Task-induced symmetry class of a learned representation

structures / Manifolds / Task-induced symmetry class of a learned representation

Task-induced symmetry class of a learned representation

PROPERTYdistribution-propertyadvancedhow it's classified →

Which symmetry group (invariance class) a trained agent's representation becomes invariant to is not fixed by the environment alone — it is empirically discovered to depend on the training objective. A distribution-property claim about the representation's response to input transformations, distinct from any single measured metric (curvature, dimension, anisotropy) of the representation's static shape.

Replicationcomputed from the corpus — never hand-assigned

1 paper1 architecture class1 domain1 model family

Filled = two or more values reported by papers that share no author — replication. Outlined = two or more values, but all from a single study — breadth, not replication. Grey = a single value. Derived from paper authorship and each model's architecture class, domain and family; it updates itself when a paper is added.

Definition

Given a set of transformations $T$ that act on an environment’s states (or a task’s inputs) without changing the underlying task-relevant content (e.g. relabelings of states that preserve transition dynamics, or permutations of actions that preserve reward structure), a learned representation $\phi$ is invariant to $T$ if $\phi(t \cdot x) = \phi(x)$ for all $t \in T$ . Rather than assuming invariance is dictated purely by the environment’s own symmetry group, this node covers papers that empirically discover which symmetry group a real trained network’s representation ends up invariant to, and show this choice tracks the training objective rather than being architecturally imposed or environment-determined alone.

Relative to other distribution-property nodes

Anisotropy and Dimensional collapse both measure a single static statistic of an embedding population (directional concentration, rank). This node instead measures a relational property — invariance to a specified group action — which requires comparing representations of transformed vs. untransformed inputs, not a property readable from one population of vectors alone.

Key evidence

Halvagal, Lee & Chung (2026) train real DQN (value-based) and PPO (policy-gradient) agents on real navigation tasks and use MDP-reduction theory to test which symmetry classes each agent’s learned representation is invariant to. They find the value-based method (DQN) learns representations invariant to MDP-homomorphism symmetries (states that are behaviorally equivalent under the task’s reward/transition structure), while the policy-gradient method (PPO) instead learns representations invariant to action symmetries — a discovered, not imposed, dependence of which invariance class emerges on the learning objective, consistent across domains and with measured downstream consequences for transfer learning. See halvagal-lee-chung-2026-dqn-and-ppo-agents-trained-on-the-same-real-navigation-task-develop-representations-invariant-to-different-symmetry-classes-depending-on-learning-objective.

Key papers

Halvagal, M. S., Lee, S. & Chung, S. (2026). Task-Induced Representational Invariances Depend on Learning Objective in Deep RL. arXiv:2606.01868 — origin of the MDP-homomorphism-vs-action-symmetry distinction and its measured dependence on RL algorithm choice.

Found in (1 observation · 1 family)

Custom research feedforward MLP

Task-Induced Representational Invariances Depend on Learning Objective in Deep RL (2026)measured

DQN and PPO agents trained on the same real navigation task develop representations invariant to different symmetry classes, depending on learning objective

Details

Real DQN (value-based) and PPO (policy-gradient) agents are trained on the same real navigation tasks and analyzed via MDP-reduction theory to test which symmetry classes their learned representations are invariant to [halvagal-lee-chung-2026-task-induced-representational-invariances] DQN's learned representation is invariant to MDP-homomorphism symmetries (behaviorally equivalent states under the task's reward/transition structure), while PPO's learned representation is instead invariant to action symmetries -- a discovered, algorithm-dependent difference in which symmetry group the representation collapses onto, not an architecturally imposed one [halvagal-lee-chung-2026-task-induced-representational-invariances] This objective-dependent invariance-class difference is consistent across multiple domains and has measured downstream consequences for transfer learning [halvagal-lee-chung-2026-task-induced-representational-invariances]

models: DQN navigation agent (Halvagal, Lee & Chung), PPO navigation agent (Halvagal, Lee & Chung) · method: