Generalization by Construction

Solution inference leaves the learned model fixed while keeping the candidate open. Learning specifies what makes a candidate good without fixing the candidate itself. A direct predictor has to learn both what makes an answer appropriate and a fixed computation for producing it. An energy function or learned evaluator separates these roles: the model scores proposed answers, while a sampler or optimizer constructs one that scores well. The important property is not stochasticity or iteration by itself. The candidate must remain an explicit object of inference—sampled, compared, or revised under the fixed model—rather than being fixed by a single learned input–output pass. An externally supplied proposal can initialize that search; adding a separately addressable constraint or evaluator changes the model and crosses into model composition.

Holding the task model fixed, the robot can search over candidate placements and revise one that is unstable or difficult for the person to reach rather than accept its first proposal. For some problems, learning to judge such a candidate may be easier than learning to produce a correct one in a single pass. A graded criterion can also indicate how the candidate should change. Learning builds a landscape that distinguishes better from worse solutions; inference searches it.

We first explored this separation in Implicit Generation and Generalization in Energy-Based Models. The learned object was a landscape rather than a fixed generator: Langevin dynamics, an iterative stochastic sampler, could search it without imposing a fixed generation order. The sampler could also start from an external proposal or run for different numbers of steps. Learning Iterative Reasoning through Energy Minimization then treated reasoning itself as minimization over a conditional landscape. Its verifier-generator analysis makes the tradeoff explicit: a criterion for recognizing a valid solution can be smaller than a procedure that constructs one, although the resulting search may still be hard.

Subsequent work asks what geometry makes this separation useful in practice. Learning Iterative Reasoning through Energy Diffusion moves through a sequence of landscapes, from broad, smooth basins toward sharper constraints. Reasoning with Sampling applies the same separation to a frozen language model, using its likelihood as the target of an iterative sampler that can revisit earlier choices. These settings differ, but they pose the same question: which learned representation makes revisable inference reliable?

Solution inference searches for a candidate under a fixed model. Model composition changes the model that defines this search. The current task determines which pieces of learned knowledge—such as a relation, goal, physical constraint, or reward—should constrain the answer. Inference selects, composes, or infers these factors. What composition produces is not yet an answer, but a problem-specific criterion or distribution that solution inference can search. A new task need not be reduced to an input for a monolithic predictor; it can become a new inference problem assembled from reusable knowledge.

The task model used to judge those placements need not be learned as a whole for this exact kitchen scene. The robot can construct it by combining learned factors for keeping the mug upright, avoiding nearby dishes, resting it securely on the table, and leaving it within the person's reach. The complete arrangement is globally unfamiliar, but each factor expresses locally familiar structure. Generalization comes from constructing a new global model from these reusable local judgments, not from asking one model to extrapolate across the entire combination at once.

Symbolic systems obtained much of their flexibility by composing reusable predicates and operators. The aim is not to recover a particular symbolic vocabulary, but the operational separation these systems exploited: reusable pieces remain addressable after the task is known, while their continuous semantics can be learned from data. The components need not share an architecture or modality, but they must agree on the object being constructed, how each component can evaluate or guide it, and an inference procedure capable of reconciling their constraints.

Our early visual work began by composing learned concept distributions through conjunction, disjunction, and negation. It then moved from assembling named spatial relations to combining independently trained score models during denoising. Iterative consensus broadened the same idea beyond a common architecture: a generator and independently trained vision, language, or task-specific scorers communicate through a shared candidate.

A compositional system must also learn the pieces it will later reuse. Unsupervised Learning of Compositional Energy Concepts discovers reusable factors without concept labels, while Few-Shot Task Learning through Inverse Generative Modeling infers a new task factor from demonstrations without changing the pretrained generator. Learning therefore need not determine the final task model in advance; it can instead produce a vocabulary of factors whose selection and combination remain open. Once learned, a new factor should compose with earlier factors without retraining them, enlarging the family of tasks the system can construct.

