbounded-weight case requires a different argument. We prove the conjectured law, up to one logarithmic factor, for every continuous piecewise-linear activation, in particular for ReLU networks. For data drawn uniformly from $\mathbb{S}^{d-1}$, $d\ge3$, or from $N(0,I_d/d)$, labels in $[-1,1]$ with noise level $σ^2>0$, and any width-$m$ two-layer network with arbitrary real weights, biases and affine skip connection, fitting the data $\varepsilon$ below the noise floor forces $\mathrm{Lip}(f)\ge c\,\varepsilon\sqrt{n/(\bar m\log(C\bar m nd/\varepsilon))}$, $\bar m=(K-1)m+1$, with high probability. A realized-kink-count version holds on the same event: every realized two-layer piecewise-linear function with $k(f)\le n$ distinct kink hyperplanes obeys the bound with $\bar m$ replaced by $k(f)+1$, irrespective of how many redundant hidden units parameterize it. The proof replaces parameter-space covering, impossible for unbounded weights, by a function-space covering. The central deterministic ingredient is a rigidity lemma: on $B_2$, and on $\mathbb{S}^{d-1}$ for $d\ge3$, the coefficient of each canonical kink is controlled by the Lipschitz constant of the realized function, because kinks on distinct hyperplanes cannot cancel at generic points. Rigidity genuinely fails at $d=2$, and an explicit two-layer ReLU interpolant with $O(1)$ Lipschitz constant at width $2n$ matches the law at the overparameterized endpoint.

Navigation for social organisms rarely is a fully independent activity. Group structure and dynamics, as well as embodied interactions, critically influence useful behavior. Individual neural network controlled agents are trained to navigate in different social contexts, where social dependence and behavioral strategy learned is determined by relative task performance and spatial effect. Increasing high quality social information drives phase transitions from individual to following navigational strategy, and to collision avoidance in response to a crowded foraging patch. Predictable, nonstationary environmental dynamics drive behavioral hybridization between individual and social navigation, far and near the patch. Our findings challenge the approach of only inspecting individual behavior for social organisms and highlight the importance of taking a bottom-up approach in understanding how organisms behave.

Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data. Biologically-informed neural networks (BINNs) seek to address this challenge by embedding mechanistic differential equations into neural network training, enabling interpretable constitutive operators to be recovered directly from sparse and noisy observations. However, reliable operator recovery depends sensitively on network architecture, optimisation strategy, and data informativeness. Here, we present a systematic empirical study of how these factors influence mechanistic inference using BINNs applied to canonical one-dimensional advection-diffusion-reaction partial differential equation models. Across a suite of benchmark problems, we investigate how network expressivity, learning rate, loss weighting, and batch size influence optimisation behaviour and operator recovery. We show that successful mechanistic inference depends on balancing competing objectives rather than maximising any single aspect of the model or optimisation. Moderately expressive architectures outperform overly complex networks, intermediate learning rates improve optimisation stability, balanced data and PDE losses are essential for accurate operator recovery, and intermediate batch sizes provide the best compromise between computational efficiency and reproducibility. We further identify practical diagnostics for recognising common failure modes, including over-fitting, unstable optimisation, and poor mechanistic recovery when the ground truth is unavailable. Together, these findings provide evidence-based guidelines for deploying BINNs as credible tools for biological model discovery.

This article offers a comprehensive overview of mechanistic interpretability, an emerging field that seeks to reverse-engineer the internal algorithms of modern neural networks. While traditional explainable AI methods often stop at surface-level input-output correlations, this approach directly addresses the opaque "black box" nature of machine learning models, which is essential for ensuring safety and auditability in high-stakes deployments. The paper provides a detailed examination of Transformer circuit analysis, exploring how internal components like the residual stream, attention mechanisms, and induction heads drive complex tasks and in-context learning. It subsequently tackles the core challenge of superposition and polysemanticity, demonstrating how tools like Sparse Autoencoders (SAEs) and transcoders can decompose tangled network activations into distinct, human-interpretable features. Furthermore, the paper explores methods for actively controlling and modifying model behavior through steering vectors and causal interventions. Finally, it connects these mechanistic insights with neurosymbolic AI frameworks designed to translate neural representations into explicit, executable logical rules.

