Why Information Has a Price in Intelligence - Alexander Mattick
Summary
Mattick’s central caution is that better prediction does not by itself remove the need for search, action selection, or guarantees—the capabilities that turn a predictor into an intelligent decision-maker. A perfect world model of chess still would not tell you how to beat Magnus Carlsen: “There’s a difference between being able to predict the future and being able to make inferences about the correct action to take.” For investors, better generative video or robot demonstrations are therefore evidence of stronger prediction, not yet proof of autonomous intelligence.
The generative-model stack has moved the expensive work from inference into training: energy-based models leave normalization to MCMC, diffusion amortizes a reversible noising process, and flow matching learns a chosen transport path as supervised regression. Mattick’s economic test is sharper than the usual generative/non-generative taxonomy: “The question is not whether they can do it, it’s whether it’s economical to do it.” His strongly stated view is that, outside niches such as physical energy functions, cheap pairwise ratios, or possible pretraining uses, energy-based modeling is “not really useful, or at least not useful anymore.”
Flow matching is useful wherever companies want language-model-like scale in continuous domains such as images, audio, video, and physical trajectories. Language comes with a natural token-by-token factorization; continuous data does not, so diffusion and flows decompose the problem through latent time, moving from noise toward the whole output rather than left to right. The trade-off is operational: flow paths can be shaped for easier sampling, but more denoising steps are not automatically better—twenty-five versus one hundred and fifty steps can turn useful refinement into visibly “overcooked” detail.
Constraints are economically valuable prior information, not an embarrassment to be hidden inside a reward function. Mattick rejects the practical version of “reward is enough” because “most information is very, very expensive”; forcing an agent to relearn knowledge already acquired through “blood, sweat and tears” wastes data, compute, and real-world trials. OpenAI Five’s hand-tuned table of reward weights is his specimen: wrong-lane behavior was effectively a constraint, while hero kills required a negative reward because gold already rewarded the same event.
Explicit constrained reinforcement learning offers clearer engineering interfaces and better composability, although it does not magically guarantee safety. Engineers can state that a load will break a robot or that a district-heating pipe must never burst more naturally than they can tune penalty coefficients; constraints also avoid retuning an entire reward when correlated bonuses are added. Yet expected-cost constraints can conceal fat tails, projection methods can hallucinate barriers, and Lagrangian methods oscillate around boundaries—so the practical differentiator is reliable constraint estimation and enforcement, not simply adding a safety objective.
Current deep-learning theory remains too fragmented to predict failures reliably, and Mattick favors functional or mean-field views over parameter-by-parameter explanations. At very large scale, he argues, networks behave more like evolving function spaces than collections of individually meaningful weights; this makes overparameterization less paradoxical and architecture less fundamental than scaling efficiency. His standard for progress is falsification: if a continuation of existing work can conceal an implementation bug for “two or three months,” theory has not yet become an engineering-grade instrument.
World models and JEPA are, in Mattick’s telling, broad brands rather than clearly bounded technical breakthroughs. A “world model” may mean a sensor predictor, video diffusion model, latent dynamics model, or model-based RL component; his proposed boundary is whether data collection remains inside the learning loop. The commercial test comes at deployment: a robot that succeeds ninety percent of the time may make a compelling demo, but a factory buyer such as BMW needs repeatability, minimum per-state reliability, and failure consequences far below “the concept of deleting your computer would be to crush someone.”
Deep dive
1. Most deep learning is already inference
Mattick pushes back on the premise that ordinary machine learning produces mere point estimates. An autoregressive language model factorizes a density over complete sentences into categorical token predictions; even mean-squared-error regression is the negative log-likelihood of the data under a normal distribution with a fixed standard deviation.
The benefit of retaining the density’s breadth is that a system can reason about alternatives rather than report only its favorite action. In reinforcement learning, Mattick contrasts a Q-learner’s point recommendation with policy-gradient methods that can preserve uncertainty, enabling tactical exploration of an action that “might be slightly worse but ends up being better in the long run.”
