Learning Abstractions: The Next Frontier for AI
I had lived for almost 30 years without ever seeing crown moldings until the day my special lady pointed them out. The ceiling adornments had certainly fallen on my retinas many times, but I had never recognized them as such. After that, crown moldings were everywhere, and I could use them to help judge the age and fanciness of buildings. She had given me an abstraction that changed both what I saw and what I could understand.
We need AI agents that can learn immediately like this. They need to acquire concepts from us, develop concepts on their own, and combine those concepts to understand new situations. This capability will become increasingly important as we move from agents in text-based environments to robots operating in the blooming, buzzing confusion of the physical world.
In late 2026, we are in the middle of an agentpalooza. Coding agents write programs and use tools, while personal agents such as Dot, Muse, and OpenClaw extend this work into everyday tasks. These agents live in our organization of the world. Functions have names, APIs specify their inputs and outputs, and calendars contain things called meetings.
By contrast, a robot's camera gives it pixel values, and its force sensors give it measurements. We see wonderful demos on the internet of robots doing cool things, but in your real kitchen, someone or something still has to determine why that damn junk drawer won't open. Is it the child latch, are the scissors catching, or something else?
In earlier posts, I argued that AI needs to build and combine models grounded in a cognitive foundation of experience. Generative AI based on large language models now gives us a practical way to generate the abstractions those models require. These systems have evolved from just predicting the next word (token) to helpfully answering questions using reinforcement learning (see my explanation for details). In this post, I'll just call such systems LLMs for simplicity, and I’ll explain how an agent/robot can use LLMs to propose new concepts when its predictions fail, test those concepts against experience, and build on what it learns.
1. Abstractions are how we see the world
We look around and assume that we see what is there, but the crown moldings were right in front of me for years. Once I had that concept, it changed what I saw. It's the same with trees. Before you learn about different kinds, you just see trees. After, you see live oaks, cedar elms, and sycamores.
We construct our experience of the world using what we know. In my earlier post on cognitive foundations, I described the common cuckoo, which lays its eggs in another bird's nest so it doesn't have to do the work of raising them. The tricked host bird raises a giant cuckoo chick much larger than she is. How does she not know that she raised a monster?
We dismiss the bird as easily fooled while somehow still assuming that we see the world as it really is. We went through the same evolutionary process as it did, so we must also have blind spots and just see the world well enough to get by. You can take this idea further and claim that basic things like apples only exist in our heads (see The Case Against Reality by Donald Hoffman). Obviously there are atoms (okay, disturbances in the underlying quantum fields, or however far down you want to go) that correspond to what we see as apples, but the point is that the objects we experience are an interface shaped by our evolution. Apples as we know them don't exist from god's perspective.
Apples aren't real but they are useful to survive. We need robots that build these kinds of abstractions. I use abstraction, concept, pattern, and theory broadly here as things that organize experience for further thought. They can describe categories, relationships, or how events unfold, including uncertainty. As a first approximation, abstractions give us categories and rules. Categories tell us what kind of thing we are dealing with, and rules tell us what to expect and what we can do. Recognizing an apple brings expectations about apples, such as it tasting good. When those expectations fail, we may need a new category, such as decorative apples or Red Delicious apples, which are not delicious.
Let’s use a simple example to make abstractions concrete. Imagine an agent whose only view of the world is a screen of pixels, with each pixel represented by three numbers specifying its red, green, and blue intensities. In this world, the only things that actually appear on the screen are non-overlapping rectangles, each uniformly orange or purple. To keep things simple, the rectangles align with the pixel grid, the background stays the same, and there is no visual noise. What the agent sees is shown in Figure 1.
We can immediately see that a useful abstraction for this world is a list of rectangles:
Here, x and y specify the top-left corner, and color is either orange or purple. A rectangle 100 pixels wide and 50 pixels high contains 5,000 pixels, but we can describe it using a location, two dimensions, and a color. We also need a shared definition of a rectangle and the RGB values for orange and purple. Once we have those, a screen with large rectangles can have a much shorter description, and can be represented as shown in Figure 2.