While accuracy, robustness, and calibration are all essential for reliable neural networks, they are often studied separately; developing models that satisfy all three simultaneously remains a central challenge. Lipschitz-constrained models guarantee robustness by design, yet the manual selection of the Lipschitz constraint L governs the resulting accuracy-robustness trade-off, and their calibration properties remain largely underexplored. In this work, we highlight a theoretical and empirical link between the enforced Lipschitz constraint and Temperature Scaling, a state-of-the-art calibration method. Specifically, we find that for a given training scheme, there exists a non-trivial value L* that yields an out-of-the-box calibrated network, and that calibration acts as a principled criterion to select a well-defined operating point on the accuracy-robustness Pareto front. Leveraging these insights, we introduce Lipschitz Scaling Training (LiST), a novel training paradigm that iteratively adjusts the global Lipschitz constant to reach this operating point. Through a margin parameter in the training loss, LiST further enables the construction of a fully calibrated Pareto front, allowing users to navigate the accuracy-robustness trade-off while remaining calibrated throughout. At convergence, LiST also enables the reintegration of calibration data into training, improving sample efficiency without sacrificing calibration. We validate LiST on CIFAR-10/100 and Tiny-ImageNet, demonstrating competitive accuracy and robustness against constrained and unconstrained baselines, while remaining calibrated out of the box. Code is available at GitHub.

Existing NAS benchmarks (e.g., NAS-Bench, NATS-Bench) cover only narrow, task-specific regions of the architectural design space and lack cross-domain or deployment-aware evaluation. LEMUR 2 introduces a large-scale, extensible framework unifying generative, evaluative, and deployment pipelines to unlock neural-network diversity. It comprises over 14,000 distinct architectures and more than 750,000 structured training records documenting model performance, hyperparameters, and task outcomes. These models were produced through AST-based code mutation, genetic and reinforcement-learning evolution, generation of fractal architectures, and synthesis guided by a Large Language Model (LLM). This includes deep models generated with the retrieval-augmented system NN-RAG, which derived and used architectural motifs from over 900 PyTorch modules extracted from public repositories. LEMUR 2 further employs NN-VR and NN-Lite pipelines for automated deployment and latency benchmarking on heterogeneous mobile and Unity-based VR platforms, providing real-device performance metadata. It spans multimodal tasks, image captioning, text-to-image synthesis, and language modeling, supporting cross-domain analysis of architectural transferability. By linking diverse architectures, tasks, and deployment data, LEMUR 2 provides the data foundation for LLM fine-tuning and coupling diverse architectural origins with large-scale, cross-platform empirical validation. This dataset defines a new basis for reproducible and data-driven AI design, advancing the emerging paradigm of LLM-driven AutoML and architectural generalization across modalities and hardware.

In this work, we investigate the fixed-architecture neural network approximation with explicit parameter bounds and elementary activations. While prior work demonstrated super-expressive approximation using fixed-size networks, they lack quantitative and non-asymptotic characterizations of parameter magnitude with respect to the approximation error. We resolve this issue by introducing the Chinese Remainder Theorem as a constructive encoding mechanism. For Lipschitz continuous functions on $[0,1]^D$, we construct a width-$\max\{D,4\}$, depth-$5$ network with explicit parameter-error trade-offs. For Hölder-smooth functions in $C^{r,γ}_A\left([0,1]^D\right)$, our fixed network of width $\max\{2D,\ D+5N+1\}$ and depth $r + 9$ achieves the parameter magnitude $\mathcal{P}$ bounded by $\log_2 \mathcal{P}=\mathcal{O}\bigl(\varepsilon^{-2D/(r+γ)}\log(1/\varepsilon)\bigr)$. This is the dual result compared to those in the parameter-bounded and architecture-unbounded paradigm.

