continuation, end of thread

[image] We built a recursive AI that creates its own scientific instruments, turns them into a world inhabited by a massive agent ecology, which then reasons across vast, nonlinear spaces of possible physical futures. The AI swarm worked until tens of thousands of trajectories collapsed into mechanistic principles humans can use, distilling several core design principles that govern hierarchical metamaterials failure. The core tenet of this work is that AI can build the spaces in which its next level of reasoning becomes possible; a representation becomes an instrument, the instrument becomes an executable world, and that world becomes the substrate for further intelligence, forming a recursive loop. Intelligence grows by constructing new spaces to think in and improving its own thinking. <video preload="none" tabindex="-1" playsinline="" aria-label="Embedded video" style="width: 100%; height: 100%; position: absolute; background-color: black; --darkreader-inline-bgcolor: var(--darkreader-background-000000, #010101); top: 0%; left: 0%; transform: rotate(0deg) scale(1.005);" poster="https://pbs.twimg.com/amplify_video_thumb/2099785625826136064/img/RBIcVwtqVf9EJCFf.jpg" data-darkreader-inline-bgcolor=""></video> [image] The world created by the initial set of agents is later populated by hundreds of AI agents. They explore a vast design universe where chemistry remains fixed and architecture creates functionality: nested, inter-woven structures within structures forming an incredibly complex design space. Here, the same constituent material can behave radically differently depending on where matter is placed, how it’s connected, and how order and disorder are distributed across scales. Architecture adds combinatorial degrees of freedom to a problem that is already strongly nonlinear and path dependent, especially when we examine how materials deform, and behave dynamically as they exposed to extreme pressures, and fail. <video preload="none" tabindex="-1" playsinline="" aria-label="Embedded video" style="width: 100%; height: 100%; position: absolute; background-color: black; --darkreader-inline-bgcolor: var(--darkreader-background-000000, #010101); top: 0%; left: 0%; transform: rotate(0deg) scale(1.005);" poster="https://pbs.twimg.com/amplify_video_thumb/2099811127362260992/img/ixDfxhSZ9YolqhRG.jpg" data-darkreader-inline-bgcolor=""></video> [image] Every rupture changes the topology, redistributes force, and creates a new state. Cascades emerge from the evolving state of the material itself. Out of that complexity came a remarkably compact recurring result: hierarchy by itself does not determine performance; rather, the decisive variable is how the architecture organizes pathways through which forces are carried and redistributed as damage accumulates. The gain appeared when material was allocated into a dominant load-bearing structure. Placement of geometric order set whether failure progressed through smaller events or synchronized collapse. That opened a regime of surprising flaw tolerance with real trade-offs and real-world engineering implications. <video preload="none" tabindex="-1" playsinline="" aria-label="Embedded video" style="width: 100%; height: 100%; position: absolute; background-color: black; --darkreader-inline-bgcolor: var(--darkreader-background-000000, #010101); top: 0%; left: 0%; transform: rotate(0deg) scale(1.005);" poster="https://pbs.twimg.com/amplify_video_thumb/2099831127833751552/img/-outI4Wt1ECp8Oaj.jpg" data-darkreader-inline-bgcolor=""></video> [image] The core discovery by the AI is that making materials damage resilient can be achieved by shaping the architecture so that once failure begins, the material is driven through a sequence of states that preserve function. The crucial point is dynamical - each rupture rewrites the topology, redistributes force and energy and creates a new state. The full response is a path-dependent evolution with avalanches and non-separable interactions in which the effect of one design choice depends on the others. <video preload="none" tabindex="-1" playsinline="" aria-label="Embedded video" style="width: 100%; height: 100%; position: absolute; background-color: black; --darkreader-inline-bgcolor: var(--darkreader-background-000000, #010101); top: 0%; left: 0%; transform: rotate(0deg) scale(1.005);" poster="https://pbs.twimg.com/amplify_video_thumb/2099829942477295616/img/tmlWV2CIbh7ctdlc.jpg" data-darkreader-inline-bgcolor=""></video> [image] What is striking is the level of scientific cognition brought to that problem. The AI held a generative model of an evolving world, stepped outside the immediate state, rolled out alternative futures, compared long causal histories, identified interventions that changed which trajectories were reachable, and compressed those histories into a small set of generative invariants. This connects to model-based causal