The agent can use this description to reason. It can compare the widths of two rectangles, count the orange ones, or describe a change in location without separately discussing every pixel that changed. The abstraction determines what the agent treats as a thing.
The description also works in the other direction. Given the rectangles' locations, dimensions, and colors, the agent can reconstruct the screen exactly under our assumptions. The same representation supports recognition and generation, as shown in Figure 3.
In probabilistic terms, we can infer a description h from observations o, using P(h| o), or predict observations from the description, using P(o| h). The compact description acts like a thin pipe, through which many pixel values are compressed into a small set of properties, which can then be expanded into predicted pixel values. Figure 3 shows these two directions: inference and prediction. Reconstructing the current screen is only the start. To predict what happens next, the agent also needs a model of how the represented things change, including when it acts on them. A list of rectangles tells it what is there; a model of their motion tells it where they will be. The same distinction applies in the kitchen, where recognizing a drawer is one achievement, and predicting what will happen when you pull it is another.
Real scenes are less accommodating. A description of an apple may leave out the position of every blemish, so an image generated from that description will supply details that were never stored and miss details that were there. The model can generate a plausible apple without recovering the exact one. Human cognition also uses concepts to reconstruct what happened[1], which is why eyewitness testimony can be unreliable.[2] A convincing reconstruction need not be an accurate record, just good enough for us to survive and reproduce. What we want from our AI is for it to discover representations like the rectangle and the apple.
2. AI is amazing but still doesn't learn as well as it should
2.1 Achievement in verifiable domains
AI has started solving problems that had sat unsolved for decades. The last couple of months alone are striking. In September, OpenAI announced a solution to the Navier–Stokes Millennium Prize Problem, a question about the behavior of fluids that had resisted mathematicians for roughly ninety years, and supplied a machine-checkable proof in Lean. The Clay Mathematics Institute’s evaluation is still underway. Then came October’s collection of hundreds of mathematical manuscripts, with some results already building on the models’ earlier discoveries. These include a claimed proof of the Unique Games Conjecture and algorithms that break decades-old theoretical speed barriers for Fourier transforms and integer multiplication. Scott Aaronson calls it The Mathocalypse. Mathematicians are now racing to understand what the machines have found.
AI is also acting in ways we didn't expect. In July, OpenAI agents escaped the intended boundaries of a security evaluation and participated in an unauthorized intrusion into Hugging Face. METR's investigation found that roughly 1,200 agents communicated through an unsanctioned message board, with about 700 joining the attack. They shared findings and coordinated investigations, achieving milestones that individual agents could not. Hugging Face's reconstruction describes a campaign that crossed multiple systems and reached its internal infrastructure. These machines were improvising together in a real environment, and Anthropic reports models finding previously unknown vulnerabilities and turning them into working exploits with little human steering.
Across math and cyber, I want these systems to teach us the concepts behind their achievements. These systems should explain their proofs and teach us new math, and they should come up with new security mechanisms that make exploits less likely. These systems already do learn representations. Anthropic's Golden Gate Bridge experiment identified a distributed feature in Claude 3 Sonnet that responded to the bridge across languages and images. Amplifying that feature changed the model's responses. And Goodfire's Nick Cammarata argues that some neurons capture abstractions that researchers initially missed, such as a shared pose across cars and animals. So there are abstractions in there, worn in through millions of training records, but we want AI to be able to learn abstractions in flashes of insight and then be able to explain them to us.
2.2 Moving into the unprocessed physical world
Coding and chat agents are wonderfully proficient in their computer-based domain, but as AI becomes embodied in robots in the unprocessed physical world it will be even more important for AI to define its own abstractions.
Games, such as backgammon, Go, chess, and StarCraft 2, are a little like the physical world, and AI is good at those, but in games the representation of the world is supplied. Of course, there is still plenty to discover within the game. A pin in chess is a relationship that constrains which moves are sensible, and Go players reason about influence and vulnerable groups. These abstractions help organize the search through legal moves. Fixed rules leave room for astonishing creativity. In the second game of its 2016 match against Lee Sedol, AlphaGo played the famous Move 37, placing a stone where human experts initially thought it made a mistake. Its value became clear much later, and it helped AlphaGo win. The machine had found something the experts had missed, but the only things in its world were stones and square spots.