Event-based cameras are gaining popularity as the sensor of choice for mobile robotics, due to their high performance in dynamic environments. However, these applications require efficient real-time data processing with low latency and power consumption. One strategy to meet these stringent requirements is hardware acceleration of efficient algorithms that preserve the temporal sparsity of event data. In this work, we propose an optimization strategy for Graph Convolutional Neural Networks models aimed at adapting their architecture to the limited resources of embedded heterogeneous FPGA platforms. Our method incorporates hardware-aware pruning and quantization, taking into account the trade-off between on-chip memory savings and inference accuracy. Strategic exploration of the design space with Fine Grid Search and Greedy layer-wise Iterative Deepening Search methods enables flexible adaptation of the model architecture to the target platform. Our approach was evaluated across various network configurations and multiple datasets, resulting in BRAM memory reductions of 28.8% for CIFAR-10 (with a 1.65% decrease in accuracy), 31.4% for MNIST-DVS (accuracy drop of 3.55%), and 26.5% for N-Caltech101 (with a 5.18% accuracy reduction).

Energy-efficient neuromorphic computing at the edge requires simulation tools that can capture the non-ideal behavior of mixed-signal spiking neural network (SNN) hardware while supporting system-level design exploration. This work presents an open-source hardware-aware simulation framework for mixed-signal SNNs that enables comparative analysis across neuron, synapse and architecture choices. The framework supports multiple neuron models, including Leaky Integrate-and-Fire (LIF), Hodgkin-Huxley (HH) and Axon-Hillock (AH), together with non-volatile analog synapses based on floating-gate transistors and ReRAM devices. By incorporating device-level nonlinearities directly into PyTorch-based training and inference, the tool enables optimization of physical synaptic parameters rather than idealized abstract weights. The framework is evaluated on standard neuromorphic benchmarks, including N-MNIST, DVS Gesture and Spiking Heidelberg Digits (SHD). For each model dataset configuration, it reports classification accuracy together with hardware-oriented metrics such as silicon area, power consumption and quantization sensitivity. These capabilities enable cross-layer design space exploration and help identify neuron-synapse configurations that best satisfy application-specific constraints on accuracy, energy efficiency, area and hardware fidelity.

Enhancing videos under extreme low-light conditions remains challenging due to the difficulty of balancing restoration quality and computational efficiency in resource-constrained settings. This paper introduces EeveeDark, a low-light video enhancement framework that combines the spatial richness of sensor-level RAW data with the temporal precision of event streams. Central to our model is a Binary Neural Network (BNN) architecture that reduces computational overhead by quantizing weights and activations while preserving detail. EeveeDark incorporates (i) modality-specific binary encoders for processing RAW frames and event data, (ii) a lightweight fusion block for integrating spatial and temporal cues, and (iii) an event-guided skip gating mechanism for dynamic spatiotemporal refinement. Experiments on synthetic and real-world datasets show that EeveeDark outperforms prior BNN-based methods and offers a favorable performance-efficiency trade-off compared to full-precision models. The project page is available at https://cyberiada.github.io/EeveeDark.

The AInstein architecture introduced an unsupervised neural method for solving the Riemannian Einstein equations on arbitrary manifolds. This Physics Informed Neural Network approach (PINN) is extended here to Lorentzian signature, validated by recovering the maximally extended Schwarzschild geometry, and tested as novel search method for arbitrary black hole solutions. The topology is built into the architecture by treating $S^{2}$ globally through its standard embedding, such that the network learns an ambient metric on the manifold $\mathbb{R}^{2} \times \mathbb{R}^{3}$, where Penrose coordinates are chosen for $\mathbb{R}^2$ and the metric on $S^{2}$ is obtained by pullback. The architecture is first trained with the objective of recovering the Schwarzschild metric via losses encoding the vacuum Einstein equation, a quadratic Weyl scalar constraint, and the $SO(3)$ symmetry of the resultant metric; directly motivated by the Birkhoff--Jebsen theorem. Following this, the objective is generalised to use the Petrov speciality index, a horizon curvature anchor, and a trapped-surface constraint, to allow search for algebraically general Petrov type I solutions, finding potentially novel general-type Lorentzian Einstein metrics with a genuinely trapped interior.