Composition must be grounded and matched to an inference procedure. Set It Up! uses a symbolic relation graph to select learned continuous factors and ground them into object poses. Reduce, Reuse, Recycle shows why the solver cannot be treated as an afterthought: standard reverse diffusion need not realize the product distribution implied by composed scores. Generalizable Reasoning through Compositional Energy Minimization carries the same principle into reasoning, where local learned criteria become reusable verifiers inside a larger problem. The factors, their interface, and the procedure that reconciles them must therefore be designed together.

Decision making is a particularly important instance of model composition. A model of the desired future represents what outcomes matter; action-conditioned dynamics represent what proposed interventions could cause. Both sides can themselves be composed: dynamics from reusable models of objects, agents, and interactions, and objectives from goals, rewards, and constraints. Model composition brings these pieces together to define the decision problem. Action planning then searches for interventions whose predicted consequences reach the desired outcome.

Composing a desired outcome with a model of what can happen defines a decision problem, but it does not yet determine the actions an agent should take to reach the outcome. In the coffee task, the robot must still choose a grasp, lift clear of nearby dishes, carry the mug without spilling, and place it at the selected location. Through planning, we infer the action sequence to execute. The planner compares the predicted consequences of possible actions until it finds an action sequence expected to reach the desired state.

A direct policy instead compiles the use of dynamics and objectives into a mapping from observations and goals to actions. This makes action selection efficient, but commits in advance to how the agent will use its knowledge. Such a policy can generalize when a new situation is covered by regularities captured in the learned mapping. When the situation demands a combination the mapping does not support, however, the policy itself exposes neither queryable dynamics nor a search process with which to construct a new behavior. The distinction is therefore not policy versus planning as permanent alternatives, but which decisions should be compiled and which must remain open.

Planning does not always operate directly on individual motor commands. It can search over subgoals, intermediate states, or complete trajectories, depending on what must be decided for the current task. Model-Based Planning with Energy-Based Models inferred intermediate states under learned dynamics, allowing a planner to route around obstacles not encountered during training. Planning with Diffusion for Flexible Behavior Synthesis instead represented complete state-action trajectories as a generative solution space, so new rewards, endpoints, or constraints could guide the same learned model. In both cases, learning captures what recurs across tasks while search resolves the route required by the task at hand.

Predictive control repeats this search as the world changes. Flexible Locomotion Learning with Diffusion Model Predictive Control combines a learned trajectory prior with new rewards and constraints, while Model-Based Diffusion Sampling for Predictive Control in Offline Decision Making composes a task planner with action-conditioned dynamics so that task-aligned trajectories remain feasible.

For longer-horizon tasks, video provides an intermediate representation between a high-level goal and low-level control. It can represent what should happen in the scene while leaving an embodiment-specific model to determine how a particular robot makes it happen. Learning Universal Policies via Text-Guided Video Generation learns a task-level visual trajectory that can serve as a proposal from which actions are extracted. Video Language Planning shows how search can compare and connect such proposals into longer-horizon plans. Video is useful because it exposes an intermediate future that subsequent search or control can compare, extend, reject, or re-ground before execution.

Different models can also divide the problem across levels of abstraction. Compositional Foundation Models for Hierarchical Planning uses language to propose high-level steps, video to ground them in a scene, and an action model to test their physical executability. Planning becomes a search for a course of action supported at every level. This is how planning grows out of model composition: the components provide complementary views of the same evolving future.

World Action Planner makes the separation between action proposal, consequence prediction, and search explicit. A vision-language model proposes actions, an action-conditioned world model predicts their consequences, and global correction and local search revise the proposal for the current task. The same verification–generation separation that motivates solution inference therefore reappears over time: judging whether an imagined consequence makes progress can be easier than generating the entire successful behavior at once. Perceptual realism alone is not enough; a planning world model must preserve the distinctions that change a decision, including controllability, contact, object persistence, and progress toward the goal.

Planning and policy can therefore occupy different points on a moving amortization boundary. Unfamiliar behavior can initially be constructed through search; behavior that recurs can later be compiled into a reusable policy or skill. Once the robot begins executing a plan, however, the world may still depart from its predictions: the mug may shift in its grasp or a dish may block the route. The planner can use the resulting state to search again rather than continue an obsolete action sequence. Replanning changes the action sequence, but it may still use the same search procedure each time.

