Moonshot AI Transformer Foundation Rebuild Deep Dive: MoonShadow Optimizer, KDA Linear Attention, and Attention Residuals Reshape LLM Training

import torch
import torch.nn as nn
from typing import Optional, Tuple

class MoonShadow(torch.optim.Optimizer):
    """
    MoonShadow Optimizer - Moonshot AI's replacement for AdamW.
    
    Key features:
    - Newton-Schulz orthogonalization of gradients
    - Adaptive rank estimation via SVD
    - Communication folding for distributed training
    """
    
    def __init__(
        self,
        params,
        lr: float = 1e-4,
        beta: float = 0.9,
        eps: float = 1e-8,
        max_rank_ratio: float = 0.1,
        ns_iterations: int = 6,
    ):
        defaults = dict(
            lr=lr, beta=beta, eps=eps,
            max_rank_ratio=max_rank_ratio,
            ns_iterations=ns_iterations,
        )
        super().__init__(params, defaults)
    
    @torch.no_grad()
    def _newton_schulz(self, G: torch.Tensor, iterations: int) -> torch.Tensor:
        """
        Newton-Schulz iteration for matrix square root inverse.
        Approximates (G·G^T)^(-1/2) without eigendecomposition.
        """
        scale = G.norm().item()
        X = G / scale
        
        for _ in range(iterations):
            X2 = X @ X
            X = X @ (3 * torch.eye(X.shape[0], device=X.device) - X2) / 2
        
        return X * scale
    
    @torch.no_grad()
    def _adaptive_rank(self, S: torch.Tensor) -> int:
        """
        Adaptive rank estimation from singular values.
        Uses energy-based threshold to determine optimal rank.
        """
        total_energy = (S ** 2).sum()
        cumulative = 0
        for i, s in enumerate(S):
            cumulative += s ** 2
            if cumulative / total_energy > 0.95:
                return max(1, i + 1)
        return len(S)
    
    @torch.no_grad()
    def step(self, closure=None):
        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()
        
        for group in self.param_groups:
            lr = group['lr']
            beta = group['beta']
            eps = group['eps']
            max_rank = group['max_rank_ratio']
            ns_iter = group['ns_iterations']
            
            for p in group['params']:
                if p.grad is None:
                    continue
                
                g = p.grad.data
                if g.ndim < 2:
                    p.data.add_(g, alpha=-lr)
                    continue
                
                orig_shape = g.shape
                if g.ndim > 2:
                    g = g.view(g.shape[0], -1)
                
                n_ortho = self._newton_schulz(g, ns_iter)
                
                state = self.state[p]
                if 'momentum' not in state:
                    state['momentum'] = torch.zeros_like(g)
                
                state['momentum'].mul_(beta).add_(n_ortho, alpha=1 - beta)
                m = state['momentum']
                
                try:
                    U, S, Vh = torch.linalg.svd(m, full_matrices=False)
                    r = min(
                        self._adaptive_rank(S),
                        int(max_rank * min(m.shape[0], m.shape[1]))
                    )
                    m_lowrank = U[:, :r] @ torch.diag(S[:r]) @ Vh[:r, :]
                except torch.linalg.LinAlgError:
                    m_lowrank = m
                
                update = m_lowrank
                if orig_shape != g.shape:
                    update = update.view(orig_shape)
                
                p.data.add_(update, alpha=-lr)
        
        return loss

package optimizer

import (
	"math"
	"sync"
)

// MoonShadowShard represents a distributed shard of MoonShadow state
type MoonShadowShard struct {
	Rank    int
	U       []float32
	S       []float32
	V       []float32
	Step    int
	Mu      float64
	MaxRank int
}

// CompressState compresses optimizer state into low-rank factors
// Original: m*n float32 -> compressed: r*(m+n) float32
// Ratio: r*(m+n)/(m*n) ≈ r/min(m,n)
func (mss *MoonShadowShard) CompressState(
	gradient [][]float32,
	energyThreshold float64,
) error {
	m := len(gradient)
	n := len(gradient[0])
	
	U, S, V := SVD(gradient, m, n)
	
	totalEnergy := 0.0
	for _, s := range S {
		totalEnergy += float64(s) * float64(s)
	}
	
	cumulative := 0.0
	rank := 0
	for i, s := range S {
		cumulative += float64(s) * float64(s)
		rank = i + 1
		if cumulative/totalEnergy >= energyThreshold {
			break
		}
	}
	
	maxRank := int(math.Min(float64(mss.MaxRank), math.Min(float64(m), float64(n))))
	if rank > maxRank {
		rank = maxRank
	}
	
	mss.U = make([]float32, m*rank)
	mss.S = make([]float32, rank)
	mss.V = make([]float32, n*rank)
	mss.Rank = rank
	
	for i := 0; i < m; i++ {
		for j := 0; j < rank; j++ {
			mss.U[i*rank+j] = U[i][j]
		}
	}
	copy(mss.S, S[:rank])
	for i := 0; i < n; i++ {
		for j := 0; j < rank; j++ {
			mss.V[i*rank+j] = V[i][j]
		}
	}
	
	return nil
}

package attention

import (
	"math"
)