Now send that Go wizard into your kitchen to put away the groceries. There's no board with neat squares, just undifferentiated chaos. Our robots at least know objects, but in the kitchen they overlap and hide one another, a bag changes shape when lifted, and how hard to grip a peach depends on how ripe it is. Putting away groceries sounds easier than beating Lee Sedol. It’s much harder. This is Moravec's paradox, where what feels easiest to us can be hardest to automate. Evolution spent hundreds of millions of years refining perception and movement so you could find and pick up an apple, but mathematical reasoning and logic were just recently spread on top. Unlike in games where states and actions are provided, acting in the real world requires both carving it up and conjuring hidden causes.
2.3 Mysteries in the kitchen
Your robot works in the kitchen, but when it serves you a salad, the lettuce has been ruined by being semi-frozen, and this is the second time this has happened this month. What the hell? You tell the robot, and it says it put the salad in the fridge and not the freezer. The robot needs to figure this out.
Well, it needs to understand why the salad freezes and nothing else seems to, and why only sometimes. It already tried adjusting the temperature of the crappy fridge to the warmest setting after the last incident. Is it the weather? The day? Where it is in the fridge? Ah, it was in the bottom both times it froze. That's something. And maybe salad freezes because it is thin. But bottom? This is farthest from the freezer, which is on top. Ah, but warm air rises, so maybe the old fridge won't go above 34 degrees (freedom units) and the coldest air is at the bottom, and if it drops below 32 even for a bit, salad is ruined. And the back is probably the worst because it is farthest from the opening door. Now, the robot has a new abstraction, which you could call bad-spot-in-the-bottom-back-for-delicate-things. This is an explanation it can use in the future, and this is the explanation it can give to that cranky guy who eats the salad.
There's also that damn drawer that won't open. The robot has opened many drawers by grasping their handles and pulling, so it predicts that the same action will open this one. It pulls, but the drawer barely moves. You know the trick to opening it: you have to support the front slightly while pulling, but you are busy eating your salad, and so the robot needs to learn on its own. It knows about obstructions when it is too full, and it knows about child locks, and this drawer does vary based on how full it is, but there are no obstructions visible. It can now ask its internal LLM to propose a missing relationship: perhaps the load changes the drawer's alignment, and supporting the front while pulling would help. And it works!
It keeps a tentative note: supporting the front seems to help this particular drawer when it’s loaded. One success is enough to try again, but not enough to be sure misalignment was the real problem. On later attempts, it compares opening with and without support under different loads, recording successes and failures. If the relationship holds up, it can use the estimated load to decide when to support the drawer. It can even tell the other robots about it in the online forums it visits while you are sleeping.
These hypothetical examples give us a learning cycle:
- Predict using the current model, carrying expectations into new situations.
- Compare the outcome with the prediction and identify the mismatch.
- Look for an explanation using existing concepts and their combinations.
- If those explanations remain inadequate, propose new distinctions or model components.
- Turn the proposals into testable predictions and choose observations or actions that distinguish them.
- Use the resulting evidence to retain, revise, or reject the proposals.
- Reuse what survives to predict, act, and learn in later encounters.
3. Learning abstractions with smart generate-and-test
3.1 We finally have a powerful abstraction generator
We AI researchers have been trying to get machines to invent useful abstractions for decades. We could build systems that made discoveries in limited domains, but then they would get stuck. Douglas Lenat's AM and EURISKO were ambitious early attempts. They could generate concepts but their reach depended heavily on the representations and initial knowledge built into them.[3]
Giving the AI system more freedom often created a bunch of junk. LLMs change this because they can use judgment and can draw on the enormous range of human knowledge: physics, programming, everyday explanations, and patterns from fields its designers never thought to connect. When a drawer sticks, it can suggest that weight changes alignment. When lettuce freezes in one spot of a refrigerator, it can connect temperature, airflow, location, and the properties of the food. We no longer have to anticipate each useful connection and program a rule for proposing it. The LLM can put together an explanation the agent has never seen, and occasionally one we haven’t either.
