Machine LearningResearch Frontiers

Emerging Directions in Machine Learning

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Duration120 mins

TopicResearch Frontiers

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World Models

Learning to Imagine the World

When you plan to catch a ball, you don't try every possible arm movement and see what happens. Instead, you maintain an internal model of how the world works—how balls move through air, how your muscles affect your arm position, how objects behave when caught. You run mental simulations: 'If I move my arm there, the ball will land in my hand.' This internal model enables planning, imagination, and reasoning about the future without physical experimentation.

World Models in artificial intelligence aim to replicate this capability: learning internal simulators of the environment that enable agents to imagine future trajectories, evaluate potential actions, and plan effectively without executing actions in the real world. This represents a fundamental shift from reactive systems that map observations directly to actions toward systems that understand the dynamics of their environment.

The world model paradigm has emerged as a major research direction because it addresses core limitations of model-free approaches—sample inefficiency, lack of generalization, and inability to reason about novel situations. Systems with accurate world models could learn new tasks from imagination alone.

What You Will Learn

By the end of this page, you will understand what world models are and why they matter, the key technical approaches to learning world models, how world models enable model-based reinforcement learning and planning, recent breakthroughs in large-scale world models, and the fundamental challenges that remain in this exciting research direction.

What Are World Models?

A world model is a learned representation of environment dynamics—a model that predicts how the environment will change in response to actions. Formally, given the current state (or observation) and an action, the world model predicts the next state, and potentially the reward or other relevant quantities.

Formal Definition

In the context of reinforcement learning, where an agent interacts with a Markov Decision Process (MDP), a world model approximates the transition dynamics:

Transition Model: P(s' | s, a) — the probability distribution over next states given current state and action
Reward Model: R(s, a) — the expected reward for taking action a in state s
Observation Model: P(o | s) — how observations relate to underlying states (for POMDPs)

The world model can be:

Dynamics model only: Predicts next state given current state and action
Full environmental model: Also models rewards, terminal conditions, etc.
Latent world model: Operates in a learned abstract state space rather than raw observations

Why World Models Matter

World models address several fundamental limitations of model-free reinforcement learning:

Sample Efficiency: Model-free methods learn directly from environment interactions, often requiring millions of samples. World models enable learning from imagined experience, dramatically reducing required real-world interactions.
Transfer and Generalization: A good world model captures invariant aspects of environment dynamics that transfer across tasks. An agent that understands physics can apply this knowledge to new goals.
Planning and Reasoning: With a world model, agents can mentally simulate action consequences, enabling look-ahead planning, counterfactual reasoning, and systematic exploration.
Safe Exploration: Agents can test dangerous or expensive actions in imagination before committing in the real world.

Model-Free vs Model-Based Reinforcement Learning
Aspect	Model-Free	Model-Based with World Model
Learning approach	Direct policy/value from interactions	Learn dynamics, then plan/optimize
Sample efficiency	Low (millions of samples)	High (orders of magnitude fewer)
Computation at inference	Fast (forward pass)	Higher (planning in model)
Generalization	Task-specific	Potentially task-agnostic
Failure mode	Needs more data	Compounding model errors
Examples	DQN, PPO, SAC	Dreamer, MuZero, PlaNet

The Central Tradeoff

Model-based methods trade interaction complexity for computational complexity. They require fewer real-world samples but more computation for learning the model and planning within it. As compute becomes cheaper while real-world interaction remains expensive (robotics, healthcare, autonomous driving), this tradeoff increasingly favors model-based approaches.

Architectures for Learning World Models

World models have evolved from simple forward models in state space to sophisticated latent-space predictors that can imagine complex environments. Understanding the architectural evolution helps contextualize current approaches.

Direct Pixel Prediction

The most straightforward approach predicts future observations (e.g., video frames) directly. Given current observations and action, predict the next observation.

Challenges:

High-dimensional output space (predicting every pixel)
Predicting irrelevant details (background, textures) that don't affect decision-making
Blurry predictions from averaging over uncertainty

Despite these challenges, video prediction models have shown impressive results, with recent large-scale models (Sora, Genie) demonstrating remarkably coherent long-horizon generation.

Recurrent State-Space Models

More powerful world models maintain a latent state that summarizes observation history and predicts forward in this abstract space:

Encoder: Compresses observations into latent states: z_t = enc(o_t)
Transition Model: Predicts next latent state given action: z_{t+1} = trans(z_t, a_t)
Decoder: Reconstructs observations from latent states: o_t = dec(z_t)
Reward Predictor: Estimates rewards from latent states: r_t = reward(z_t, a_t)

This architecture, pioneered by systems like PlaNet and Dreamer, enables efficient planning in the compact latent space rather than expensive planning in observation space.

world_model_architecture.py
Python
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# Conceptual World Model Architecture (Dreamer-style)
import torch
import torch.nn as nn
import torch.nn.functional as F
from typing import Tuple, Dict
 
class RecurrentStateSpaceModel(nn.Module):
    """
    A latent world model that maintains belief state and predicts dynamics.
    
    Components:
    - Encoder: observations → latent
    - RSSM: recurrent dynamics in latent space
    - Decoder: latent → observations
    - Reward model: latent → rewards
    """
    
    def __init__(
        self,
        obs_dim: int,
        action_dim: int,
        latent_dim: int = 256,
        hidden_dim: int = 512,
        deterministic_dim: int = 256,
        stochastic_dim: int = 32,
    ):
        super().__init__()
        
        # Observation encoder
        self.encoder = nn.Sequential(
            nn.Linear(obs_dim, hidden_dim),
            nn.LayerNorm(hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, hidden_dim),
            nn.ELU(),
        )
        
        # Recurrent State-Space Model (RSSM) components
        # Deterministic state transition
        self.gru = nn.GRUCell(hidden_dim + action_dim, deterministic_dim)
        
        # Prior: p(z_t | h_t) - predictions without observation
        self.prior_net = nn.Sequential(
            nn.Linear(deterministic_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, stochastic_dim * 2),  # mean and std
        )
        
        # Posterior: q(z_t | h_t, o_t) - incorporates observation
        self.posterior_net = nn.Sequential(
            nn.Linear(deterministic_dim + hidden_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, stochastic_dim * 2),
        )
        