Integrating complex, multi-omics data presents significant challenges. Existing approaches often face a trade-off between model interpretability and representational capacity, with most either relying on post-hoc interpretation or use linear models that may overlook complex interactions. We report Pathway Activity Autoencoders for the multi-omics setting, which embed prior knowledge via pathway-informed architectural constraints, fostering interpretability, while preserving representational power. Our multi-omic framework is applied in the context of breast cancer and is evaluated in survival prediction and subtype classification with results indicating a positive effect of integration. We conduct analysis of individual omics layer impact on end-task performance, revealing that gene, protein, and microRNA expression layers provide the strongest contribution. Repeatability studies indicate that, while dropout improves model robustness and consistency, excessive regularisation can reduce predictive performance. Finally, visualizations of the learned feature space illustrate the framework's intrinsic transparency and clinical relevance. The results underscore the value of multi-omic integration and delineate the impact of individual omics layers, establishing practical guidelines for integration within our framework. Overall, our pathway activity autoencoder frameworks yield superior latent representations that are biologically meaningful and are directly translatable into clinically relevant insights.

Physics-informed neural networks (PINNs) often face ill-posed optimization, competing losses, and parameter compensation in partial differential equation (PDE) inverse problems. Transfer learning can reuse source-task representations, but direct fine-tuning may induce negative transfer when source and target physics differ, leading to low field error but inaccurate parameter recovery. To address this issue, we propose Target-Guided Selective Reweighting PINN (TGSR-PINN), a target-evidence-driven representation correction method for PINN inverse transfer learning. TGSR-PINN transfers source network weights and biases but initializes target physical parameters independently. After short target adaptation, it scores neurons using first-order Taylor sensitivity and pre-activation variance on fixed batches. These scores are converted into continuous weak-adaptation signals using a Gaussian mixture model with rank fallback. TGSR-PINN then applies bounded selective soft decay to the corresponding input weight rows and biases without pruning or resetting them. Experiments on a zero-source high-Péclet inflow--outflow problem with nonzero Dirichlet data and an outflow boundary layer, Allen--Cahn to Burgers cross-PDE transfer, and 5%-noise reaction--diffusion inverse problems show that TGSR-PINN improves parameter recovery while maintaining low field error. Ablation studies indicate that neuron target scoring, weak-adaptation estimation, layer protection, and selective soft decay jointly contribute to the observed benefits.

Neural network verification and data privacy are inherently in tension: verification demands full access to model parameters and input data, yet both are increasingly restricted by privacy regulations and intellectual property constraints. This tension has left robustness verification impractical in privacy-sensitive domains. In this work, we address this gap with SecureCROWN, the first framework for privacy-preserving neural network robustness verification. Built upon secure two-party computation (2PC), our framework enables a model owner and a data owner to jointly compute certified robustness bounds -- revealing only the final result while provably protecting both parties' private data under the semi-honest security model. A key challenge is securely computing the conditional operations in Linear Bound Propagation, where the data-dependent branching is incompatible with standard secure computation protocols. We eliminate branching by formulating conditional logic as continuous arithmetic operations. Additionally, we introduce a Newton--Raphson refinement method to improve numerical stability. Extensive analysis and experiments show that SecureCROWN strictly matches plaintext verification results, while completing in 0.1--200s across varied model sizes and communication settings (LAN/WAN), demonstrating the feasibility of privacy-preserving neural network verification.

