Specialized Lab · Dedicated ViewTopology & Network Architectures

Neural Network Architecture Zoo

Complete taxonomy: Perceptrons, CNNs, RNNs, Transformers, Autoencoders, and Diffusion

Interactive catalog featuring tensor flow diagrams of the primary neural topologies throughout AI history, from multilayer perceptrons and ResNets to diffusion models and Graph Neural Networks.

Fundamental Law
$$y = \sigma(W x + b)$$
Architectural Taxonomy

Conceptual Map: The Neural Network Zoo

From hyperplanes in classical perceptrons to score diffusion models and continuous operators in SciML. An analytical taxonomy grounded in spatial transformations, symmetry preservation, and information flows.

FUNDAMENTAL

Perceptrón Multicapa (MLP)

$$y = \sigma \left( \sum_{i=1}^n W_i x_i + b \right)$$

Nonlinear affine composition. Bedrock of the Universal Approximation Theorem (Cybenko, 1989; Hornik, 1991): any continuous function over compact subsets of $\mathbb{R}^n$ can be arbitrarily approximated by a single hidden layer.

Invariance:None
Canonical use:Tabular data, dense regression
VISION

Redes Convolucionales (CNN)

$$(f * g)(t) = \sum_{\tau} f(\tau) g(t - \tau)$$

Leverages spatial locality and translation equivariance via shared receptive field kernels (LeCun, 1989). Drastically reduces free parameters in high-dimensional tensors (2D/3D images).

Invariance:Spatial translation
Canonical use:Object detection, segmentation, ResNet
SEQUENCE

Celdas LSTM & GRU

$$C_t = f_t \odot C_{t-1} + i_t \odot \tilde{C}_t$$

Resolves the vanishing gradient dilemma through multiplicative gating mechanisms ($f_t, i_t, o_t$) and an additive linear memory highway $C_t$ (Hochreiter & Schmidhuber, 1997).

Invariance:Temporal causality
Canonical use:Time series, audio signals, classic NLP
GENERATIVE

Autoencoders Variacionales (VAE)

$$\mathcal{L}_{\text{ELBO}} = \mathbb{E}[\log p(x|z)] - D_{\text{KL}}(q(z|x) \parallel p(z))$$

Learns a smooth continuous latent manifold by mapping inputs to Gaussian distributions $\mathcal{N}(\mu, \Sigma)$. Employs the reparameterization trick ($z = \mu + \sigma \odot \epsilon$) for stochastic backprop.

Invariance:Regularization via $D_{\text{KL}}$
Canonical use:Data compression, generation, latent embeddings
GENERATIVE

Redes Generativas Adversarias (GAN)

$$\min_G \max_D \mathbb{E}_x[\log D(x)] + \mathbb{E}_z[\log(1 - D(G(z)))]$$

Zero-sum minimax game between two competing networks: a Generator synthesizing candidates from latent noise and a Discriminator estimating real-vs-fake probability (Goodfellow et al., 2014).

Invariance:Jensen-Shannon Divergence
Canonical use:Photorealistic image synthesis, StyleGAN
ATTENTION

Transformers & Multi-Head Attention

$$\text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V$$

Replaces sequential recurrence with parallel pairwise scaled dot-product attention across all tokens simultaneously (Vaswani et al., 2017). The foundation of LLMs and Vision Transformers (ViT).

Invariance:Permutation (with Positional Encoding)
Canonical use:LLMs (GPT, Claude, Llama), ViTs
SCIML

Redes Informadas por la Física (PINNs)

$$\mathcal{L}_{\text{pinn}} = \mathcal{L}_{\text{data}} + \lambda_{\text{edp}} \|\mathcal{N}[u_\theta]\|_2^2 + \lambda_{\text{bc}} \mathcal{L}_{\text{bc}}$$

Embeds partial differential operators (PDEs) directly into the loss objective via continuous automatic differentiation (Raissi et al., 2019). Operates completely mesh-free.

Invariance:Physical conservation laws
Canonical use:Fluid dynamics, thermal heat transport
GENERATIVE

Modelos de Difusión (DDPM)

$$q(x_t | x_{t-1}) = \mathcal{N}\left(x_t; \sqrt{1 - \beta_t} x_{t-1}, \beta_t \mathbf{I}\right)$$

Inspired by non-equilibrium statistical thermodynamics (Sohl-Dickstein, 2015; Ho et al., 2020). Gradually add Gaussian noise to signals and train a neural network to invert the diffusion trajectory step-by-step.

Invariance:Stochastic Score Matching
Canonical use:Stable Diffusion, Midjourney, DALL-E