        # Observation decoder
        self.decoder = nn.Sequential(
            nn.Linear(deterministic_dim + stochastic_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, obs_dim),
        )
        
        # Reward predictor
        self.reward_model = nn.Sequential(
            nn.Linear(deterministic_dim + stochastic_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, 1),
        )
        
        self.deterministic_dim = deterministic_dim
        self.stochastic_dim = stochastic_dim
    
    def _sample_latent(self, stats: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
        """Sample from Gaussian with reparameterization trick."""
        mean, std = torch.chunk(stats, 2, dim=-1)
        std = F.softplus(std) + 0.1  # Ensure positive std
        
        # Reparameterization: z = mean + std * epsilon
        epsilon = torch.randn_like(std)
        sample = mean + std * epsilon
        
        return sample, (mean, std)
    
    def observe(
        self,
        obs: torch.Tensor,
        action: torch.Tensor,
        hidden: torch.Tensor,
    ) -> Dict[str, torch.Tensor]:
        """
        Process an observation and update the world model state.
        Returns posterior latent state (uses observation).
        """
        # Encode observation
        obs_embed = self.encoder(obs)
        
        # Update deterministic state
        hidden_input = torch.cat([hidden, action], dim=-1)
        new_hidden = self.gru(hidden_input, hidden)
        
        # Compute prior (without observation)
        prior_stats = self.prior_net(new_hidden)
        prior_sample, prior_dist = self._sample_latent(prior_stats)
        
        # Compute posterior (with observation)
        posterior_input = torch.cat([new_hidden, obs_embed], dim=-1)
        posterior_stats = self.posterior_net(posterior_input)
        posterior_sample, posterior_dist = self._sample_latent(posterior_stats)
        
        return {
            'hidden': new_hidden,
            'posterior': posterior_sample,
            'prior': prior_sample,
            'posterior_dist': posterior_dist,
            'prior_dist': prior_dist,
        }
    
    def imagine(
        self,
        action: torch.Tensor,
        hidden: torch.Tensor,
        stochastic: torch.Tensor,
    ) -> Dict[str, torch.Tensor]:
        """
        Imagine forward one step without observation.
        Uses prior distribution for next stochastic state.
        """
        # Combine deterministic and stochastic for GRU input
        model_input = torch.cat([stochastic, action], dim=-1)
        new_hidden = self.gru(model_input, hidden)
        
        # Sample from prior (no observation to condition on)
        prior_stats = self.prior_net(new_hidden)
        prior_sample, prior_dist = self._sample_latent(prior_stats)
        
        return {
            'hidden': new_hidden,
            'stochastic': prior_sample,
            'prior_dist': prior_dist,
        }
    
    def decode(self, hidden: torch.Tensor, stochastic: torch.Tensor) -> torch.Tensor:
        """Reconstruct observation from model state."""
        state = torch.cat([hidden, stochastic], dim=-1)
        return self.decoder(state)
    
    def predict_reward(self, hidden: torch.Tensor, stochastic: torch.Tensor) -> torch.Tensor:
        """Predict reward from model state."""
        state = torch.cat([hidden, stochastic], dim=-1)
        return self.reward_model(state)

Stochastic vs Deterministic Models

World models must handle environment stochasticity—the inherent randomness in dynamics. Two paradigms exist:

Deterministic Models: Predict a single next state: z' = f(z, a)

Simpler to train and use
Cannot capture multimodal futures
May average over possibilities, producing unrealistic predictions

Stochastic Models: Predict a distribution over next states: p(z' | z, a)

Capture uncertainty and multimodality
Enable sampling diverse futures
More complex training (variational inference, generative modeling)

Modern world models typically use stochastic components for representing uncertainty while maintaining deterministic recurrent states for stability. The RSSM (Recurrent State-Space Model) architecture combines both: a deterministic GRU state carries long-term information, while stochastic latents capture moment-to-moment uncertainty.

Discrete vs Continuous Latent Spaces

Recently, some world models have adopted discrete latent representations:

VQ-VAE style: Quantize latents to a finite codebook
Categorical latents: Represent uncertainty through discrete distributions

Discrete representations can be more robust, enable token-based sequence modeling (GPT-style world models), and connect to symbolic reasoning. MuZero and DreamerV3 use discrete or hybrid representations successfully.

The Representation Learning Challenge

The quality of world model predictions depends critically on the learned representation. The latent space must capture aspects of the observation relevant for dynamics and decisions while ignoring irrelevant details. This connects world model learning to broader questions in representation learning and raises the question: what is the 'right' representation for a world model?

Planning with World Models

Once we have a learned world model, we can use it to plan—searching over possible action sequences to find those that lead to desirable outcomes. This enables agents to act intelligently on new tasks even without task-specific training, simply by specifying goals and planning toward them.

Planning Problem Formulation

Given:

A world model that predicts future states and rewards
A current state or observation
A planning horizon H

Find an action sequence (a_0, a_1, ..., a_{H-1}) that maximizes expected cumulative reward:

max_{a_0:H-1} E[Σ_{t=0}^{H-1} γ^t r_t | world model]

This is solved through search in the model rather than real-world execution.

Model Predictive Control (MPC)

A common planning approach in continuous control:

Sample action sequences: Generate candidate trajectories through random sampling or optimization
Rollout in world model: Predict outcomes for each candidate sequence
Select best sequence: Choose the sequence with highest predicted return
Execute first action: Apply only the first action of the best sequence
Re-plan: After observing the new state, repeat the process

The 'model predictive' aspect refers to only executing the first action and then re-planning—this handles model errors by continuously correcting the plan based on actual observations.

Cross-Entropy Method (CEM)

A popular optimization method for MPC planning:

Initialize a distribution over action sequences (e.g., Gaussian)
Sample K candidate sequences from the distribution
Evaluate each sequence in the world model
Select the top-performing sequences (elite set)
Fit a new distribution to the elite set
Repeat until convergence or budget exhausted

CEM is simple but effective, handling high-dimensional action spaces better than random search.

