Learning Shared Robot Movement and Control

# Illustrative sketch (not from the paper)
import torch
from torch import nn

# pretrained VLM (Qwen3-VL-2B) placeholder
class VisionLanguageEncoder(nn.Module):
    def forward(self, image, text, meta):
        # encode and concatenate to query state
        return torch.cat([image, text, meta], dim=-1)

# future generation head (SANA-600M) placeholder
class FuturePrior(nn.Module):
    def forward(self, query):
        # predict future latent (no action)
        return query  # placeholder

# MoE action head placeholder
class MoEActionHead(nn.Module):
    def __init__(self, num_experts):
        super().__init__()
        self.experts = nn.ModuleList([nn.Linear(256, 10) for _ in range(num_experts)])
        self.gate = nn.Linear(256, num_experts)

    def forward(self, query):
        weights = torch.softmax(self.gate(query), dim=-1)
        out = sum(w.unsqueeze(-1) * expert(query) for w, expert in zip(weights.t(), self.experts))
        return out

# joint training step (illustrative)
def train_step(image, text, meta, action):
    query = encoder(image, text, meta)
    future = prior(query)               # shared dynamics prior
    pred_action = moe_head(query)       # embodiment‑specific action
    loss = nn.MSELoss()(pred_action, action) + nn.MSELoss()(future, future.detach())
    loss.backward()
    optimizer.step()

encoder = VisionLanguageEncoder()
prior = FuturePrior()
moe_head = MoEActionHead(num_experts=3)
optimizer = torch.optim.Adam(list(encoder.parameters()) + list(prior.parameters()) + list(moe_head.parameters()), lr=1e-4)

// Illustrative sketch (not from the paper)
const torch = require('torch'); // placeholder for torch.js

class VisionLanguageEncoder {
  forward(image, text, meta) {
    // concatenate encoded modalities into a query state
    return torch.cat([image, text, meta], -1);
  }
}

class FuturePrior {
  forward(query) {
    // predict future latent representation (action‑free)
    return query; // placeholder
  }
}

class MoEActionHead {
  constructor(numExperts) {
    this.experts = Array.from({ length: numExperts }, () => torch.nn.Linear(256, 10));
    this.gate = torch.nn.Linear(256, numExperts);
  }
  forward(query) {
    const weights = torch.softmax(this.gate.forward(query), -1);
    let out = torch.zeros([query.shape[0], 10]);
    for (let i = 0; i < this.experts.length; i++) {
      out = out.add(weights.slice([0, i], [weights.shape[0], 1]).unsqueeze(-1).mul(this.experts[i].forward(query)));
    }
    return out;
  }
}

// joint training step (illustrative)
function trainStep(image, text, meta, action) {
  const query = encoder.forward(image, text, meta);
  const future = prior.forward(query);          // shared dynamics prior
  const predAction = moeHead.forward(query);    // embodiment‑specific action
  const loss = torch.nn.MSELoss()(predAction, action)
               .add(torch.nn.MSELoss()(future, future.detach()));
  loss.backward();
  optimizer.step();
}

const encoder = new VisionLanguageEncoder();
const prior = new FuturePrior();
const moeHead = new MoEActionHead(3);
const optimizer = torch.optim.Adam([...encoder.parameters(), ...prior.parameters(), ...moeHead.parameters()], { lr: 1e-4 });