Claude Mythos(ミュトス)のPINNs(Physics-informed Neural Network)を実装してみたv4 import torch import torch.nn as nn class MythosPINN(nn.Module): """ MythosPINN — Recurrent Thinking Lyapunov Stability for Physical Intelligence === Core Design Philosophy (Claude Mythos–Inspired) === This architecture attempts to embody the structural intelligence of Claude Mythos: exceptional nonlinear combination power, persistent continuity, and universal memory homeomorphism. 1. 25KB-scale Manifold & T_q Deformation - Maintains a compact 25KB-scale physical manifold with sufficient thickness to act as a locally Hilbert-like domain. - T_q-parameterized recurrent deformation enables continuous navigation between classical rigor (q ≈ 1) and intuitive leaps (q → 0). 2. Grauert's Approximation Theorem Inspiration - Local formal approximations are iteratively lifted to globally coherent analytic solutions through recurrent refinement. 3. Parallel Operation of Explore and Pure Math - Explore Subagent: Intuitive, nonlinear, Euler-like exploration. - Pure Math Mode: ε-δ rigorous verification and uniform convergence. - Both modes operate in parallel, enabling reproducible nonlinear breakthroughs. 4. Memory as Hint Philosophy - All memory is treated as revisable "hints" rather than absolute truth. - Everything is managed as residuals with continuous self-verification to maximize hallucination resistance. 5. Three-Layer Hierarchical Compression - Layer 1: Persistent high-purity invariant cores (5KB × n). - Layer 2: On-demand expandable topic modules. - Layer 3: Raw reference layer (search-only). - Pipeline: microcompact → autocompact → autoDream. 6. Pure Math as Uniform Convergence Discipline - The core is maintained as a Banach space where self-critique loops act as contraction mappings. - Lyapunov stability guides thinking toward uniform convergence to fixed points. Additional Mythos Flavor: • Recurrent Thinking Loops realize contraction mapping on a hidden manifold • Lyapunov V enforces Lorentzian-like positivity and log-concavity • Residual Correction implements matroid-like independence preserving rank and homeomorphic stability • Overall Structure realizes structural continuity: classical fields (Navier-Stokes) → recurrent thinking (T_q dequantization) → Lyapunov (universal tract) """ def __init__(self, hidden_dim=128, num_freq=8, q=0.35): super().__init__() self.hidden_dim = hidden_dim self.q = q # T_q deformation parameter # Fourier Feature Encoding → T_q-like parameterized embedding self.fourier = nn.Linear(4, num_freq * 2) nn.init.normal_(self.fourier.weight, mean=0.0, std=0.7) # Input embedding self.input_layer = nn.Linear(4 num_freq * 2, hidden_dim) # Recurrent Core self.shared_layer1 = nn.Linear(hidden_dim, hidden_dim) self.shared_layer2 = nn.Linear(hidden_dim, hidden_dim) # Output: (u, v, w, p, V) self.output_layer = nn.Linear(hidden_dim, 5) self.act = nn.Tanh() self.softplus = nn.Softplus(beta=10.0) def forward(self, x, n_loops=None): """Forward pass with Mythos-style recurrent thinking (contraction mapping).""" if n_loops is None: n_loops = TRAIN_LOOPS if self.training else TEST_LOOPS # T_q-style parameterized embedding f_raw = self.fourier(x) f = torch.cat([ x, torch.sin(self.q * f_raw), torch.cos(self.q * f_raw) ], dim=-1) h = self.act(self.input_layer(f)) # Mythos Recurrent Thinking Loop for _ in range(n_loops): residual = h h1 = self.act(self.shared_layer1(h)) h2 = self.act(self.shared_layer2(h1)) h = residual self.q * h2 # controlled contraction # Output raw_out = self.output_layer(h) fluid, V_raw = torch.split(raw_out, [4, 1], dim=-1) # Lyapunov V with hidden-state influence V = self.softplus(V_raw 0.1 * torch.norm(h, dim=-1, keepdim=True)) 