What counts as a “good” density depends on the use. A generative image model needs high likelihood around real or prompt-consistent images; a statistician may instead want a posterior that distinguishes a fair coin from one that lands on tails. Priors supply the interpolation rule between finite observations—without one, “the exact solution would be just memorize the data.”
2. Classical inference traded expressive power for crushing sampling costs
The earliest convenient approach was to choose parameterized distributions that remain normalized for every parameter value. That makes fitting tractable but constrains the answer: placing one normal distribution over two separated modes puts probability mass in the empty middle, “kind of try[ing] to split the difference.”
Rejection sampling removes some functional restrictions by placing an envelope around the target, like estimating π by scattering points across a square containing a circle. It does not scale well in high dimensions because most proposals are rejected; MCMC improves the framing but remains slow when chains become trapped in modes and repeatedly perform work “that doesn’t end up going anywhere.”
Tim Scarfe’s GFlowNet challenge produces a narrower concession. A GFlowNet can construct samples through a graph, amplifying paths toward greater terminal reward while balancing inflow and outflow, but it assumes the construction structure is correct. That can fit molecular assembly; Mattick does not regard it as a general replacement for unrestricted inference.
3. Energy-based models are theoretically generative but economically awkward
Energy-based models inherit their language from statistical physics: low-energy states are favored, while the learned energy acts as an unnormalized density. Their flexibility comes from postponing normalization, but sample generation then requires expensive MCMC, repeatedly paying at inference for work that diffusion-style systems amortize during training.
Mattick rejects LeCun’s description of EBMs as non-generative in a literal sense. Give an ideal energy function to an MCMC sampler and it will generate data; the operative distinction is cost. “The question is not whether they can do it, it’s whether it’s economical to do it,” and for EBMs it usually is not.
Relative comparisons remain the clearest niche. The unknown normalization constant cancels when comparing two observations, so an EBM can cheaply determine that one is more likely than another. But it cannot readily provide an absolute judgment—the result resembles saying a movie is “a five” without specifying whether that means five out of five, ten, or one hundred.
Mattick’s strongly stated verdict is that energy-based models are “not really useful, or at least not useful anymore,” except where an energy-like quantity already exists, ratios suffice, or the model serves as a possible pre-training objective. Deep learning complicates the verdict because bad formulations often degrade gracefully rather than fail; even his own implementation bug “still kind of worked.”
4. Diffusion replaces accept-reject sampling with a learned reversible path
Mattick describes latent variables as computational power: conditioning on enough intermediate states can split an intractable density into simpler local problems. Diffusion takes that idea toward an effectively infinite sequence of latents, replacing MCMC’s rejected proposals and mode-hopping with a smooth Markov process indexed by synthetic time.
Training repeatedly corrupts a real sample with normal noise, then teaches the model to reverse an individual corruption step. At inference, the process begins with normal noise and follows the learned vector field backward. Because this corresponds to a reversible stochastic differential equation, likelihood can also be recovered by following a target sample toward noise and accumulating divergence.
The price is the extra time variable and many small denoising problems during training. Mattick considers that favorable because it is predominantly a one-time training expense, while inference follows a vector field that sophisticated ODE solvers can accelerate, rather than rerunning an expensive normalization procedure for every generated sample.
Normalizing flows attack the same problem through invertible reparameterization: transform a known base measure into the target and track local expansion through the Jacobian. Continuous normalizing flows loosen architectural invertibility by learning a vector field whose path is itself reversible—“instead of going downhill, you just go back uphill.”
5. Flow matching fixes the route so learning becomes supervised regression
Flow matching sits between diffusion and continuous normalizing flows. Rather than solve a full ODE during every maximum-likelihood update, it selects a reference coupling—perhaps a straight line between a base sample and a real sample—and trains a model to reproduce the known local directions along that route.
Fixing the path yields two advantages. Every intermediate point supplies a supervision target without simulating the entire trajectory, and the designer can choose sampling-friendly geometry: straight paths are generally easier to integrate than highly nonlinear ones. Mattick’s summary is “all the flexibility of normalizing flows” with diffusion-like training and sampling properties.
