Inductive biases encoding known data symmetries are key to make deep learning models generalize in high-dimensional settings such as computer vision, speech processing and computational neuroscience, just to name a few.

A.1 Mixedoperation For spiking neurons, we can either mix the operation at the spike activation or at the input of the membranepotential. For mixed operation at the input of membrane potential, as Eq. 4 shows, the gradient ofαk applies a unified SGfunctiong(u)fordifferent candidate operations which limits theexploration ofdiverse SGfunctions. However,sinceIk directly depends ontheweight, whenappliedforDGSmethod it strictly reflects different changes oftheoriginal weight, thus giving more accurate learning signals forαk. Meanwhile it's also a spike emitter to transmit floating numbers to spikes. Then we employ cell structure as our basic unit to construct our whole searching structure.

The Differentiable ARchiTecture Search (DARTS) has dominated the neural architecture search community due to its search efficiency and simplicity. DARTS leverages continuous relaxation to convert the intractable operation selection problem into a continuous magnitude optimization problem which can be easily handled with gradient-descent, while it poses an additional challenge in measuring the operation importance or selecting an architecture from the optimized magnitudes. The vanilla DARTS assumes the optimized magnitudes reflect the importance of operations, while more recent works find this naive assumption leads to poor generalization and is without any theoretical guarantees. In this work, we leverage influence functions, the functional derivatives of the loss function, to theoretically reveal the operation selection part in DARTS and estimate the candidate operation importance by approximating its influence on the supernet with Taylor expansions. We show the operation strength is not only related to the magnitude but also second-order information, leading to a fundamentally new criterion for operation selection in DARTS, named Influential Magnitude. Empirical studies across different tasks on several spaces show that vanilla DARTS and its variants can avoid most failures by leveraging the proposed theory-driven operation selection criterion.

This work introduces MorphNAS, a novel differentiable neural architecture search framework designed to address these challenges. MorphNAS enhances Differentiable Architecture Search (DARTS) by incorporating linguistic meta-features--such as script type and morphological complexity--to optimize neural architectures for Named Entity Recognition (NER). It automatically identifies optimal micro-architectural elements tailored to language-specific morphology. By automating this search, MorphNAS aims to maximize the proficiency of multilingual NLP models, leading to improved comprehension and processing of these complex languages.

--We introduce RegimeNAS, a novel differentiable architecture search framework specifically designed to enhance cryptocurrency trading performance by explicitly integrating market regime awareness. Addressing the limitations of static deep learning models in highly dynamic financial environments, RegimeNAS features three core innovations: (1) a theoretically grounded Bayesian search space optimizing architectures with provable convergence properties; (2) specialized, dynamically activated neural modules (V olatility, Trend, and Range blocks) tailored for distinct market conditions; and (3) a multi-objective loss function incorporating market-specific penalties (e.g., volatility matching, transition smoothness) alongside mathematically enforced Lipschitz stability constraints. Regime identification leverages multi-head attention across multiple timeframes for improved accuracy and uncertainty estimation. Rigorous empirical evaluation on extensive real-world cryptocurrency data demonstrates that RegimeNAS significantly outperforms state-of-the-art benchmarks, achieving an 80.3% Mean Absolute Error reduction compared to the best traditional recurrent baseline and converging substantially faster (9 vs. 50+ epochs). Ablation studies and regime-specific analysis confirm the critical contribution of each component, particularly the regime-aware adaptation mechanism. This work underscores the imperative of embedding domain-specific knowledge, such as market regimes, directly within the NAS process to develop robust and adaptive models for challenging financial applications.