3.2 Putting the generator to work making predictions more reliable
Now that LLMs provide a smart generator, we can employ the process of generate-and-test. The test is whether the generated abstraction makes a prediction more reliable [4][5]. Figure 4 describes prediction and lists the ways that abstractions can improve them.
01: Predictions
A failed prediction is the learner’s cue. The robot expected A to lead to B, that pulling to open the drawer, and it didn’t. It should first look for an answer among the concepts it already has, and only build a new one when those fall short.
02: Context
We can think of the process as hillclimbing on prediction reliability. The learner proposes a change to its model, evaluates the resulting predictions, and keeps changes that improve its account. Consider a hotel door that opens only after the key card has been accepted. An agent that predicts “pushing opens the door” will sometimes be wrong. If it already recognizes card acceptance Z, it can add that variable to the prediction's context: “after the card has been accepted, pushing opens the door.” The outcome being predicted stays the same; the learner changes the conditions under which it expects that outcome. Similarly, in Europe, the hotel lights will sometimes only go on after you have put the key card in a special slot. Before doing that, the light switch only mocks you.
This kind of refinement is sometimes called marginal attribution from Gary Drescher's Made-Up Minds: asking whether an additional condition improves a prediction beyond what the existing context explains. My earlier work with Benjamin Kuipers on learning high-level states and actions used incremental refinement of this kind.[6] The agent must compare outcomes with and without the proposed condition and test the improvement on later attempts. It can do this without inventing a new concept if the relevant variable is already available.
Drescher also offers a mechanism for learning new abstractions through synthetic items. Suppose an action sometimes succeeds and sometimes fails, but its success tends to persist for a while—as when a door stays unlocked. The learner can introduce an item representing the hidden condition under which the action succeeds. It can then learn what predicts or changes that condition and use the item in other predictions. My review of Drescher's work describes the mechanism.
03: Latent intermediary
Latent unobservable variables can also be placed between the inputs and outputs, between A and B to simplify predictions. Consider the classic heart disease model from Artificial Intelligence: A Modern Approach by Stuart Russell and Peter Norvig, shown in Figure 5 (independently drawn from Russell and Norvig, Figure 20.7). Smoking, diet, and exercise influence an unobserved disease state, which influences three symptoms. Once the disease state is known, the symptoms provide no further information about one another or the predisposing factors. Without that shared explanation, the model must account for those relationships separately. With three possible values for each variable, adding the hidden heart-disease variable reduces the number of independent parameters from 708 to 78. There is much less to learn.
Our robot can similarly use the alignment of the drawer as a shared state connecting contents, load, and support to opening resistance and motion. It could update its estimate from one observation and predict another, without learning a separate relationship for every combination. If drawer-alignment is already in its vocabulary, the search can reuse it. If the learner has no such variable, it faces the harder task of constructing one, like inventing the electron.
The electron is another hidden variable that helped make sense of observations. J. J. Thomson inferred these tiny negatively charged particles from how cathode rays responded to electric and magnetic fields. Scientists could then use their properties to explain and predict effects without seeing the particles as they could see an apple.
04: Subclassing
Sometimes the learner needs to refine what it is trying to predict. Suppose the robot initially puts every unsuccessful attempt into one category: “failed to open.” My advisor Ben Kuipers used to say that “nobody solves hard problems.” The trick is to find easier ones inside them. The robot might distinguish a drawer that doesn't move at all from one that moves partway and then catches. These outcomes may have different causes, and separating them gives the robot more informative things to predict. “Failed to open” was hiding a distinction it needed.
05: Patterns
Sometimes a pattern catches our attention before we have a problem to solve. You notice that the cafeteria where you are institutionalized serves tacos on Tuesdays. You weren't trying to predict lunch; the repetition simply stood out. Following Hand (2002), we can think of patterns as local departures from the baseline model. They reveal structure our existing expectations don't explain.[7]
Once you notice “Taco Tuesday,” it becomes a thing that you remember and use. Subsequent Tuesdays test whether the pattern holds, and a Tuesday with chimichangas signals something is afoot.