Diffusion appears in this framing as a special reference flow whose noising process implicitly defines the path and aims to minimize KL divergence. Its vector field depends on the evolving density, which partly explains why training can be awkward; flow matching removes that self-coupling by specifying the reference direction in advance.
Mattick’s distinction is that a naive normalizing-flow transformation must be invertible, while the neural function producing a continuous-flow vector field need not itself be invertible. In the continuous-flow formulation, the trajectory supplies the reversible route: follow the same path backward.
6. Continuous modalities need a different decomposition from language
Language has a naturally discrete left-to-right factorization: predict a token, condition on it, and repeat. Images, audio, video, and physical trajectories can be forced into discrete tokens “by basically hitting [them] with a hammer long enough,” but autoregression is not necessarily their natural density decomposition.
Diffusion instead decomposes continuous data “from bottom to top”: begin with every variable present but corrupted, then progressively restore the complete object. Flow matching supplies the same general latent-space decomposition; Mattick notes that systems presented as diffusion often contain flow matching because it can be more stable, including the Voxtral example Tim raises.
Discussing the third version of AlphaFold, Tim points to large molecular structure appearing before fine detail. Mattick considers coarse-to-fine emergence plausible but not mathematically mandatory: small later steps cannot easily reconstruct missing global structure, so “sane models” will likely learn it first. A contrary ordering might work, but could require “thousands of times more parameters.”
More iterations do not guarantee a better sample. Tim’s Stable Diffusion example contrasts twenty-five and one hundred and fifty steps: excessive refinement can produce unnatural micro-detail. Mattick treats this as a property of what happens to be easy for the model, rather than an intrinsic requirement of diffusion.
7. JEPA is too broad a label to identify a distinct mechanism
Joint Embedding Predictive Architecture can, in Mattick’s view, “describe literally anything” beyond loosely indicating a non-contrastive objective. He prefers DINO-style embeddings to JEPA-style embeddings in his own experiments, while conceding that the comparison is slippery: if DINO appeared now, its advocates could plausibly call it a JEPA.
Contrastive systems such as SimCLR pull augmented views together and push batch examples apart. The weakness is a moving, batch-dependent target with many mathematically acceptable but useless configurations; SimCLR becomes effective only with huge batches, while MoCo approximates those batches with a momentum-maintained buffer.
Mattick agrees with LeCun that contrast alone is not a sufficiently strong learning principle. Variational autoencoders, DINO, VICReg, and JEPA-like approaches instead seek compact or non-collapsed embeddings. He highlights Ledger-style methods more specifically as using statistical tests against a fixed reference density: the target is stable rather than defined by the current batch, with a repulsive effect if points crowd the reference mode.
8. Structured inference grows with the problem instead of compressing it once
“Inference” is overloaded across logic, Bayes, and model execution, but Mattick retains a useful common denominator: break a large problem into conditional dependencies and marginalizations. That view captures autoregressive generation, diffusion trajectories, tree search, and agents that acquire evidence before updating the next decision.
In his mixed-integer-programming work, branch-and-bound becomes a probabilistic path. Each left-or-right branching choice contributes a conditional probability, and the probability of reaching a leaf composes those local decisions. As the optimization tree expands to thousands of open nodes, the inference procedure expands with it and absorbs the additional structure.
This is also Mattick’s proposed mental model for agents: research gathers data, incorporates it into the current conditional belief, and lets the next action depend on that enlarged information set. He thinks “all these agentic things” could gain structure from treating tool use as Bayesian updating rather than undifferentiated test-time computation.
Q-learning supplies the counterpoint. It learns current reward plus the future value—the “head” and “tail”—so action can again be greedy with respect to long-run return. SARSA backs up the action actually taken; Q-learning backs up the estimated optimal next action, thereby learning toward Q-star but introducing a counterfactual gap between the experienced and imagined trajectories.
9. Architecture matters mainly through scaling efficiency
At billion-parameter scale, Mattick doubts that architectural distinctions matter as fundamentally as practitioners suppose. Inputs must still fit the model—a fixed-input MLP cannot simply impersonate an open-ended language model—but sufficiently large networks behave less like specific parameterizations and more like function spaces.