Low-precision neural networks are attractive for resource-constrained hardware, but fixed-point arithmetic introduces failure modes that are often hidden by idealised quantisation models. In particular, two's-complement overflow wrapping can corrupt hidden activations by changing both their magnitude and sign, leading to unstable numerical error propagation and severe accuracy degradation. This paper proposes a Lyapunov-stabilised quantisation framework for low-precision neural networks operating under hardware-style wrapping arithmetic. The hidden-state energy is monitored through a layerwise Lyapunov function, and a monotone projection is applied to enforce bounded and non-increasing state evolution across depth. The method is evaluated on MNIST using a compact patch-based transformer under post-training quantisation and quantisation-aware training with fixed-point bit-widths from 4 to 16 bits. Monte Carlo results show that unconstrained wrapped quantisation-aware training collapses to near-chance accuracy across 6-16 bits, with activation overflow rates exceeding 11%. In contrast, the proposed monotone Lyapunov projection suppresses activation overflow to below 0.012% and restores stable low-precision learning, achieving 86.55% accuracy at 12 bits. These results demonstrate that Lyapunov-based state control can act as a hardware-aware stabilisation mechanism for reliable fixed-point neural inference and training.

Deep neural networks often contain substantial hidden-state redundancy, but most compression methods operate directly on weights, neurons, or quantised representations without explicitly characterising the dynamical role of internal states. This paper proposes a controllability-observability framework for empirical state-order reduction of deep neural networks. By viewing a trained network as a depth-indexed nonlinear dynamical system, we construct data-driven reachability, observability, and balanced Gramians from hidden-state snapshots and output Jacobians. The resulting A/B/C tests estimate layer-wise reachable, observable, and jointly reachable--observable ranks. These ranks are then used not only as diagnostic measures of hidden-state redundancy, but also as actual compressed layer widths for realised reduced networks. Experiments on MNIST and CIFAR-10 compare the proposed balanced realisation against projection-based reduction, unstructured pruning, structured pruning, low-rank SVD, dynamic INT8 quantisation, and linear baselines. On MNIST, a four-layer SiLU DNN is reduced from state order 1024 to 277, giving 72.95% state compression and 73.48% parameter compression, while maintaining 95.45% accuracy compared with 96.60% for the full model. On CIFAR-10, a larger SiLU DNN is reduced from state order 4608 to 1339, giving 70.94% state compression and 83.09% parameter compression, while preserving accuracy from 54.45% to 54.44% and reducing CUDA inference latency by approximately 3X. The results show that balanced reachable-observable ranks provide a principled empirical minimal-realisation criterion for designing compact neural architectures with little or no loss in accuracy.

We present CoFINN (Conservation Flux Informed Neural Networks), a physics-informed deep learning framework for predicting compressible flow fields governed by conservation laws. Unlike conventional data-driven convolutional neural networks (CNNs), which optimize only pixel-wise similarity metrics, CoFINN embeds finite-volume conservation physics directly into the training process. Unlike classical physics-informed methods which enforce differential-equation residuals at collocation points through automatic differentiation, CoFINN adopts a finite-volume perspective consistent with modern CFD methodology. CoFINN interprets CNN output fields as structured computational grids, where each pixel represents a finite-volume cell, and enforces conservation consistency through sophisticated numerical flux calculations. The framework is evaluated on transonic flow prediction around airfoils at (M=0.7, Re=6 * 10^6), including challenging conditions involving shock waves and high angles of attack. Results show that CoFINN improves aerodynamic force prediction accuracy, reducing drag prediction error by up to 34% at extreme angles of attack and by approximately 15% on average across the test set. Improvements are particularly significant in limited-data regimes, demonstrating that the conservation-based loss acts as an effective physical regularizer. The proposed approach maintains the computational efficiency advantages of CNN surrogates while significantly improving physical consistency and conservation behavior. The framework is architecture-agnostic and extensible to broader classes of conservation-law-governed physical systems.

