By Dewan Mukto Browse All
Licensed under CC BY 4.0 （Unless specified otherwise)
During my current research on various state-of-the-art AI algorithms for a thesis on artificial general intelligence (AGI), here are the most suitable algorithms I found:
| Algorithm Name | Algorithm Type(s) | Mathematical Expression (LaTeX) | ||
|---|---|---|---|---|
| Transformer | Deep Learning, Sequence Modeling | $( \text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V )$ | ||
| Mixture-of-Experts (MoE) | Deep Learning, Scalable Architecture | $( y = \sum_{i=1}^N G(x)_i \cdot E_i(x) )$, where $( G(x) )$ is the gating function, $( E_i(x) )$ is the $( i )$-th expert | ||
| MuZero | Reinforcement Learning, Planning | $( \pi(s, a) = \text{MCTS}(s, \theta), \text{loss} = \sum_t (r_t - \hat{r}_t)^2 + (v_t - \hat{v}_t)^2 + \text{KL}(\pi_t, \hat{\pi}_t) )$ | ||
| Model-Agnostic Meta-Learning (MAML) | Meta-Learning | $( \theta’ = \arg\min_\theta \sum_{\mathcal{T}i} \mathcal{L}{\mathcal{T}i}\left(f{\theta - \alpha \nabla_\theta \mathcal{L}{\mathcal{T}_i}(f\theta)}\right) )$ | ||
| Denoising Diffusion Probabilistic Model (DDPM) | Generative Modeling | $( p_\theta(x_0) = \int p_\theta(x_{0:T}) dx_{1:T}, \text{loss} = \mathbb{E}[|\epsilon - \epsilon_\theta(x_t, t)|^2] )$ | ||
| Topological Swarm Optimizer (TSO) | Optimization, Swarm Intelligence | $( x_{t+1}^i = x_t^i + v_t^i, v_t^i = v_t^i + \alpha (\text{centroid}_N - x_t^i) + \beta (g - x_t^i) )$ (approximate) | ||
| Proximal Policy Optimization (PPO) | Reinforcement Learning | $( \theta_{t+1} = \arg\max_\theta \mathbb{E} \left[ \min \left( r_t(\theta) \hat{A}_t, \text{clip}(r_t(\theta), 1-\epsilon, 1+\epsilon) \hat{A}_t \right) \right] )$, where $( r_t(\theta) )$ is the policy ratio, $( \hat{A}_t )$ is the advantage | ||
| Multi-Agent Deep Deterministic Policy Gradient (MADDPG) | Reinforcement Learning, Multi-Agent | $( \nabla_{\theta_i} J(\theta_i) = \mathbb{E} \left[ \nabla_{\theta_i} Q_i(s, a_1, \dots, a_N) \nabla_{\theta_i} \pi_i(s) \right] )$, for agent $( i )$ | ||
| Dynamic Team Formation (DTF) | Multi-Agent Systems, Optimization | No standard expression; approximates $( \text{Team}t = \arg\max_T \sum{i \in T} u_i(s, T) )$, where $( u_i )$ is utility for agent $( i )$ | ||
| Few-Shot Learning (FSL) | Meta-Learning, Supervised Learning | Varies; often uses MAML-like loss: $( \theta’ = \theta - \alpha \nabla_\theta \mathcal{L}{\text{support}}(f\theta) )$ | ||
| Reptile | Meta-Learning | $( \theta \leftarrow \theta + \beta (\tilde{\theta} - \theta) )$, where $( \tilde{\theta} )$ is the updated parameter after task-specific gradient steps | ||
| Reinforcement Learning (RL) | Reinforcement Learning | $( Q(s, a) \leftarrow Q(s, a) + \alpha [r + \gamma \max_{a’} Q(s’, a’) - Q(s, a)] )$ (Q-Learning as representative) | ||
| Bayesian Opinion/Preference Aggregation | Probabilistic Modeling | $( P(\theta | D) \propto P(D | \theta) P(\theta) )$, aggregates preferences via Bayesian inference |
| Federated Learning (FL) with Consensus Mechanisms | Distributed Learning | $( w_{t+1} = \sum_{k=1}^K \frac{n_k}{n} w_k^t )$, where $( w_k^t )$ is client $( k )$’s model, $( n_k )$ is data size (FedAvg as representative) | ||
| Graph-based Decision Aggregation (GDA) | Graph-Based Learning | No standard expression; approximates $( d_v = \sum_{u \in N(v)} w_{uv} \cdot d_u )$, where $( d_v )$ is decision at node $( v )$, $( N(v) )$ is neighbors | ||
| Hedge Algorithm | Online Learning | $( w_{t+1}(i) = w_t(i) \cdot \beta^{l_t(i)} / Z_t )$, where $( l_t(i) )$ is loss for expert $( i )$, $( Z_t )$ is normalization | ||
| Exponentiated Gradient | Online Learning | $( w_{t+1}(i) \propto w_t(i) \exp(-\eta l_t(i)) )$, where $( \eta )$ is learning rate | ||
| Adaptive Gradient Descent (AdaGrad) | Optimization | $( \theta_{t+1} = \theta_t - \frac{\eta}{\sqrt{G_t + \epsilon}} \nabla_\theta \mathcal{L} )$, where $( G_t = \sum_{\tau=1}^t g_\tau^2 )$, $( g_\tau = \nabla_\theta \mathcal{L} )$ | ||
| Adaptive Gradient Descent (Adam) | Optimization | $( \theta_{t+1} = \theta_t - \eta \frac{\hat{m}_t}{\sqrt{\hat{v}_t} + \epsilon} )$, where $( \hat{m}_t, \hat{v}_t )$ are bias-corrected moment estimates | ||
| Adaptive Gradient Descent (Adafactor) | Optimization | $( \theta_{t+1} = \theta_t - \eta \frac{m_t}{\sqrt{v_t} + \epsilon} )$, with low-rank approximation of $( v_t )$ | ||
| Online Mirror Descent | Optimization | $( \theta_{t+1} = \arg\min_\theta { \eta \langle \nabla \mathcal{L}_t, \theta \rangle + D(\theta, \theta_t) } )$, where $( D )$ is Bregman divergence | ||
| Elastic Weight Consolidation (EWC) | Continual Learning | $( \mathcal{L} = \mathcal{L}_{\text{new}} + \lambda \sum_i F_i (\theta_i - \theta_i^)^2 )$, where $( F_i )$ is Fisher information, $( \theta_i^ )$ is old task parameters | ||
| Gradient Episodic Memory (GEM) | Continual Learning | $( \min_\theta \mathcal{L}{\text{new}}, \text{s.t.} \langle \nabla \mathcal{L}{\text{old}}, \theta - \theta_{\text{old}} \rangle \geq 0 )$ | ||
| Tree of Thought (ToT) | Reasoning, Search | No standard expression; approximates $( \text{Score}(n) = \sum_{p \in \text{paths}} w_p \cdot v_p )$, where $( v_p )$ is value of reasoning path | ||
| Hierarchical Reinforcement Learning (HRL) | Reinforcement Learning | Varies; e.g., $( Q(s, o) = \max_{o’} [r(s, o) + \gamma V(s’, o’)] )$, where $( o )$ is high-level option |