His analogy is fluid mechanics: nobody tracks “billions, cajillions” of individual hydrogen molecules to model a stream; Navier–Stokes describes the bulk. Mean-field analysis similarly treats parameter populations statistically, because the movement of any one weight has little meaning compared with the evolution of the whole field.
Architecture still determines how efficiently that limit is approached. One design may need one billion parameters where another needs one hundred billion, just as a deep network may scale more gracefully than an extremely wide shallow one. Mattick therefore declines to prescribe a supposedly ideal diffusion architecture: “I don’t think it matters” beyond information flow and scaling cost.
10. Functional theories explain overparameterization better than parameter counting
The parametric view treats a neural network as a giant nonlinear program and asks about convergence, global optima, linear regions, or local geometry. Spline theory and related combinatorial approaches can illuminate architecture-specific details; Mattick likes, for example, an explanation of batch normalization as concentrating things in the middle and changing how the hyperplanes are distributed.
The limitation is that individual parameters lose explanatory force at scale. Mean-field theory replaces a finite hidden layer with a density over an effectively infinite population of feature tests, allowing training to be analyzed as movement of a distribution. Neural tangent kernels simplify further by describing learning directly in function space.
A stationary neural tangent kernel captures “lazy” learning but misses evolving representations. Letting the kernel itself change connects the theory to mean-field feature learning, though analysis becomes much harder: one must track both the current local function and the dynamics of the function space used to express it.
Function-space analysis makes overparameterization less mysterious. A billion-parameter model is not merely a dangerously bloated finite program; it may be closer to the relevant infinite function class than a fifty-parameter approximation. The framing also survives architectural turnover from ReLU splines to gated activations or from transformers to MLP-Mixers.
11. A useful theory must survive contact with experiments
Mattick is pluralistic about mathematical style: a parametric, geometric, computability, statistical-physics, or functional account earns its place if it makes correct predictions. His objection is that theory papers too rarely attempt falsification—“you go and you actually check whether the test works” and identify precisely where the explanation breaks.
Real data prevents the complete guarantees available for Gaussian mixtures or kernels under known source and capacity conditions. Researchers rarely know the target function’s true structure, so Mattick favors a physics-to-engineering loop: approximate the solvable parts, predict a real system, test the result, and revise the theory rather than assuming the real world is fully captured by idealized “spherical cows.”
He offers his own two-or-three-month implementation bug as an indictment. If an extension of existing research can appear successful while implemented incorrectly, the field cannot reliably distinguish theoretical failure from software error. Parametric theory, functional theory, and mechanistic interpretability all currently fall short of that diagnostic standard.
Fragmentation compounds the problem. Barron’s dimension-free bound already explains why complexity can depend on a target’s frequency structure rather than ambient dimension—a high-dimensional constant can be easier than a two-dimensional heartbeat. Yet conference incentives reward incremental papers across three or four annual cycles, not a durable “standard model” likely to remain current through an entire PhD.
12. Manifold pictures are beautiful but not yet operational explanations
Tim contrasts Randall Balestriero’s input-sensitive “honeycomb” regions, where a small perturbation can teleport an example elsewhere, with Goodfire’s PCA projections of days, months, and geography into clean curves. The latter suggests models converge on geometric invariants; the former resists a simple low-dimensional-manifold story.
Mattick grants that some compressible structure must exist: if reality were already its own smallest description, modeling would accomplish nothing. But he thinks “the manifold hypothesis” is too blunt to adjudicate what that structure is, while current interpretability methods are too fragile to prove or disprove it.
Transformer-circuit analyses often assume routing remains stable under changes that may actually alter it, and small experimental variations can reverse conclusions. The grokking work extracting sine-and-cosine algorithms for modular arithmetic is among his favorite interpretability results, yet it exposes the gap: even a perfect account of modular arithmetic offers no language for how a network represents “a duck.”