A central goal of current Spiking Neural Network (SNN) research is to improve their accuracy toward becoming low-power alternatives to Artificial Neural Networks (ANNs). This work further argues that realizing this ambition requires improving not only accuracy but also robustness, defined as the ability to maintain correct predictions under input perturbations. We identify two key issues in existing SNN methods that undermine robustness. First, binary spiking activations can produce large activation-state changes under small perturbations. Second, the lack of effective weight constraints makes network outputs more sensitive to input variations. To this end, we propose Burst Spiking Neural Networks (BuSNNs), built upon Burst-enhanced Spiking Neurons (BSNs) and a Dynamic Weight Constraint (DWC) mechanism. BSNs incorporate burst firing to provide a graded spiking pattern. This spiking mechanism mitigates perturbation-induced transitions in activation states and thereby enhances robustness. DWC penalizes connection weights based on activation states, effectively reducing weight magnitudes and improving robustness while preserving accuracy. We provide theoretical analyses to support these robustness effects. Experimental results further show that, on smaller-scale benchmarks such as CIFAR-10, BuSNNs outperform both SNN and ANN counterparts in accuracy and robustness. On large-scale ImageNet, BuSNN with the MS ResNet-34 backbone further improves top-1 accuracy and corruption robustness over the corresponding SNN baseline by 3.18% and 2.66%, respectively. Despite using spike-based activations, BuSNNs surpass 4-bit activation-quantized ANN baselines and approach 8-bit ANN baselines on ImageNet. They also preserve SNNs' low-power advantage. This work studies the accuracy-robustness problem in SNNs, advancing their practical viability in robust and energy-efficient applications.

Convection-dominated convection-diffusion problems often develop thin layers, where the solution has sharp transition profiles and its derivatives are highly localized. This creates a structural mismatch for standard physics-informed neural networks (PINNs), whose trial spaces are not designed to match the value--derivative structure of such layers. We propose a Layer-Resolving XNet Physics-Informed Neural Network (LRX-PINN) based on integrated Cauchy activations. The proposed basis is transition-type at the solution level, while its derivative recovers a localized Cauchy kernel. We show that this structure matches the scaling of convection-dominated layers, inherits the Cauchy approximation mechanism at the derivative-profile level, and identifies $d/\|w\|$ as the effective physical width of a ridge neuron. For analytic layer profiles, this yields derivative-stable exponential approximation in the stretched coordinate and a layer-scaled estimate for the strong residual of the singularly perturbed operator. Numerical experiments on several convection-dominated benchmarks show that LRX-PINN achieves higher accuracy than PIKAN and Fourier-feature PINNs while using less than $30\%$ of their trainable parameters. On more challenging benchmarks, embedding the proposed representation into hp-VPINN-based frameworks further improves the best results obtained by existing hp-VPINN-based baselines without changing their original loss functionals or stabilization strategies. These results show that neural representations aligned with layer structure provide a compact and effective approach for convection-dominated problems.

Weight space learning aims to learn representations of neural network (NN) weights, enabling different downstream tasks. Existing approaches show promising performance, but lacking a way to shape these weight-space representations using information about the datasets the models were trained on, thus limiting downstream applications. We propose WeightCLIP, a method for learning a dataset-aligned latent space for neural networks, where datasets information is induced during training. The NNs are encoded as latent representations using an autoencoder, while dataset samples are encoded using a dataset encoder. The two representations are aligned using a contrastive objective, effectively reshaping the weight-space representations according to the datasets. We demonstrate that such representations can be used for different downstream tasks, including mapping dataset information to a weight-space representation that decode to strong models. In addition, we introduce a latent refinement process for generating models that outperforms standard fine-tuning. Overall, our results demonstrate that explicitly incorporating dataset information improves what can be achieved with weight-space representations across retrieval, generation, and refinement. Code will be available at https://github.com/HSG-AIML/WeightCLIP.

Deep reinforcement learning (DRL) offers powerful control for industrial cyber-physical systems (ICPSs), but its "black-box" exploration risks violating strict hardware safety limits. Typically, these constraints are managed through complex reward shaping. In this work-in-progress paper, we embed a differentiable physics model directly into the proximal policy optimization (PPO) actor loss function. By simulating short-horizon future trajectories during training, the policy is penalized for anticipated safety violations independent of the task-reward signal. Evaluated on a simulated 1-degree-of-freedom helicopter testbed with strict pitch constraints, our physics-informed soft regularizations substantially reduce constraint violations while maintaining reliable target tracking.