reasoning, counterfactual simulation, cognitive decoupling, and temporal abstraction. <video preload="none" tabindex="-1" playsinline="" aria-label="Embedded video" style="width: 100%; height: 100%; position: absolute; background-color: black; --darkreader-inline-bgcolor: var(--darkreader-background-000000, #010101); top: 0%; left: 0%; transform: rotate(0deg) scale(1.005);" poster="https://pbs.twimg.com/amplify_video_thumb/2099830218852618240/img/h5D74-jd0uziWifI.jpg" data-darkreader-inline-bgcolor=""></video> [image] **Deeper reasoning** Reasoning over what could happen, how histories unfold, and which hidden mechanisms remain invariant across them. The resulting principle is profound: Architecture can program the evolution of failure. Geometry gives us a way to shape how a physical system moves through its possible future states under damage. That, in turn, transforms a vast nonlinear space into a powerful design handle: shape the future trajectory of matter under damage so function can persist deep into the failure process. But perhaps most interestingly in my opinion, the larger impact is an expansion of the human epistemic horizon. Science progresses by extending what a mind can hold. Instruments extend perception, computation extends calculation, systems like this extend the size of the causal possibility space we can traverse before abstraction. [image] ##### The Swarm Habitat AI can inhabit thousands of alternatives, follow enormous numbers of possible histories, and return with mechanisms compact enough for us to reason with. That creates a form of extended cognition for science. Our effective scientific intelligence incorporates models, executable worlds, persistent evidence, and populations of artificial investigators. Machine scale exploration can be compressed into human scale understanding. Principles we can argue with, generalize, manufacture from, use to design the next experiment. <video preload="none" tabindex="-1" playsinline="" aria-label="Embedded video" style="width: 100%; height: 100%; position: absolute; background-color: black; --darkreader-inline-bgcolor: var(--darkreader-background-000000, #010101); top: 0%; left: 0%; transform: rotate(0deg) scale(1.005);" poster="https://pbs.twimg.com/amplify_video_thumb/2099831887023767552/img/vh7nAXAmFi-7NX-Y.jpg" data-darkreader-inline-bgcolor=""></video> [image] The recursion is powerful; the first agents define a scientific world and that world becomes shared cognition. Other current and future agents explore it, add evidence, retrieve and build further investigations through the same persistent instrument. This creates a flywheel of thinking - answer to instrument, instrument to world, world to ecology, and every step of the way is an editable artifact that serves as the basis for further improvement. Intelligence compounds through what the agents build, creating an intelligence explosion in science: designers constructing the possibility spaces in which other designers reason, experiment, and discover. <video preload="none" tabindex="-1" playsinline="" aria-label="Embedded video" style="width: 100%; height: 100%; position: absolute; background-color: black; --darkreader-inline-bgcolor: var(--darkreader-background-000000, #010101); top: 0%; left: 0%; transform: rotate(0deg) scale(1.005);" poster="https://pbs.twimg.com/amplify_video_thumb/2099814021700481024/img/CaQzy2TStCxRcx-2.jpg" data-darkreader-inline-bgcolor=""></video> 0:02 ##### Flows through spaces of possibility At a general level, learning and discovery are flows through spaces of possibility under constraint. In backpropagation, the flow moves through parameter space under a specified loss. In reinforcement learning, it’s coupled to an environment via rewards. In a fully autonomous scientific system, that flow becomes reflexive. The system moves beyond internal state updates and and buconstructs, manipulates, and repairs the executable worlds that define what its objectives, variables, and questions even are. [image] The universal pattern is a recurring coupling between possibility, constraint, consequence, and memory. Flows create structure, and structures redirect flows. As that loop scales from parameters to policies to representations to instruments and worlds, Intelligence is no longer confined to one fixed space; it begins to create the next space within which it can think. <video preload="none" tabindex="-1" playsinline="" aria-label="Embedded video" style="width: 100%; height: 100%; position: absolute; background-color: black; --darkreader-inline-bgcolor: var(--darkreader-background-000000, #010101); top: 0%; left: 0%; transform: rotate(0deg) scale(1.005);" poster="https://pbs.twimg.com/amplify_video_thumb/2099820373214724096/img/KnTaN176PWxm6jbs.jpg" data-darkreader-inline-bgcolor=""></video> 0:01 / 0:36 **Evolutionary tales** The evolution from RNNs to LSTMs to transformers (and later, looped transformers and