Pure functional analysis also idealizes away finite size, while pure spline analysis risks mistaking local partitions for the complete computation. Mattick’s deliberately unsatisfying conclusion is that the manifold hypothesis is neither clearly true nor false—and “even if it’s true, I don’t think it’s a useful way of thinking about the problem.”
13. “Reward is enough” is true only as a formal tautology
Any objective can technically become a reward. Given the solution X-star to an enormous mixed-integer nonlinear program, one can minimize the distance between X and X-star, turning the original problem into a trivial convex objective. That proves representability, not that anyone can discover or optimize the required reward.
Mattick understands Sutton’s stronger claim as optimism that an adequate reward exists for every task and that sufficiently capable maximization could make other machinery obsolete. He hedges his attribution—“I’m not sure how far he himself would be going with this”—but rejects the practical premise and doubts it even as a useful infinite-limit ideal.
Control theory clarifies what RL has discarded. A controller begins with a plant model, response estimate, or human-designed structure; reinforcement learning begins with interaction and must discover both how the environment works and what actions produce long-run return. That generality is powerful, but it internalizes exploration rather than eliminating its cost.
Expected success is also weaker than worst-case safety. A controller can perform perfectly on average while containing one catastrophic trajectory where “the robot clocks you on the head.” Mattick cites a result he recalls as roughly “training deep neural networks to uniform accuracy is intractable”: enforcing maximum-error guarantees may require data exponential in the number of parameters.
14. Prior information is too expensive to throw away
Tim’s defense of constraints begins with RLVR: a base language model already possesses enough conceptual knowledge to search meaningfully rather than wander like an uninitialized deep Q-network. How the search space is shaped is therefore part of the capability, not an impurity layered on top of a supposedly general learner.
Mattick’s applied Fraunhofer experience makes the cost concrete: “Most information is very, very expensive.” A system that refuses constraints must relearn knowledge already purchased with “blood, sweat and tears,” even when engineers possess reliable physical, operational, or historical information before the first new trial.
Industrial reward functions quietly admit this. Penalties for prohibited states are constraints written in a different column, accompanied by hand-tuned coefficients. Mattick’s canonical example is OpenAI Five’s appendix: a large table of gameplay attributes and “a bunch of random numbers” used as reward weights, with no plausible systematic way to derive the complete combination.
Correlation makes those weights brittle. Being in the wrong lane for too long is naturally a constraint; killing an enemy hero received negative reward because the resulting gold was already rewarded. Without that correction, the agent could farm kills in the middle indefinitely instead of winning—two correlated bonuses had transformed guidance into a loophole.
15. Constrained RL offers several guarantees, none without failure modes
In a constrained Markov decision process, the agent maximizes cumulative reward while keeping expected cumulative cost below a threshold. Expectation can hide dangerous tails: fifty trajectories costing zero and fifty costing fifty satisfy an average-cost limit of twenty-five, even though half the runs violate the intuitive safety requirement badly.
Alternatives target different risk concepts. Conditional value at risk emphasizes the severity and probability of tail outcomes; percentile constraints might demand compliance with ninety-nine percent probability. Mattick’s district-heating example requires something stronger still: pipes should not burst, rather than merely remaining intact on average.
CPO adapts TRPO-style performance bounds to costs, but recovery becomes awkward once a policy begins outside the feasible set, encouraging oscillation around the boundary. Projection methods estimate a feasible surface and map policies back onto it; an erroneously learned constraint can instead create a hallucinated barrier that an increasingly competent optimizer becomes increasingly unwilling to cross.
Lagrangian approaches exploit zero duality gap but tend to alternate between excessive caution and violation as the multiplier rises and falls; PID-style tuning moderates rather than removes this behavior. Local methods such as CBPO or FOCOPS can be precise, while Safe-MPO-style approximations risk batches whose subproblem is infeasible. Model-based variants inherit constrained MPC’s dependence on model fidelity.
16. Explicit constraints buy communication and composability
The first cash value is legibility. An engineer can state that a certain load will break a robot before performing the experiment; asking that engineer to express the same knowledge as a globally correct penalty coefficient is both less natural and more likely to admit accidental threshold violations.