The first three scopes leave an object of inference open—a candidate, a task model, or a course of action—but may still run a fixed outer procedure. The same construction principle can be applied to that procedure. The need to replan, for example, raises a further question: what part of the current computation should be preserved, and what should run next? Procedure control leaves this next reasoning operation open. It does not require inventing a new algorithm at test time; the outer controller may remain fixed. What remains unresolved is which member of an explicit repertoire—sample, expand, verify, repair, switch methods, or stop—should be applied next to the current reasoning state, and how much computation it deserves. If every problem receives the same solver for a preset number of steps, only the object is being inferred; the procedure remains fixed.

Temporal Backtracking Search for Test-time Generative Video Reasoning makes this distinction concrete for generative video. The video model is trained to resume from an arbitrary valid prefix. After each rollout, a process verifier localizes the first failure, identifies a safe restart point, and ranks the surviving prefixes. The outer generate–verify–restart loop remains fixed, but evidence from the current rollout determines where generation resumes, which prefix receives the next computation, and whether search stops. This kind of procedure control is possible because the model exposes the intermediate state that the controller needs to preserve and revise.

Procedure control must also decide how much of an existing solution to preserve and how much computation the situation permits. Adaptive Online Replanning with Diffusion Models uses evidence from execution to choose whether a plan should be retained, repaired, or regenerated. Win Fast or Lose Slow dynamically selects model size and quantization according to real-time demands, showing that the best procedure depends on the cost of delay as well as answer quality. A controller therefore needs signals about both what can be recovered and how much time the current problem allows.

For the robot, this means that a poor view of the mug or a slight shift in its grasp need not trigger a complete restart. The controller may move the camera, resample the grasp, check that the mug is still upright, repair only the affected part of the plan, switch methods, or stop deliberating and continue.

Procedure control assumes that the sources of knowledge available to the system are already fixed. When the next computation also depends on which differentiated generator, verifier, or specialist participates and how their outputs are connected, the organization itself remains open.

Learning can create a population of reasoners with different knowledge, tools, local state, and procedures. Reasoner organization leaves open how those members are assembled for the current problem: who participates, what roles they play, and how their outputs are connected.

Procedure control asks what operation the available system should run next. Reasoner organization asks which differentiated sources should contribute and how their outputs should be connected. Running the same verifier again changes the procedure; adding or replacing a verifier changes the organization because it changes the evidence brought to bear. Running several copies of the same model and voting does not cross this boundary, nor does packaging a scorer or solver as an “agent.”

Changing the procedure is not always enough: if the robot encounters an unfamiliar, fragile mug and lacks a reliable model of safe contact, another search step cannot supply that knowledge. It can consult a grasp specialist, pass the proposed contact geometry to the motion planner, and invoke a perception specialist if additional visual evidence is needed.

Earlier work established the value of multiple reasoners while keeping their organization fixed. Multiagent Debate made identical model instances expose and challenge one another's reasoning through a fixed interaction pattern. Multi-Agent Verification combined a fixed, domain-specific set of aspect verifiers whose different prompts, strategies, or base models supplied complementary judgments. These systems expose organizational variables—who participates, what each reasoner checks, and how their outputs are combined—even though those choices remain fixed within a deployment.

SLM-MUX makes group composition an explicit design variable. It searches before deployment for a complementary subset of small language models. The selected group remains fixed across test problems within a benchmark, but the result shows why choosing complementary participants can matter more than simply adding more interaction.

Multiagent Finetuning asks how learning can create useful differences among reasoners. Starting from the same base model, separate generation and critic agents are fine-tuned on distinct data produced through multiagent interaction. This preserves diverse reasoning chains across repeated rounds of self-improvement. Its participant set and debate protocol remain fixed at test time; its contribution here is to learn the differentiated population that organization can later draw upon.

Economy of Minds makes the organization itself adaptive. At each step, eligible agents compete for the right to act, producing a problem-dependent sequence of specialists without a central scheduler. Over longer timescales, wealth, bankruptcy, and mutation reshape the population according to the downstream value its members create.