Monte Carlo Tree Search (MCTS)

For discrete action spaces or when exploration is critical, MCTS provides a principled approach:

Selection: Traverse the tree using UCB-style selection (balance exploration and exploitation)
Expansion: Add new node when reaching unexplored state-action
Evaluation: Rollout from new node using policy or world model
Backup: Propagate values up the tree

MCTS with learned world models achieved superhuman performance in Go (AlphaGo Zero) and later in Atari (MuZero).

Learning to Plan: Policy Optimization in Imagination

Rather than planning at test time, we can use the world model to train a policy:

Imagination phase: Generate synthetic trajectories by rolling out the policy in the world model
Learning phase: Update the policy on imagined trajectories as if they were real experience

This is the approach taken by Dreamer and related methods. Advantages include:

Amortized planning: computation happens during training, not inference
Can use sophisticated policy optimization (actor-critic, PPO)
Policy can generalize patterns across imagined experiences

The policy essentially 'compiles' extensive planning into learned behavior.

Behavior Learning in Latent Space

The most efficient approach learns behavior directly in the world model's latent space:

Encode observations into latent states
Imagine forward in latent space using the transition model
Train value/policy on predicted latent returns
Execute by decoding actions from the policy

This avoids expensive observation prediction during training—we only need latent dynamics, which are faster to compute.

The Model Error Problem

All planning methods face the fundamental challenge of model error. Small prediction errors compound over long rollouts, leading to unrealistic imagined trajectories. Strategies to mitigate this include: short planning horizons, ensembling multiple models, conservative uncertainty-aware planning, and model-free policy refinement. No approach completely solves this challenge yet.

Landmark World Model Systems

The development of world models has been marked by several breakthrough systems, each introducing key innovations. Understanding these landmarks provides context for the current state of the field.

Ha & Schmidhuber's 'World Models' (2018)

This influential paper crystallized the modern world model paradigm:

VAE encoder: Compresses video frames to compact latent codes
MDN-RNN: Recurrent network predicts future latent codes as mixture of Gaussians
Small controller: Simple linear policy operates on latent state + RNN hidden state

Key insight: The 'large' complex model learns the world; the 'small' policy learns to act within it. Demonstrated that agents can learn largely from imagined experience, solving CarRacing from pixels with ~100x fewer real environment steps.

PlaNet (2019)

DeepMind's 'Learning Latent Dynamics for Planning from Pixels' introduced:

RSSM architecture: Combined deterministic and stochastic latent states
CEM planning: Cross-entropy method for action optimization in latent space
Image-based control: Solved continuous control tasks from raw pixels

PlaNet demonstrated strong results on DeepMind Control Suite tasks, establishing latent planning as a viable approach to image-based control.

Dreamer (2020) and DreamerV2/V3

Building on PlaNet, Dreamer introduced policy learning in imagination:

Actor-critic in latent space: Learn policy by imagining trajectories
Propagate value gradients: Train policy using backpropagation through imagined returns
Scalable learning: Train entirely from imagined experience after initial exploration

DreamerV2 (2021) added discrete latent representations for more stable learning. DreamerV3 (2023) achieved significant scaling, learning to play Minecraft from raw pixels—including the challenging 25-minute task of collecting a diamond.

DreamerV3's success on Minecraft demonstrated world models can handle:

Long time horizons (thousands of steps)
Open-ended goals requiring complex subgoals
Partially observable, stochastic environments

MuZero (2020)

MuZero represents perhaps the most impressive model-based success story:

Learned dynamics without observation prediction: Model predicts values, rewards, and policy outputs—not observations
MCTS planning: Uses learned model for tree search
Superhuman Atari from scratch: Matches AlphaZero performance on board games while also excelling on visually complex Atari games

MuZero's key insight: the world model need only capture aspects relevant for decision-making. Predicting future values and rewards is more tractable than predicting future pixels, and sufficient for planning.

Video Prediction Models: Sora and Beyond

Recent advances in large-scale video diffusion models suggest a new paradigm for world models:

Sora (OpenAI, 2024): Generates coherent videos up to a minute long, demonstrating impressive understanding of physics, lighting, and object permanence
Implicit world knowledge: These models learn substantial world structure as a byproduct of video prediction
Zero-shot generalization: Can imagine scenarios never seen in training

While not yet integrated into agentic systems, video diffusion models represent a possible future where world models emerge from large-scale pretraining, similar to how language understanding emerged in LLMs.

Genie (2024)

DeepMind's Genie learns world models from unlabeled internet videos:

Latent action discovery: Infers action spaces from video sequences without labels
Controllable generation: User can 'play' the generated worlds
Scalable pretraining: Learns from 200K hours of gameplay videos

Genie suggests that foundation world models—trained on diverse video data—might provide general-purpose environment understanding transferable to downstream tasks.

Evolution of World Model Systems
System	Year	Key Innovation	Domain
World Models	2018	VAE + RNN architecture, imagination training	CarRacing
PlaNet	2019	RSSM, CEM planning in latent space	DMC Suite
Dreamer	2020	Actor-critic in imagination	DMC Suite
MuZero	2020	Value-equivalent models, MCTS	Atari, Board Games
DreamerV3	2023	Scalability, discrete latents	Minecraft (diamond)
Sora/Genie	2024	Large-scale video diffusion	Open-ended video

The Arc of Progress

In just six years, world models have advanced from solving simple racing games to collecting diamonds in Minecraft and generating coherent minute-long videos. This trajectory suggests world models may be approaching a capability threshold where they become practical for real-world applications in robotics, scientific simulation, and interactive systems.

Object-Centric World Models

A crucial aspect of human world understanding is its compositional, object-centric nature. We represent the world not as a homogeneous field of pixels but as collections of distinct objects with properties and relations. Object-centric world models aim to capture this structure, decomposing scenes into discrete object representations and modeling dynamics at the object level.

Why Object-Centric?

Object-centric representations offer several advantages:

Compositionality: New scenes can be constructed from familiar objects in novel configurations
Relational reasoning: Physics involves object interactions, naturally expressed in object terms
Generalization: Similar objects share properties; understanding one ball helps understand all balls
Interpretability: Object representations are more humanly comprehensible than distributed latents
Efficiency: Dynamics often factor across objects (ball A's motion doesn't directly affect ball C's)

Unsupervised Object Discovery

A key challenge is discovering objects from raw observations without supervision:

MONet (Multi-Object Network): Iteratively segments scenes using attention, representing each segment with a separate VAE latent.