The second is composability. Reward weights are relative, so adding a gold bonus can invalidate the old weight for hero kills and force system-wide retuning. A constraint such as maintaining an acceptable kill deficit has a target of its own; in a Lagrangian formulation, the multiplier can adjust automatically to enforce that target.
Some constraints belong directly in the architecture: mask impossible actions, project controls into a valid range, or scale outputs to actuator limits. State-dependent environmental constraints are harder because feasibility depends jointly on policy and world state; general constraint-satisfaction problems can be NP-hard, ruling out a universal static architectural trick.
Fairly proving that constraints improve learning is itself difficult. Constrained problems are mathematically harder and may require stationary stochastic or non-stationary deterministic policies where ordinary Q-learning is insufficient. But comparing against an unconstrained reward encoding biases the experiment too, because designing a reward that exactly reproduces the same feasible task may already require solving the constraint problem.
17. Abstraction works only when lower levels make enforceable promises
Tim’s “reality is protean” framing suggests low-level representations should remain flexible because interaction changes the world, while higher abstractions preserve more stable invariants. Mattick translates that into an interface condition: a lower layer must guarantee something its upper layer can safely rely upon, without prescribing every detail of the lower layer’s implementation.
He sees the absence of such guarantees as a reason hierarchical reinforcement learning never fully took off. Control can provide strong worst-case commitments, including H-infinity-style robustness; an RL subpolicy may simply “do whatever,” leaving the higher-level planner without a dependable contract on which to build.
Every abstraction is constrained from two directions: the layer below supplies capability, and the layer above supplies need—“a robot needs to not crush you.” Even casual appeals to universal approximation play this role, though Mattick notes that most people invoking the theorem have not read what it actually guarantees.
Useful abstractions survive because someone adopts them and they work, not because every candidate is discovered or historically inevitable. Mattick offers fuzzy logic as a discarded alternative for uncertain decisions: probability and Bayesian inference proved more reusable partly because Bayesian methods can themselves infer Bayesian models. Other valuable abstractions may simply never meet the right user.
18. World-model demos do not yet meet the standard for intelligence
“World model” is as overloaded as JEPA: it can mean a tactile sensor predictor, robot dynamics model, video diffusion system, latent-state predictor, the newer Dreamer setup trained on Minecraft video, or ordinary model-based RL. Mattick’s personal boundary is procedural—data gathering inside the loop makes it model-based RL; fixed offline training makes it a world model.
He calls both JEPA and world models “ultimately branding.” Their shared core is a dynamics model predicting the next state from the previous state and an action, something researchers did long before the current terminology. NVIDIA’s Cosmos 3 Omni and similar systems may be powerful foundations, but the category name does not establish a new mechanism.
Nor can a dynamics model replace reinforcement learning merely by becoming accurate. “I can give you a perfect world model of chess, and you still cannot solve it”; predicting legal future boards is different from selecting the line that defeats Magnus Carlsen. Cheap learned simulators nevertheless matter enormously because they enable near-unlimited rollouts and GRPO-style on-the-fly advantage estimates without a learned value function.
Robotics exposes the remaining gap. Backflips avoid the contact-rich sensing problem of walking to a fridge, finding milk at the back, grasping it, and returning safely. Mattick grants that the “physical prompting” robot Tim describes might brush a stuck ball away, but an accurate NMPC controller could also discover that maneuver; the issue is whether either system remains feasible, fast, and reliable across diverse states.
Production values repeatability over peak impressiveness. A BMW buyer will not accept a robot that behaves correctly ninety percent of the time and unpredictably for the remaining ten percent; software errors can sometimes be rolled back, while their physical analogue may “crush someone.” Mattick would rather see a lower but uniform per-state success probability that repeated measurements can amplify than an exceptional demo with undisclosed failures.
That is his final challenge to the world-model thesis: current systems are optimized “to look very nice in demos” and can do genuinely impressive things, but a demo does not reveal how many attempts failed or what failure costs. Prediction scale captures low-hanging fruit; intelligence in the physical world additionally requires planning, constraints, sensing, and guarantees.