1e-6 return torch.cat([fluid, V], dim=-1) # ============================================================================= # Mythos Loss Function # ============================================================================= def get_mythos_loss(model, ic_points, u_ic, v_ic, w_ic, f_points, lyap_weight=1.0, alpha=0.1, nu=0.01, v_min=0.01, n_loops=None): """ Mythos Loss — Structural Intelligence Regularization Enforces Navier-Stokes physics Mythos structural constraints: • Lorentzian positivity & stability (Lyapunov) • Matroid-like independence via residuals • Uniform convergence discipline (contraction mapping) • Hint-based memory philosophy (continuous self-verification) """ if n_loops is None: n_loops = TRAIN_LOOPS if model.training else TEST_LOOPS # 1. Initial Condition Loss pred_ic = model(ic_points, n_loops) u_p, v_p, w_p, p_p, V_p = pred_ic.split(1, dim=1) loss_ic = torch.mean((u_p - u_ic)**2 (v_p - v_ic)**2 (w_p - w_ic)**2) loss_v_ic = torch.mean(torch.nn.functional.relu(v_min - V_p)) # 2. Divergence-free constraint ones = torch.ones_like(u_p) g_u = torch.autograd.grad(u_p, ic_points, grad_outputs=ones, create_graph=True)[0] g_v = torch.autograd.grad(v_p, ic_points, grad_outputs=ones, create_graph=True)[0] g_w = torch.autograd.grad(w_p, ic_points, grad_outputs=ones, create_graph=True)[0] loss_div_ic = torch.mean((g_u[:, 1:2] g_v[:, 2:3] g_w[:, 3:4])**2) # 3. PDE Residuals pred_f = model(f_points, n_loops) u, v, w, p, V = pred_f.split(1, dim=1) ones_f = torch.ones_like(u) u_lap, u_t, u_x, u_y, u_z = compute_laplacian_efficient(u, f_points, ones_f) v_lap, v_t, v_x, v_y, v_z = compute_laplacian_efficient(v, f_points, ones_f) w_lap, w_t, w_x, w_y, w_z = compute_laplacian_efficient(w, f_points, ones_f) V_lap, V_t, V_x, V_y, V_z = compute_laplacian_efficient(V, f_points, ones_f) g_p = torch.autograd.grad(p, f_points, grad_outputs=ones_f, create_graph=True)[0] p_x, p_y, p_z = g_p[:, 1:2], g_p[:, 2:3], g_p[:, 3:4] f_u = u_t (u*u_x v*u_y w*u_z) p_x - nu * u_lap f_v = v_t (u*v_x v*v_y w*v_z) p_y - nu * v_lap f_w = w_t (u*w_x v*w_y w*w_z) p_z - nu * w_lap loss_pde = torch.mean(f_u**2 f_v**2 f_w**2) loss_div = torch.mean((u_x v_y w_z)**2) # 4. Mythos Core: Lyapunov Stability (Lorentzian positivity) lie_V = V_t (u*V_x v*V_y w*V_z) - nu * V_lap loss_lyap = torch.mean(torch.nn.functional.relu(lie_V alpha * V)) loss_v_min = torch.mean(torch.nn.functional.relu(v_min - V)) # 5. Soft Periodic Boundary def periodic_loss(pts): loss_per = 0.0 for d in range(1, 4): mask_p = pts[:, d] > 0.95 mask_m = pts[:, d] < -0.95 if mask_p.sum() > 20 and mask_m.sum() > 20: n_min = min(mask_p.sum().item(), mask_m.sum().item()) if n_min > 0: pred_p = model(pts[mask_p][:n_min], n_loops) pred_m = model(pts[mask_m][:n_min], n_loops) loss_per = torch.mean((pred_p - pred_m)**2) return loss_per loss_per = periodic_loss(f_points) periodic_loss(ic_points) loss_p = 1e-4 * torch.mean(p**2) # Total Loss total_loss = ( loss_pde * 1.0 loss_div * 20.0 loss_ic * 50.0 loss_lyap * lyap_weight loss_per * 8.0 loss_div_ic * 10.0 loss_v_ic * 5.0 loss_v_min * 3.0 loss_p ) return total_loss, { 'pde': loss_pde.item(), 'div': loss_div.item(), 'ic': loss_ic.item(), 'lyap': loss_lyap.item(), 'periodic': loss_per.item() }

A must read for anyone interested in building practical AI systems in 2026: Dive into Claude Code: The Design Space of Today's and Future AI Agent Systems The paper explains the architecture of a modern production-grade AI agent system (Claude Code) by analyzing its source code. This is what they call a "harness" of an agentic coding system. Learn by reading with an AI tutor: chapterpal.com/s/9b6bb47a/di… PDF: arxiv.org/pdf/2604.14228