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.
Score-based diffusion models have achieved remarkable empirical success in generative modeling, yet their approximation-theoretic foundations remain incomplete. In particular, although classical universal approximation theorems guarantee that neural networks can approximate score…
In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions. Indeed, whi…
We investigate whether symbolic regression can discover explicit neural network weight-update rules that outperform standard hand-designed optimizers on small symbolic regression benchmarks. Candidate update rules are represented as fixed-depth symbolic expressions over operands…
In this work, we explore how the inference time of a Transformer Neural Network can be efficiently optimized with applications to real-time anomaly detection in financial time series. The financial time series are price series such as asset prices. Unfortunately, the data is ofte…
Branch and Bound (BaB) aims to achieve complete verification of neural networks by adaptively partitioning the problem and applying off-the-shelf verifiers to subproblems. Its problem-splitting history can be represented as a tree, where each subproblem corresponds to a child nod…
Chemists and materials scientists increasingly use machine learning models, such as graph neural networks (GNNs), to predict properties of molecules and the outcomes of their reactions. Beyond predictive performance, understanding how these models organize chemical information in…