IODINE (Iterative Object Decomposition Inference Network): Refines object representations through iterative amortized inference.

Slot Attention: Uses attention mechanism with 'slots' that compete to represent different objects. Particularly successful and efficient, enabling object discovery from single images.

These methods can discover individual objects in complex scenes, enabling subsequent object-level reasoning.

Object-Centric Dynamics

Given object representations, we can learn dynamics at the object level:

Graph Neural Networks for Dynamics: Represent objects as nodes and potential interactions as edges. GNN message passing models how objects influence each other:

Interaction Networks: Learn pairwise object interactions for physics prediction
C-SWM (Contrastive Structured World Models): Learn object representations with contrastive loss, predict dynamics via GNN

Relational World Models: Explicitly model relations between objects (touching, contains, supports) and how actions affect these relations. Enables more symbolic-like reasoning about object interactions.

Hierarchical Abstraction: Some approaches learn hierarchies of increasingly abstract representations:

Low level: Pixel dynamics
Mid level: Object dynamics
High level: Scene graphs, symbolic relations

This enables reasoning at appropriate abstraction levels for different tasks.

Challenges in Object-Centric World Modeling

Scalability: Handling scenes with many objects requires efficient attention or approximations
Object identity: Maintaining consistent object slots across time (object permanence)
Novel objects: Generalizing to object types not seen during training
Background modeling: Distinguishing meaningful objects from background elements
Evaluation: Measuring quality of object discovery without ground truth

The Binding Problem

Object-centric learning faces a version of the 'binding problem' from cognitive science: how do we bind together features that belong to the same object? Slot Attention addresses this through competitive attention—features must compete for slot membership. This mirrors theories of attention in human perception as a binding mechanism.

World Models for Robotics

Robotics presents perhaps the most compelling application domain for world models. Physical robot interaction is slow, expensive, and potentially dangerous. World models that enable learning in simulation and imagination could dramatically accelerate robot learning while improving safety.

The Sim-to-Real Challenge

A major challenge in robot world models is sim-to-real transfer—models trained in simulation often fail when deployed on real robots due to:

Reality gap: Simulated physics differs from real physics
Sensor noise: Real sensors are noisier and less idealized
Actuator dynamics: Real motors have delays, backlash, and non-linearities not modeled in simulation
Visual differences: Simulated rendering differs from real images

Domain Randomization: Make models robust by training with randomized simulation parameters:

Vary physics parameters (friction, mass, damping)
Randomize visual appearance (textures, lighting, colors)
Add noise to observations and actions

The hope is that the real world becomes 'just another sample' from the randomized distribution.

Learning from Real Data: Alternatively, learn world models directly from real robot experience:

Data-efficient methods are essential given slow physical data collection
Model uncertainty is critical for safe exploration
Continual learning enables adaptation to changing conditions

Dexterous Manipulation

World models have shown particular promise for dexterous manipulation—complex object manipulation requiring fine motor control:

Contact dynamics: Modeling when and how the robot contacts objects
Object state estimation: Predicting object pose and velocity from touch and vision
Long-horizon planning: Chaining many actions for complex tasks (e.g., fabric folding)

Recent work from DeepMind and others has demonstrated sim-to-real transfer of complex manipulation skills including Rubik's cube solving, in-hand reorientation, and bimanual coordination.

Mobile Robots and Navigation

For mobile robots, world models capture:

Geometry: Where obstacles and pathways exist
Dynamics: How the robot's motion commands affect its position
Semantic understanding: What different regions of the environment afford

Foundation Models for Robotics

Emerging work explores using large pretrained models as world models for robotics:

Vision-Language Models: Ground language instructions in visual observations
Video Prediction Models: Imagine future visual outcomes of robot actions
Internet Pretraining: Leverage knowledge from internet images and videos

Systems like RT-2 and PaLM-E demonstrate that pretrained multimodal models contain substantial world knowledge applicable to robot control.

Key Challenges in Robot World Models

•Contact modeling: Predicting when and how the robot contacts objects—discontinuous and complex physics
•Deformable objects: Cloth, rope, and soft materials require different modeling approaches than rigid bodies
•Long horizons: Many tasks require minute- to hour-long reasoning; current models struggle beyond seconds
•Multimodal sensing: Integrating vision, touch, proprioception, and audio into coherent world models
•Safety guarantees: Ensuring robot actions won't cause damage even when model predictions are wrong
•Continuous adaptation: Real-world conditions change; robots must update world models over deployment lifetime

The Embodiment Hypothesis

Some researchers argue that true world understanding requires embodiment—physical interaction with the world rather than just observation. If true, robot world models may need to be learned through physical experience rather than from internet-scale observation alone. This remains an open and fascinating question at the intersection of AI and cognitive science.

Open Challenges and Future Directions

Despite impressive progress, world models face fundamental challenges that represent active research frontiers. Solving these could unlock transformative capabilities.

Long-Horizon Prediction and Compounding Errors

World models inevitably have prediction errors. Over long rollouts, these errors compound catastrophically:

Predicted trajectories diverge from reality
Planning quality degrades with horizon
Imagination-trained policies may exploit model errors

Current approaches mitigate but don't solve this:

Short planning horizons
Re-planning from actual observations (MPC)
Uncertainty-aware planning that avoids low-confidence predictions
Training policies to be robust to model errors

Fundamental solutions might require:

Hierarchical planning at multiple abstraction levels
Abstract world models that predict high-level outcomes rather than full trajectories
Better uncertainty quantification and propagation

Generalization Across Environments

Most world models are trained on specific environments and don't transfer:

A model of CarRacing can't play Breakout
A model of one kitchen doesn't work in another

The dream of foundation world models—trained on diverse data and applicable to novel environments—remains largely unrealized. Key questions:

What representations enable cross-environment transfer?
How should we structure inductive biases for physical understanding?
Can we learn world models that capture invariant physics while adapting to specific environments?

The Abstraction Problem

Humans reason at multiple levels of abstraction—from muscle movements to high-level plans. Most world models operate at a single fixed granularity. Key challenges:

Learning abstraction hierarchies: Discovering useful levels of abstraction from data
Variable temporal resolution: Some predictions should span milliseconds, others years
Connecting abstractions: How do high-level predictions ground in low-level dynamics?