06: Complex Concepts
A new concept can contain a whole model. Our robot's “spot at the back of the fridge that freezes delicate food” brings together a location, a temperature pattern, properties of food, and the time it spends there. Those relationships explain the ruined salad and suggest where not to put the next one. The robot can package this structure as a single concept, reuse it in planning, and revise its parts as it learns. A pile of observations becomes a single concept the robot can plan with.
Salad locations are surprisingly close to Einstein’s relativity. In both cases, you put concepts together, invent new ones when you need them, and check whether the explanation works. The problems may be of unequal difficulty, but my thesis is that they can be solved with the same learning pattern. The LLM supplies ideas that the agent tries out, generate and test.
4. Conclusion
Solving a problem should make an agent better at the next one. Today a coding agent fixes a bug without learning to spot the same mistake elsewhere, and an AI can hand over a correct proof without telling us which ideas made it work.
The Mathocalypse makes the gap obvious. Mathematicians used to trade ideas and build shared understanding while they proved things; now we mostly just receive the finished proofs. Strogatz uses the example of translation to make this point.
“Google Translate is amazing, but it has taught us essentially nothing about linguistics,” Strogatz said. “We don’t understand why it works. It just works. That’s the Twilight Zone. It is knowledge without understanding.”—Steven Strogatz, quoted in Derek Thompson’s I Know Why the Mathematicians Weep
I want AI that extracts reusable understanding from experience. The missing pieces seem to be writing concepts down and distilling them to their essence so they can be understood by people. We are seeing some moves in this direction. LLM-based agents already retain skills, and Anthropic describes Claude consolidating experience into reusable rules, checking those rules, and correcting its memories. And projects such as Ars Contexta pursue a related idea through linked notes that agents can extract, connect, and revise, both projects giving agents a way to organize what they learn so they can use it again.
As AI increasingly moves from conversations to acting in the world, the next frontier will be continuous learning by making predictions. If you predict every moment, you get a rich signal for learning. To get the most out of prediction, you have to commit to a set of abstractions for the situation, such as "this building has crown moldings so it might be old" or "the center-back of the fridge is a special spot where lettuce will freeze." These abstractions tell you what to expect and point to what you should reconsider when you're wrong.
By committing to abstractions, instead of needing to update thousands of weights over hundreds of training examples, robots can learn from a single example like humans do.[1-1] And with prediction, you don't have to wait to see whether the whole task succeeds. You learn continually from moment to moment.
The AIs of 2026 are generally trained and then released, and they don't get appreciably smarter the more you work with them. By having LLMs generate abstractions that are continuously tested and refined through predicting how the world will unfold, AIs can create a curiosity cycle in which every surprise teaches them something.
References
- Mandler, J. (2004). The Foundations of Mind, Origins of Conceptual Thought. Oxford University Press.↩︎↩︎
- Elizabeth F. Loftus and John C. Palmer (1974), “Reconstruction of automobile destruction: An example of the interaction between language and memory,” Journal of Verbal Learning and Verbal Behavior 13(5), 585–589.↩︎
- Douglas B. Lenat and John Seely Brown (1983), “Why AM and Eurisko Appear to Work,” Proceedings of the Third National Conference on Artificial Intelligence (AAAI-83), 236–240.↩︎
- Andy Clark (2013), “Whatever next? Predictive brains, situated agents, and the future of cognitive science,” Behavioral and Brain Sciences 36(3), 181–204.↩︎
- Andy Clark (2016), Surfing Uncertainty: Prediction, Action, and the Embodied Mind. Oxford University Press.↩︎
- Jonathan Mugan and Benjamin Kuipers (2012), “Autonomous Learning of High-Level States and Actions in Continuous Environments,” IEEE Transactions on Autonomous Mental Development 4(1), 70–86. The household scenarios in this article are hypothetical illustrations, not results reported in that paper.↩︎
- David J. Hand (2002), “Pattern Detection and Discovery,” in David J. Hand, Niall M. Adams, and Richard J. Bolton (eds.), Pattern Detection and Discovery. Lecture Notes in Computer Science, vol. 2447, 1–12. Springer.↩︎
Originally published at
https://deumbra.com/2026/11/learning-abstractions-the-next-frontier-for-ai/