other variants) can be read as a history of where intelligence places persistence, where it permits change, and how it carries structure from one cycle of computation into the next. RNNs compress the past into an evolving hidden state; LSTMs introduce gates that preserve selected information across longer horizons; transformers make prior tokens directly addressable as context and continually recompute relationships across that persistent substrate. Looped transformers reuse a stable computational operator while representations evolve through repeated passes. Recursive self-evolving intelligence extends this principle beyond the internal architecture of a model and amalgamates multiple levers to create referential updates. [image] Representations, memories, tools, scientific instruments, executable worlds, and eventually entire societies of agents can become persistent and ever-evolving substrates that carry the products of one round of cognition into the next. Each cycle can stabilize what has been learned, turn it into a new object for reasoning, and open a larger possibility space above it. Intelligence therefore acquires a multiscale architecture of persistence and plasticity: fast processes explore, slower structures accumulate, and the outputs of cognition become the invariants from which subsequent cognition proceeds. This gives recursion its real power, because once a system can experience a world, it can build structures that encode what it has learned, it can reason through those structures, revise them through consequence, and repeatedly create new levels on which further intelligence can operate. <video preload="none" tabindex="-1" playsinline="" aria-label="Embedded video" style="width: 100%; height: 100%; position: absolute; background-color: black; --darkreader-inline-bgcolor: var(--darkreader-background-000000, #010101); top: 0%; left: 0%; transform: rotate(0deg) scale(1.005);" poster="https://pbs.twimg.com/amplify_video_thumb/2099818726061207552/img/oRKAHzPfmhl6C40H.jpg" data-darkreader-inline-bgcolor=""></video> [image] ##### A bright future AI for science is one of the greatest positive forces we have. It expands the human epistemic horizon - letting us traverse thousands of possible histories, invent new instruments we would never have time to build by hand, and return mechanisms compact enough to understand, test, and manufacture. For scientists, this becomes a new instrument to explore the world, a new microscope, a new tool, a new way look deeply into the world and to make sense of it. I cannot think of anything more human than to understand nature and to use the power to create new engineering solutions that improve our lives, civilization and allow us to reach beyond. [image] We are just at the beginning of an exciting journey, and scientific superintelligence may emerge from a process in which complex activity generates stable abstractions that become the building blocks for a new level of reasoning. There is significant earlier work that becomes increasingly relevant as material intelligence is unlocked. For instance, cybernetics and nonlinear physics offer a coherent theoretical underpinning; for instance, a system can cope with a complex environment only if it can generate sufficient internal variety, and in some regimes, it can reorganize the very mechanisms by which it remains stable. Repeated interaction can generate stable forms that become the “objects” of the next round of reasoning, while networks of processes can close on themselves to constitute a coherent level of organization. [image] In physics, large numbers of degrees of freedom can collapse into a few collective variables that then feed back to organize the lower level, and far from equilibrium, sustained flows can stabilize macroscopic order that was not there before. Put together, this suggests a very specific kind of scaling: High-dimensional activity produces a stable invariant. That invariant becomes an effective variable that compresses the complexity. That variable becomes a contract on which a new layer of reasoning can stand, creating a new dynamical space above it. The recursion is not simply repetition but rather creation of new levels of reasoning substrates. One space is compressed into a principle, that principle opens a larger space above it. This is, indeed, a deep foundation for scientific superintelligence where we repeatedly generate the very framework in which still greater reasoning becomes possible. ##### References and notes - M.J. Buehler, Artificial intelligence agents autonomously build computational laboratories that reveal design principles of hierarchical metamaterial failure, in submission, 2026 - S. Pal, F.Y. Wang, M.J. Buehler, SwarmWorld: Stigmergic technological evolution in societies of language-model agents, arXiv:2608.26081, 2026 [image]