Open-World Generalization

Real-world agents must handle novelty—objects, situations, and dynamics never seen in training:

Out-of-distribution detection: Know when predictions are unreliable
Rapid adaptation: Quickly update models given new evidence
Compositional generalization: Combine known concepts in novel ways
Causal structure learning: Infer underlying causal mechanisms, not just correlations

Integration with Language and Reasoning

Current world models are largely non-linguistic. Integrating natural language could enable:

Goal specification: 'Make me a sandwich' rather than reward functions
Common sense: Leverage language-encoded world knowledge
Explanation: Articulate model predictions and uncertainties
Instruction following: Complex multi-step task completion

Vision-language models like Flamingo and GPT-4V demonstrate rich world knowledge in language form—connecting this to action remains a frontier.

The Big Picture

Many believe that world models—systems that truly understand how the world works through learned internal simulators—represent a necessary component of artificial general intelligence. Current systems are impressive but narrow. The path to general-purpose world models that enable flexible reasoning, planning, and adaptation across domains remains one of AI's grand challenges.

Summary: Toward World Understanding

We've explored the rich landscape of world models—from basic concepts to cutting-edge research. Let's consolidate the key insights:

Key Takeaways

•Definition and Purpose — World models are learned environment simulators that predict how the world changes in response to actions, enabling planning, imagination, and sample-efficient learning.
•Architectural Evolution — From direct pixel prediction through recurrent state-space models to modern systems with discrete latents and scalable transformers, world model architectures have become increasingly sophisticated.
•Planning Paradigms — World models enable planning through MPC, MCTS, and policy optimization in imagination. Each trades off computation, robustness, and flexibility differently.
•Landmark Systems — World Models, PlaNet, Dreamer, MuZero, and recent video prediction models mark the evolution from research concepts to systems solving complex real-world tasks.
•Object-Centric Structure — Decomposing world models into object-centric representations enables compositional generalization and more interpretable dynamics.
•Robotics Applications — World models are particularly valuable for robotics, enabling simulation-based learning and safe exploration, though sim-to-real transfer remains challenging.
•Open Frontiers — Long-horizon prediction, cross-environment generalization, abstraction learning, and language integration remain fundamental challenges driving ongoing research.

What's Next:

Having explored world models' approach to environment simulation and planning, we'll next examine AI Safety—the crucial research direction focused on ensuring AI systems, including those with capable world models, remain beneficial and aligned with human values as they become more powerful.

Page Complete

You now understand world models—from their theoretical foundations through architectural innovations to frontier research challenges. This foundation prepares you to engage with cutting-edge work on systems that truly understand and can reason about the physical world.

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Machine LearningResearch Frontiers

Emerging Directions in Machine Learning

LevelAdvanced

Duration120 mins

TopicResearch Frontiers

3 / 5

World Models

Learning to Imagine the World

What You Will Learn

What Are World Models?

Formal Definition

In the context of reinforcement learning, where an agent interacts with a Markov Decision Process (MDP), a world model approximates the transition dynamics:

Transition Model: P(s' | s, a) — the probability distribution over next states given current state and action
Reward Model: R(s, a) — the expected reward for taking action a in state s
Observation Model: P(o | s) — how observations relate to underlying states (for POMDPs)

The world model can be:

Dynamics model only: Predicts next state given current state and action
Full environmental model: Also models rewards, terminal conditions, etc.
Latent world model: Operates in a learned abstract state space rather than raw observations

Why World Models Matter

World models address several fundamental limitations of model-free reinforcement learning:

Sample Efficiency: Model-free methods learn directly from environment interactions, often requiring millions of samples. World models enable learning from imagined experience, dramatically reducing required real-world interactions.
Transfer and Generalization: A good world model captures invariant aspects of environment dynamics that transfer across tasks. An agent that understands physics can apply this knowledge to new goals.
Planning and Reasoning: With a world model, agents can mentally simulate action consequences, enabling look-ahead planning, counterfactual reasoning, and systematic exploration.
Safe Exploration: Agents can test dangerous or expensive actions in imagination before committing in the real world.

Model-Free vs Model-Based Reinforcement Learning
Aspect	Model-Free	Model-Based with World Model
Learning approach	Direct policy/value from interactions	Learn dynamics, then plan/optimize
Sample efficiency	Low (millions of samples)	High (orders of magnitude fewer)
Computation at inference	Fast (forward pass)	Higher (planning in model)
Generalization	Task-specific	Potentially task-agnostic
Failure mode	Needs more data	Compounding model errors
Examples	DQN, PPO, SAC	Dreamer, MuZero, PlaNet

The Central Tradeoff

Architectures for Learning World Models

Direct Pixel Prediction

The most straightforward approach predicts future observations (e.g., video frames) directly. Given current observations and action, predict the next observation.

Challenges:

High-dimensional output space (predicting every pixel)
Predicting irrelevant details (background, textures) that don't affect decision-making
Blurry predictions from averaging over uncertainty

Despite these challenges, video prediction models have shown impressive results, with recent large-scale models (Sora, Genie) demonstrating remarkably coherent long-horizon generation.

Recurrent State-Space Models

More powerful world models maintain a latent state that summarizes observation history and predicts forward in this abstract space:

Encoder: Compresses observations into latent states: z_t = enc(o_t)
Transition Model: Predicts next latent state given action: z_{t+1} = trans(z_t, a_t)
Decoder: Reconstructs observations from latent states: o_t = dec(z_t)
Reward Predictor: Estimates rewards from latent states: r_t = reward(z_t, a_t)

This architecture, pioneered by systems like PlaNet and Dreamer, enables efficient planning in the compact latent space rather than expensive planning in observation space.

world_model_architecture.py
Python
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# Conceptual World Model Architecture (Dreamer-style)
import torch
import torch.nn as nn
import torch.nn.functional as F
from typing import Tuple, Dict
 
class RecurrentStateSpaceModel(nn.Module):
    """
    A latent world model that maintains belief state and predicts dynamics.
    
