Exploration for autonomous machines

Let's learn to explore the galaxy.

TopoRobotics builds the exploration layer for autonomous machines: agents that read the global shape of a world to know where they haven't looked, so learning goes where it matters instead of where it's convenient.

01 — The problem

Exploration is the unsolved bottleneck of reinforcement learning.

In sparse-reward environments, which is what the real world is, an agent that does not know how to look never finds the reward at all. Today's exploration methods treat a world as a bag of states to be counted. Humans don't. We read the shape of a space, its rooms, loops, and dead ends, what encloses what, and aim our search with it.

Robots headed into caves, under ice, or around orbital structures cannot afford to wander. Every wrong branch costs battery, tether, or Δv, and there is no reset button.

The failure is not only physical. A coding agent can degrade on a context that looks like territory its training explored all around, but never actually entered. Gaps in understanding are the same object: holes, enclosed by the explored, invisible to local signals.

ICM · curiosity baseline15/189held-out TopoGym worlds solved, despite far more compute at a matched step budget.
Go-Explore · prior best152/189the leading hard-exploration algorithm, run at one million steps per world.
TopoExplore · ours169/189our early algorithm, with none of the advanced machinery, blind to what the shapes are.

TopoGym v1 benchmark, 189 held-out worlds, 9,450 episodes measured. Full results in the forthcoming paper.

02 — The thesis

Look beyond the gradient.

Gradient descent decides how to learn. The global shape of what you have seen should decide where.

Topology formalizes what a human explorer tracks intuitively: how many separate regions there are, what is enclosed, and which loops cannot be pulled shut. It can be computed, exactly, from the space an agent moves through. An agent builds that map from its own trajectory as it goes, and every gap it discovers comes with a route it can actually retrace. That is a frontier to push, or a place to go back to.

Local geometry fills in the rest. Cheap walkability signals such as Ollivier–Ricci curvature read whether the agent is in a corridor, a junction, or an open room, long before the global shape resolves.

The same machinery over a learned latent space finds holes in an agent's understanding: enclosed, unvisited regions of knowledge worth exploring. The topology of the visited set decides where to explore next. We think this increased efficiency from better targeting is most salient for robotics, where every step is paid for and the machine has to come back.

03 — What we build

From gridworlds to a machine that comes back.

Shipped · open source

TopoGym

A Gymnasium-compatible library of exploration-training environments varied by their topology: chambers, decoys, loops, dead ends, misleading signals. Every world ships with its exact shape as the answer key, so progress on exploration is measured, not eyeballed. Same seed, same world, every time.

63 environment families in the frozen v1 benchmark. Used in a university reinforcement-learning course.

v0.3.0 · MIT · PyPI
Next · platform

TopoGym Robotics

Realistic 3D environments and generated skill ladders for simulated robots at cluster scale, built on Isaac Sim with sim-to-sim across MuJoCo and other engines. The data and evaluation plane for serious exploration-based skill acquisition, delivered through partnerships with RL labs, simulation vendors, and robotics companies.

In development
North star · research

Exploration algorithms

Algorithms that fuse latent representations with the topological structure an agent has uncovered, surfacing the relevant structure at each decision: which frontier to push, which hole to enter, which loop to stop re-searching. Certification by topology, valuation by learning.

TopoExplore, our extension of Go-Explore, is on arXiv as a preliminary report, with an ICLR submission to follow. A provisional patent covers the advanced system and its mission applications.

arXiv · 2607.09971
# every world reports its structure through one interface
env = gym.make("TopoGym/Decoys4-50-v0", seed=3)
obs, info = env.reset()
info["topology"]["betti_z2"]   # → [1, 4, 0]: one component, four enclosed regions, no cavities
04 — Where this goes

Missions where wandering is not an option.

Where the topology is literally the terrain, every entry is priced in the exit direction, and the machine must never commit to a step it cannot afford to reverse.

Under ice

A vehicle enters through a borehole. Every step of the route stays return-certified to the surface, and currents decide which entries are survivable at all.

Lava tubes

Solar-denied below the skylight, so the power budget is strictly monotone. Dropped relays extend the safe-state set. A one-way descent is terminal-class.

Subterranean

Collapsed branches, flooded sections, and long corridors that enclose nothing. Return is priced to the nearest relay, not to the entrance.

Orbital inspection

A free-flyer surveying a resident space object: occluded pockets, keep-out fences, and entries priced in Δv with egress certified before entry.

Agents

Language and coding agents look brilliant until a small gap in explored context makes them fall off a cliff. Those gaps are topological holes, and they can be found.

05 — Roadmap

From gridworlds to an exploration robot.

Adoption of the open environments is the wedge. The place you measure exploration becomes the place you train it.

Shipped

TopoGym 2D

Open-source exploration environments varied by topology. Free, MIT, in use.

Next

TopoGym Robotics

Realistic 3D robotics environments and skill ladders generated at cluster scale.

Then

The platform

Managed training and evaluation with partners, so their agents learn to explore.

North star

Our algorithms

Latent representations fused with the structure the agent has uncovered.

Endgame

Our robot

An exploration robot of our own, built on what worked in simulation.

06 — People

Shipped and working, not a roadmap.

Founder · creator of TopoGym

Jason Carlson

ML researcher. MA in Mathematics, BS in Computer Science. Formerly a software engineer at Amazon and AppLovin on production ML systems, publishing independently since 2025, and now a visiting researcher in Benjamin Rivière's robotics lab at NYU. Builds and runs everything on this page.

Collaborators & community

NYU · TopoGym contributors

Robotics collaboration with Benjamin Rivière's lab at NYU, including a proof of concept of the topological signal for dexterous manipulation. A growing contributor community around TopoGym.

Join us

If the thesis resonates, we want to hear from you.

We are a small team raising a seed round and looking for people who think about exploration, topology, world models, and robots that have to come back.

Careers Partner with us