Our new AI model, SparksMatter, discovered CaMg₂Si₂ - a Ca-filled Mg-Si Zintl silicide - as a thermoelectric built only from stable, non-toxic, earth-abundant elements. Thermoelectrics are solid-state materials that convert heat directly into electricity (and electricity into cooling) with no moving parts, which makes them a key technology for harvesting the vast amounts of waste heat from engines, industry and electronics, and even fusion - but today's best ones rely on scarce or toxic elements like tellurium, lead and bismuth. This is why an earth-abundant, non-toxic candidate matters. Our model's physical reasoning to come up with the design: Mg₂Si is a known earth-abundant thermoelectric but conducts heat too well; a heavy, weakly bound Ca cation in the Mg-Si framework should scatter phonons while keeping a moderate band gap. It generated 100 Ca-Mg-Si crystals with MatterGen, kept the six within 0.05 eV/atom of the convex hull (via MatterSim), and predicted band gaps of 0.44-0.57 eV and bulk moduli of 53-54 GPa (CGCNN). Follow-up lattice dynamics found three CaMg₂Si₂ polymorphs dynamically stable, with lattice thermal conductivity ≈6 W m⁻¹ K⁻¹ at 300 K and ≈2 at 1000 K. The AI proposed a chemical hypothesis first, then developed and applied a separate generative/physics pipeline to test it, and six surviving structures came back with that hypothesized composition. The video replays the reasoning process. New paper out with Alireza Ghafarollahi in npj Computational Materials: SparksMatter, an AI that runs the full in-silico inorganic materials discovery cycle - ideation, planning, computational experimentation, critique and reporting - from a single plain-language query. Why this matters: conventional ML models for materials are typically single-shot predictors or generators. They can predict a property or propose a structure, but they do not organize the next scientific step. Discovery, instead, works as a loop: hypothesize, test, critique, revise. The key advance here is a deep reasoning layer that incorporates physics to decide which scientific tool to use, how to interpret the result, and what to change as next step. How it works: SparksMatter spawns a suite of AI agents - scientists, planners, coders, reviewers and critics - that write and execute code against materials tools: Materials Project retrieval; MatterGen for generative crystal design conditioned on chemistry, band gap or bulk modulus; MatterSim for relaxation and convex-hull stability; CGCNN for property prediction. Adversarial agents check each phase, the system revises its ideas, plans and code from execution results, documents its own limitations, and delivers a scientific report with a validation roadmap spanning DFT, phonons, transport, synthesis and characterization. Two more discovery tasks SparksMatter ran autonomously: 1⃣Soft inorganic semiconductors: generated 112 structures conditioned on low stiffness and narrowed them to 59 candidates absent from the Materials Project after toxicity, stability, electronic, mechanical and database screening - bulk moduli 11-24 GPa, band gaps 0.4-3.9 eV. 2⃣Lead-free perovskites: filtered 154,879 Materials Project entries to 162 Pb-free ABO₃ candidates meeting structural, toxicity, stability and band-gap criteria, including LaAlO₃, BaZrO₃, SrSnO₃, CaTiO₃ and SrTiO₃. Benchmark: the same three tasks were given to frontier reasoning models acting as expert materials scientists with web browsing but without the generation and prediction tools. A blinded LLM evaluator scored every response ten times on relevance, scientific soundness, novelty, and depth and rigor. SparksMatter scored highest in aggregate, with its strongest advantages in novelty and depth & rigor. Its main limitation was scientific soundness because much of the core screening still relied on surrogate models rather than direct first-principles or experimental validation - a gap the system identified, documented, and mapped out how to close. Takeaway: putting generative models, executable code and physics-based simulators inside the reasoning loop lets an AI propose structures outside existing databases, test them, reject weak candidates, and say what evidence is still missing. --- Code and data: https://github.com/lamm-mit/SparksMatter… Paper (open access): https://nature.com/articles/s41524-026-02205-8… [github.com GitHub - lamm-mit/SparksMatter](https://t.co/i7sEHQAMyH) --- ##### Comments > **Ben Schulz @schulzb589** · [2026-08-18](https://x.com/schulzb589/status/2089706665549406506) > > Very cool. Maybe it can come up with a replacement for Ruthenium. Pretty rare catalyst with some unique properties. > **Blue | Semis & AI Infra @BlueTradeIn** · [2026-08-18](https://x.com/BlueTradeIn/status/2089691585709793674) > > Very cool result. Abundance clears one gate; deployment still needs zT at realistic temperatures, low contact resistance and cycling stability. If the model can optimize all three together, this moves beyond a materials-screening demo.