    Components:
    - Encoder: observations → latent
    - RSSM: recurrent dynamics in latent space
    - Decoder: latent → observations
    - Reward model: latent → rewards
    """
    
    def __init__(
        self,
        obs_dim: int,
        action_dim: int,
        latent_dim: int = 256,
        hidden_dim: int = 512,
        deterministic_dim: int = 256,
        stochastic_dim: int = 32,
    ):
        super().__init__()
        
        # Observation encoder
        self.encoder = nn.Sequential(
            nn.Linear(obs_dim, hidden_dim),
            nn.LayerNorm(hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, hidden_dim),
            nn.ELU(),
        )
        
        # Recurrent State-Space Model (RSSM) components
        # Deterministic state transition
        self.gru = nn.GRUCell(hidden_dim + action_dim, deterministic_dim)
        
        # Prior: p(z_t | h_t) - predictions without observation
        self.prior_net = nn.Sequential(
            nn.Linear(deterministic_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, stochastic_dim * 2),  # mean and std
        )
        
        # Posterior: q(z_t | h_t, o_t) - incorporates observation
        self.posterior_net = nn.Sequential(
            nn.Linear(deterministic_dim + hidden_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, stochastic_dim * 2),
        )
        
        # Observation decoder
        self.decoder = nn.Sequential(
            nn.Linear(deterministic_dim + stochastic_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, obs_dim),
        )
        
        # Reward predictor
        self.reward_model = nn.Sequential(
            nn.Linear(deterministic_dim + stochastic_dim, hidden_dim),
            nn.ELU(),
            nn.Linear(hidden_dim, 1),
        )
        
        self.deterministic_dim = deterministic_dim
        self.stochastic_dim = stochastic_dim
    
    def _sample_latent(self, stats: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
        """Sample from Gaussian with reparameterization trick."""
        mean, std = torch.chunk(stats, 2, dim=-1)
        std = F.softplus(std) + 0.1  # Ensure positive std
        
        # Reparameterization: z = mean + std * epsilon
        epsilon = torch.randn_like(std)
        sample = mean + std * epsilon
        
        return sample, (mean, std)
    
    def observe(
        self,
        obs: torch.Tensor,
        action: torch.Tensor,
        hidden: torch.Tensor,
    ) -> Dict[str, torch.Tensor]:
        """
        Process an observation and update the world model state.
        Returns posterior latent state (uses observation).
        """
        # Encode observation
        obs_embed = self.encoder(obs)
        
        # Update deterministic state
        hidden_input = torch.cat([hidden, action], dim=-1)
        new_hidden = self.gru(hidden_input, hidden)
        
        # Compute prior (without observation)
        prior_stats = self.prior_net(new_hidden)
        prior_sample, prior_dist = self._sample_latent(prior_stats)
        
        # Compute posterior (with observation)
        posterior_input = torch.cat([new_hidden, obs_embed], dim=-1)
        posterior_stats = self.posterior_net(posterior_input)
        posterior_sample, posterior_dist = self._sample_latent(posterior_stats)
        
        return {
            'hidden': new_hidden,
            'posterior': posterior_sample,
            'prior': prior_sample,
            'posterior_dist': posterior_dist,
            'prior_dist': prior_dist,
        }
    
    def imagine(
        self,
        action: torch.Tensor,
        hidden: torch.Tensor,
        stochastic: torch.Tensor,
    ) -> Dict[str, torch.Tensor]:
        """
        Imagine forward one step without observation.
        Uses prior distribution for next stochastic state.
        """
        # Combine deterministic and stochastic for GRU input
        model_input = torch.cat([stochastic, action], dim=-1)
        new_hidden = self.gru(model_input, hidden)
        
        # Sample from prior (no observation to condition on)
        prior_stats = self.prior_net(new_hidden)
        prior_sample, prior_dist = self._sample_latent(prior_stats)
        
        return {
            'hidden': new_hidden,
            'stochastic': prior_sample,
            'prior_dist': prior_dist,
        }
    
    def decode(self, hidden: torch.Tensor, stochastic: torch.Tensor) -> torch.Tensor:
        """Reconstruct observation from model state."""
        state = torch.cat([hidden, stochastic], dim=-1)
        return self.decoder(state)
    
    def predict_reward(self, hidden: torch.Tensor, stochastic: torch.Tensor) -> torch.Tensor:
        """Predict reward from model state."""
        state = torch.cat([hidden, stochastic], dim=-1)
        return self.reward_model(state)

Stochastic vs Deterministic Models

World models must handle environment stochasticity—the inherent randomness in dynamics. Two paradigms exist:

Deterministic Models: Predict a single next state: z' = f(z, a)

Simpler to train and use
Cannot capture multimodal futures
May average over possibilities, producing unrealistic predictions

Stochastic Models: Predict a distribution over next states: p(z' | z, a)

Capture uncertainty and multimodality
Enable sampling diverse futures
More complex training (variational inference, generative modeling)

Discrete vs Continuous Latent Spaces

Recently, some world models have adopted discrete latent representations:

VQ-VAE style: Quantize latents to a finite codebook
Categorical latents: Represent uncertainty through discrete distributions

The Representation Learning Challenge

Planning with World Models

Planning Problem Formulation

Given:

A world model that predicts future states and rewards
A current state or observation
A planning horizon H

Find an action sequence (a_0, a_1, ..., a_{H-1}) that maximizes expected cumulative reward:

max_{a_0:H-1} E[Σ_{t=0}^{H-1} γ^t r_t | world model]

This is solved through search in the model rather than real-world execution.

Model Predictive Control (MPC)

A common planning approach in continuous control:

Sample action sequences: Generate candidate trajectories through random sampling or optimization
Rollout in world model: Predict outcomes for each candidate sequence
Select best sequence: Choose the sequence with highest predicted return
Execute first action: Apply only the first action of the best sequence
Re-plan: After observing the new state, repeat the process

The 'model predictive' aspect refers to only executing the first action and then re-planning—this handles model errors by continuously correcting the plan based on actual observations.

Cross-Entropy Method (CEM)

A popular optimization method for MPC planning:

Initialize a distribution over action sequences (e.g., Gaussian)
Sample K candidate sequences from the distribution
Evaluate each sequence in the world model
Select the top-performing sequences (elite set)
Fit a new distribution to the elite set
Repeat until convergence or budget exhausted

CEM is simple but effective, handling high-dimensional action spaces better than random search.

