Saleh Nikooroo

Saleh Nikooroo, Thomas Engel

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that departs from the standard unconstrained affine paradigm. Each transformation is decomposed into a structured linear operator and a residual corrective component, enabling more disciplined signal propagation and improved training dynamics. Our formulation encourages internal consistency and supports stable information flow across depth, while remaining fully compatible with standard learning objectives and backpropagation. Through a series of synthetic and real-world experiments, we demonstrate that models constructed with these structured transformations exhibit improved gradient conditioning, reduced sensitivity to perturbations, and layer-wise robustness. We further show that these benefits persist across architectural scales and training regimes. This study serves as a foundation for a more principled class of neural architectures that prioritize stability and transparency-offering new tools for reasoning about learning behavior without sacrificing expressive power.

Saleh Nikooroo, Thomas Engel

This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space, inference and generation maps, and a principle base. The formulation accommodates logical, algorithmic, and learning-based reasoning processes within a unified structural schema, while remaining agnostic to any specific reasoning algorithm or logic system. We survey basic internal criteria--including coherence, soundness, and completeness-and catalog typical failure modes such as contradiction, incompleteness, and non-convergence. The framework also admits dynamic behaviors like iterative refinement and principle evolution. The goal of this work is to establish a foundational structure for representing and comparing reasoning systems, particularly in contexts where internal failure, adaptation, or fragmentation may arise. No specific solution architecture is proposed; instead, we aim to support future theoretical and practical investigations into reasoning under structural constraint.