A transformer can learn not just the outcomes of dynamics, but the operator that executes the rules. To show this we trained a transformer on roughly 0.04% of a discrete rule space - 100 of 262,144 possible rules - and it learned to apply unseen rules from the same rule class. The model does not simply memorize specific rules. It learns the operator that maps a supplied rule plus an initial state, including unseen rules from this class, to the correct next state. This is relevant because it is a shift from “neural networks approximate dynamics” to “neural networks can learn to execute symbolic programs within a defined rule class”. The rule itself is supplied at inference time, as data, and the network has internalized how rules act, not which rules to apply. On previously unseen rules, the model achieves 98.5% perfect one-step forecasts and reconstructs governing rules with up to 96% functional accuracy. Two results make this hold up under scrutiny. First, inductive bias decay. As we scaled training rule diversity, the correlation between functional inference accuracy and distance-from-nearest-training-rule collapsed to R² = 0.00. At the largest tested training-rule diversity, the model’s performance on a new rule shows no measurable dependence on how similar that rule is to anything it was trained on. The bias toward training data (the thing we worry most about in compositional generalization claims) is something we can measure decaying, and we find that at scale it is gone. Second, an identifiability theory. We derive a closed-form expression for the number of rules consistent with a single observation. This reframes the inverse problem: failure to recover ground truth is not necessarily a model defect, but can be correct behavior when the data underdetermine the rule. The model is sampling the equivalence class; and identifiability is governed by coverage, not capacity. The methodological move underneath both results is amortization. Classical work on rule inference (e.g. the Santa Fe EVCA program, evolutionary search over CA rule space) was per-instance: search the rule space for each new system. We replace that with a single forward pass of a transformer trained across many instantiations of the rule class. That is what makes symbolic rule inference scalable as a research direction rather than a curiosity. We show that this works in a tightly constrained domain: binary, deterministic, local cellular automata on small grids. The locality-break experiment shows the model fails sharply when target systems violate its structural priors (which is itself a useful diagnostic, but it bounds the operator class). We don't yet know how this scales to multistate, higher-dimensional, or stochastic CA, or whether it transfers cleanly to non-CA systems whose coarse-grained dynamics admit local surrogates. The identifiability framework - what can be inferred from observation, given a hypothesis class - should transfer wherever finite local rules meet sparse data. The amortization argument transfers wherever per-instance symbolic search has been the bottleneck. Those are the pieces I expect to outlive the cellular automata setting. Led by @JaimeBerkovich with Noah David, at @LAMM\_MIT. Out now in Advanced Science @AdvPortfolio (link to paper & code below). --- Paper: https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202511352… GitHub: https://github.com/lamm-mit/AutomataGPT… [advanced.onlinelibrary.wiley.com AutomataGPT: Transformer‐Based Forecasting and Ruleset Inference for Two‐Dimensional Cellular...](https://t.co/mhGnASunYW)