Monte Carlo Tree Search (MCTS)

For discrete action spaces or when exploration is critical, MCTS provides a principled approach:

Selection: Traverse the tree using UCB-style selection (balance exploration and exploitation)
Expansion: Add new node when reaching unexplored state-action
Evaluation: Rollout from new node using policy or world model
Backup: Propagate values up the tree

MCTS with learned world models achieved superhuman performance in Go (AlphaGo Zero) and later in Atari (MuZero).

Learning to Plan: Policy Optimization in Imagination

Rather than planning at test time, we can use the world model to train a policy:

Imagination phase: Generate synthetic trajectories by rolling out the policy in the world model
Learning phase: Update the policy on imagined trajectories as if they were real experience

This is the approach taken by Dreamer and related methods. Advantages include:

Amortized planning: computation happens during training, not inference
Can use sophisticated policy optimization (actor-critic, PPO)
Policy can generalize patterns across imagined experiences

The policy essentially 'compiles' extensive planning into learned behavior.

Behavior Learning in Latent Space

The most efficient approach learns behavior directly in the world model's latent space:

Encode observations into latent states
Imagine forward in latent space using the transition model
Train value/policy on predicted latent returns
Execute by decoding actions from the policy

This avoids expensive observation prediction during training—we only need latent dynamics, which are faster to compute.

The Model Error Problem

Landmark World Model Systems

The development of world models has been marked by several breakthrough systems, each introducing key innovations. Understanding these landmarks provides context for the current state of the field.

Ha & Schmidhuber's 'World Models' (2018)

This influential paper crystallized the modern world model paradigm:

VAE encoder: Compresses video frames to compact latent codes
MDN-RNN: Recurrent network predicts future latent codes as mixture of Gaussians
Small controller: Simple linear policy operates on latent state + RNN hidden state

PlaNet (2019)

DeepMind's 'Learning Latent Dynamics for Planning from Pixels' introduced:

RSSM architecture: Combined deterministic and stochastic latent states
CEM planning: Cross-entropy method for action optimization in latent space
Image-based control: Solved continuous control tasks from raw pixels

PlaNet demonstrated strong results on DeepMind Control Suite tasks, establishing latent planning as a viable approach to image-based control.

Dreamer (2020) and DreamerV2/V3

Building on PlaNet, Dreamer introduced policy learning in imagination:

Actor-critic in latent space: Learn policy by imagining trajectories
Propagate value gradients: Train policy using backpropagation through imagined returns
Scalable learning: Train entirely from imagined experience after initial exploration

DreamerV3's success on Minecraft demonstrated world models can handle:

Long time horizons (thousands of steps)
Open-ended goals requiring complex subgoals
Partially observable, stochastic environments

MuZero (2020)

MuZero represents perhaps the most impressive model-based success story:

Learned dynamics without observation prediction: Model predicts values, rewards, and policy outputs—not observations
MCTS planning: Uses learned model for tree search
Superhuman Atari from scratch: Matches AlphaZero performance on board games while also excelling on visually complex Atari games

Video Prediction Models: Sora and Beyond

Recent advances in large-scale video diffusion models suggest a new paradigm for world models:

Sora (OpenAI, 2024): Generates coherent videos up to a minute long, demonstrating impressive understanding of physics, lighting, and object permanence
Implicit world knowledge: These models learn substantial world structure as a byproduct of video prediction
Zero-shot generalization: Can imagine scenarios never seen in training

Genie (2024)

DeepMind's Genie learns world models from unlabeled internet videos:

Latent action discovery: Infers action spaces from video sequences without labels
Controllable generation: User can 'play' the generated worlds
Scalable pretraining: Learns from 200K hours of gameplay videos

Genie suggests that foundation world models—trained on diverse video data—might provide general-purpose environment understanding transferable to downstream tasks.

Evolution of World Model Systems
System	Year	Key Innovation	Domain
World Models	2018	VAE + RNN architecture, imagination training	CarRacing
PlaNet	2019	RSSM, CEM planning in latent space	DMC Suite
Dreamer	2020	Actor-critic in imagination	DMC Suite
MuZero	2020	Value-equivalent models, MCTS	Atari, Board Games
DreamerV3	2023	Scalability, discrete latents	Minecraft (diamond)
Sora/Genie	2024	Large-scale video diffusion	Open-ended video

The Arc of Progress

Object-Centric World Models

Why Object-Centric?

Object-centric representations offer several advantages:

Compositionality: New scenes can be constructed from familiar objects in novel configurations
Relational reasoning: Physics involves object interactions, naturally expressed in object terms
Generalization: Similar objects share properties; understanding one ball helps understand all balls
Interpretability: Object representations are more humanly comprehensible than distributed latents
Efficiency: Dynamics often factor across objects (ball A's motion doesn't directly affect ball C's)

Unsupervised Object Discovery

A key challenge is discovering objects from raw observations without supervision:

MONet (Multi-Object Network): Iteratively segments scenes using attention, representing each segment with a separate VAE latent.

IODINE (Iterative Object Decomposition Inference Network): Refines object representations through iterative amortized inference.

Slot Attention: Uses attention mechanism with 'slots' that compete to represent different objects. Particularly successful and efficient, enabling object discovery from single images.

These methods can discover individual objects in complex scenes, enabling subsequent object-level reasoning.

Object-Centric Dynamics

Given object representations, we can learn dynamics at the object level:

Graph Neural Networks for Dynamics: Represent objects as nodes and potential interactions as edges. GNN message passing models how objects influence each other:

Interaction Networks: Learn pairwise object interactions for physics prediction
C-SWM (Contrastive Structured World Models): Learn object representations with contrastive loss, predict dynamics via GNN

Hierarchical Abstraction: Some approaches learn hierarchies of increasingly abstract representations:

Low level: Pixel dynamics
Mid level: Object dynamics
High level: Scene graphs, symbolic relations

This enables reasoning at appropriate abstraction levels for different tasks.