// KDA represents Kimi Delta Attention
type KDA struct {
	HiddenDim    int
	NumHeads     int
	HeadDim      int
	DecayLB      float64
	State        [][][]float32
	UseUnifiedKernel bool
}

func NewKDA(hiddenDim, numHeads int, decayLB float64) *KDA {
	headDim := hiddenDim / numHeads
	return &KDA{
		HiddenDim:   hiddenDim,
		NumHeads:    numHeads,
		HeadDim:     headDim,
		DecayLB:     decayLB,
		State:       make([][][]float32, numHeads),
		UseUnifiedKernel: decayLB > 0,
	}
}

func (k *KDA) FeatureMap(x []float32) []float32 {
	result := make([]float32, len(x))
	for i, val := range x {
		if val >= 0 {
			result[i] = val + 1.0
		} else {
			result[i] = float32(math.Exp(float64(val)))
		}
		if result[i] < float32(k.DecayLB) {
			result[i] = float32(k.DecayLB)
		}
	}
	return result
}

func (k *KDA) Forward(q, kVec, v []float32, headIdx int) []float32 {
	headDim := k.HeadDim
	qPhi := k.FeatureMap(q)
	kPhi := k.FeatureMap(kVec)
	
	if k.State[headIdx] == nil {
		k.State[headIdx] = make([][]float32, 2)
		k.State[headIdx][0] = make([]float32, headDim*headDim)
		k.State[headIdx][1] = make([]float32, headDim)
	}
	
	kvState := k.State[headIdx][0]
	normState := k.State[headIdx][1]
	
	for i := 0; i < headDim; i++ {
		for j := 0; j < headDim; j++ {
			kvState[i*headDim+j] += kPhi[i] * v[j]
		}
	}
	
	for i := 0; i < headDim; i++ {
		normState[i] += kPhi[i]
	}
	
	output := make([]float32, headDim)
	for j := 0; j < headDim; j++ {
		var sum float32
		for i := 0; i < headDim; i++ {
			sum += qPhi[i] * kvState[i*headDim+j]
		}
		output[j] = sum
	}
	
	var denom float32
	for i := 0; i < headDim; i++ {
		denom += qPhi[i] * normState[i]
	}
	if denom < 1e-8 {
		denom = 1e-8
	}
	
	for j := 0; j < headDim; j++ {
		output[j] /= denom
	}
	
	return output
}

import torch
import torch.nn as nn
import torch.nn.functional as F
import math

class AttentionResidual(nn.Module):
    """
    Attention Residuals (AttnRes) - Replacing standard residual connections
    with block-level attention-gated cross-layer shortcuts.
    """
    
    def __init__(self, hidden_dim: int, num_cross_layers: int = 4, 
                 num_heads: int = 2, dropout: float = 0.1):
        super().__init__()
        self.hidden_dim = hidden_dim
        self.num_cross_layers = num_cross_layers
        self.num_heads = num_heads
        self.head_dim = hidden_dim // num_heads
        
        self.cross_q = nn.Linear(hidden_dim, hidden_dim, bias=False)
        self.cross_k = nn.Linear(hidden_dim, hidden_dim, bias=False)
        self.cross_v = nn.Linear(hidden_dim, hidden_dim, bias=False)
        self.cross_out = nn.Linear(hidden_dim, hidden_dim)
        
        self.gate_net = nn.Sequential(
            nn.Linear(hidden_dim, hidden_dim // 4),
            nn.SiLU(),
            nn.Linear(hidden_dim // 4, hidden_dim),
            nn.Sigmoid(),
        )
        
        self.residual_bank = []
        self.dropout = nn.Dropout(dropout)
        self.layer_norm = nn.LayerNorm(hidden_dim)
    
    def forward(self, x: torch.Tensor, sublayer_output: torch.Tensor,
                store_residual: bool = True) -> torch.Tensor:
        gate = self.gate_net(self.layer_norm(x))
        gated_output = gate * sublayer_output
        
        cross_attn = torch.zeros_like(x)
        if self.residual_bank:
            residuals = torch.stack(self.residual_bank, dim=0)
            q = self.cross_q(x).view(-1, self.num_heads, self.head_dim).transpose(0, 1)
            k = self.cross_k(residuals).view(
                len(residuals), -1, self.num_heads, self.head_dim
            ).permute(2, 1, 0, 3)
            v = self.cross_v(residuals).view(
                len(residuals), -1, self.num_heads, self.head_dim
            ).permute(2, 1, 0, 3)
            
            scale = 1.0 / math.sqrt(self.head_dim)
            attn = torch.einsum('hbd,hbld->hbl', q, k) * scale
            weights = F.softmax(attn, dim=-1)
            cross_attn = torch.einsum('hbl,hbld->hbd', weights, v)
            cross_attn = cross_attn.transpose(0, 1).contiguous().view(-1, self.hidden_dim)
            cross_attn = self.cross_out(cross_attn)
        
        output = x + self.dropout(gated_output + cross_attn)
        
        if store_residual:
            self.residual_bank.append(gated_output.detach())
            if len(self.residual_bank) > self.num_cross_layers:
                self.residual_bank.pop(0)
        
        return output

package training

import "fmt"

type TrainingMetrics struct {
	ModelParams    int64
	ThroughputTSPD float64
	MemoryPerGPU   float64
}

func CompareEfficiency() {
	standard := TrainingMetrics{2_800_000_000_000, 1250, 80.0}
	combined := TrainingMetrics{2_800_000_000_000, 3125, 20.0}
	
	totalTokens := 15_000_000_000_000.0
	numGPUs := 16384.0
	
	standardDays := totalTokens / (standard.ThroughputTSPD * 86400 * numGPUs)
	combinedDays := totalTokens / (combined.ThroughputTSPD * 86400 * numGPUs)
	
	fmt.Printf("Standard: %.1f days, Combined: %.1f days (%.1fx)\n",
		standardDays, combinedDays, standardDays/combinedDays)
}