Challenges in Object-Centric World Modeling

Scalability: Handling scenes with many objects requires efficient attention or approximations
Object identity: Maintaining consistent object slots across time (object permanence)
Novel objects: Generalizing to object types not seen during training
Background modeling: Distinguishing meaningful objects from background elements
Evaluation: Measuring quality of object discovery without ground truth

The Binding Problem

World Models for Robotics

The Sim-to-Real Challenge

A major challenge in robot world models is sim-to-real transfer—models trained in simulation often fail when deployed on real robots due to:

Reality gap: Simulated physics differs from real physics
Sensor noise: Real sensors are noisier and less idealized
Actuator dynamics: Real motors have delays, backlash, and non-linearities not modeled in simulation
Visual differences: Simulated rendering differs from real images

Domain Randomization: Make models robust by training with randomized simulation parameters:

Vary physics parameters (friction, mass, damping)
Randomize visual appearance (textures, lighting, colors)
Add noise to observations and actions

The hope is that the real world becomes 'just another sample' from the randomized distribution.

Learning from Real Data: Alternatively, learn world models directly from real robot experience:

Data-efficient methods are essential given slow physical data collection
Model uncertainty is critical for safe exploration
Continual learning enables adaptation to changing conditions

Dexterous Manipulation

World models have shown particular promise for dexterous manipulation—complex object manipulation requiring fine motor control:

Contact dynamics: Modeling when and how the robot contacts objects
Object state estimation: Predicting object pose and velocity from touch and vision
Long-horizon planning: Chaining many actions for complex tasks (e.g., fabric folding)

Recent work from DeepMind and others has demonstrated sim-to-real transfer of complex manipulation skills including Rubik's cube solving, in-hand reorientation, and bimanual coordination.

Mobile Robots and Navigation

For mobile robots, world models capture:

Geometry: Where obstacles and pathways exist
Dynamics: How the robot's motion commands affect its position
Semantic understanding: What different regions of the environment afford

Foundation Models for Robotics

Emerging work explores using large pretrained models as world models for robotics:

Vision-Language Models: Ground language instructions in visual observations
Video Prediction Models: Imagine future visual outcomes of robot actions
Internet Pretraining: Leverage knowledge from internet images and videos

Systems like RT-2 and PaLM-E demonstrate that pretrained multimodal models contain substantial world knowledge applicable to robot control.

Key Challenges in Robot World Models

•Contact modeling: Predicting when and how the robot contacts objects—discontinuous and complex physics
•Deformable objects: Cloth, rope, and soft materials require different modeling approaches than rigid bodies
•Long horizons: Many tasks require minute- to hour-long reasoning; current models struggle beyond seconds
•Multimodal sensing: Integrating vision, touch, proprioception, and audio into coherent world models
•Safety guarantees: Ensuring robot actions won't cause damage even when model predictions are wrong
•Continuous adaptation: Real-world conditions change; robots must update world models over deployment lifetime

The Embodiment Hypothesis

Open Challenges and Future Directions

Despite impressive progress, world models face fundamental challenges that represent active research frontiers. Solving these could unlock transformative capabilities.

Long-Horizon Prediction and Compounding Errors

World models inevitably have prediction errors. Over long rollouts, these errors compound catastrophically:

Predicted trajectories diverge from reality
Planning quality degrades with horizon
Imagination-trained policies may exploit model errors

Current approaches mitigate but don't solve this:

Short planning horizons
Re-planning from actual observations (MPC)
Uncertainty-aware planning that avoids low-confidence predictions
Training policies to be robust to model errors

Fundamental solutions might require:

Hierarchical planning at multiple abstraction levels
Abstract world models that predict high-level outcomes rather than full trajectories
Better uncertainty quantification and propagation

Generalization Across Environments

Most world models are trained on specific environments and don't transfer:

A model of CarRacing can't play Breakout
A model of one kitchen doesn't work in another

The dream of foundation world models—trained on diverse data and applicable to novel environments—remains largely unrealized. Key questions:

What representations enable cross-environment transfer?
How should we structure inductive biases for physical understanding?
Can we learn world models that capture invariant physics while adapting to specific environments?

The Abstraction Problem

Humans reason at multiple levels of abstraction—from muscle movements to high-level plans. Most world models operate at a single fixed granularity. Key challenges:

Learning abstraction hierarchies: Discovering useful levels of abstraction from data
Variable temporal resolution: Some predictions should span milliseconds, others years
Connecting abstractions: How do high-level predictions ground in low-level dynamics?

Open-World Generalization

Real-world agents must handle novelty—objects, situations, and dynamics never seen in training:

Out-of-distribution detection: Know when predictions are unreliable
Rapid adaptation: Quickly update models given new evidence
Compositional generalization: Combine known concepts in novel ways
Causal structure learning: Infer underlying causal mechanisms, not just correlations

Integration with Language and Reasoning

Current world models are largely non-linguistic. Integrating natural language could enable:

Goal specification: 'Make me a sandwich' rather than reward functions
Common sense: Leverage language-encoded world knowledge
Explanation: Articulate model predictions and uncertainties
Instruction following: Complex multi-step task completion

Vision-language models like Flamingo and GPT-4V demonstrate rich world knowledge in language form—connecting this to action remains a frontier.

The Big Picture

Summary: Toward World Understanding

We've explored the rich landscape of world models—from basic concepts to cutting-edge research. Let's consolidate the key insights:

Key Takeaways

•Definition and Purpose — World models are learned environment simulators that predict how the world changes in response to actions, enabling planning, imagination, and sample-efficient learning.
•Architectural Evolution — From direct pixel prediction through recurrent state-space models to modern systems with discrete latents and scalable transformers, world model architectures have become increasingly sophisticated.
•Planning Paradigms — World models enable planning through MPC, MCTS, and policy optimization in imagination. Each trades off computation, robustness, and flexibility differently.
•Landmark Systems — World Models, PlaNet, Dreamer, MuZero, and recent video prediction models mark the evolution from research concepts to systems solving complex real-world tasks.
•Object-Centric Structure — Decomposing world models into object-centric representations enables compositional generalization and more interpretable dynamics.
•Robotics Applications — World models are particularly valuable for robotics, enabling simulation-based learning and safe exploration, though sim-to-real transfer remains challenging.
•Open Frontiers — Long-horizon prediction, cross-environment generalization, abstraction learning, and language integration remain fundamental challenges driving ongoing research.

What's Next:

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