Nima Dehghani
⌥ Arc · 2016 → 2026 · matter, dynamics, recurrence, computation

fullmetal_decade

fullmetal_decade is the map behind the papers: roughly ten years of trying to understand what biological systems are doing when they process information, how much of that can legitimately be called computation, and what happens when the answer is turned around and used to design new architectures that can themselves be realized in physical matter.

There is already a Paper Maze on this site. This is not another bibliography — it is the arc that runs underneath it.

Research homes

Investigations carried out across a sequence of research homes that shaped different parts of the program: the Wyss Institute for Biologically Inspired Engineering at Harvard, then MIT Physics and the Center for Brains, Minds and Machines (CBMM), the Allen Discovery Center, and now the McGovern Institute for Brain Research at MIT and the NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI).

The institutions changed; the underlying questions did not.

The map behind the papers

the loop · not a bibliography

The observation starts from both parts and function: what the components are, how they are connected, what dynamics they generate, and what those dynamics do. In the brain that means cell types, connectivity and microcircuitry, but also ensemble activity, state, context and computation. In cells and tissues it means channels, coupling, fields and patterns, but also control, memory and repair.

The central question has stayed remarkably stubborn:

How does a physical system acquire, retain, transform, and use information in order to control what happens next?

The path I keep taking through that question is:

matter dynamics scale effective state prediction control recurrence closure computation composition design matter

The last arrow matters as much as the first. I am not only trying to understand biological computation. I want the theory to become constructive enough to guide the design of new computational architectures — including ones that can be built as physical devices — and then use those constructed systems to ask better questions of biology.

That loop is the decade.

Start with the parts — and what they do

My way into this problem was the cortex.

The early question was not “is the brain a computer?” It was much less forgiving: what actually organizes the activity of large populations of neurons, and what biological machinery produces that organization?

That means refusing to separate anatomy from function too early. A cortical theory has to care about which cells are excitatory or inhibitory, what kinds of inhibitory cells they are, how populations are connected, how thalamic and cortical loops interact, and what happens to ensemble dynamics across wakefulness, sleep and pathology.

The most direct version of that problem begins with the parts themselves. Morphoelectric properties of inhibitory neurons shift gradually and regardless of cell type along the depth of the cerebral cortex separates two sources of inhibitory-neuron diversity: a molecular cell-type-specific structure that is largely depth-independent, and a gradual depth-dependent modulation shared across inhibitory types. The point is not simply to classify interneurons, but to understand which properties belong to type and which belong to the cortical environment in which that type is embedded.

From there, the question moves from parts to collective function. In Dynamic Balance of Excitation and Inhibition in Human and Monkey Neocortex, excitatory and inhibitory populations co-fluctuate across many temporal scales and across the wake–sleep cycle, while seizure disrupts that coordination. In Ensemble inhibition and excitation in the human cortex, the same system is asked a different question: how much of the collective statistics can a pairwise maximum-entropy model actually capture, and what goes wrong when inhibition is ignored? A Computational Perspective of the Role of the Thalamus in Cognition pushes beyond a relay picture and asks how thalamocortical loops can reconfigure cortical computation according to context.

This is what I mean by neurophysics grounded in biology.

I am interested in statistical physics, nonlinear dynamics, criticality and scaling of neural activity, but I do not want critical, balanced, collective, or emergent to become free-floating descriptions. I am not interested in placing a beautiful physics frame around a biological system and stopping there. The tools are useful because they let us dig beneath those words: identify the degrees of freedom, find invariances, locate the order parameters, ask what breaks the symmetry, and then connect the effective description back to the cells, circuits and interactions that generate it.

The physics has to remain attached to the machinery.

The ruler is part of the theory

A second idea became impossible for me to avoid: the answer depends on the scale at which the question is asked.

That does not mean that anything goes. It means that scale itself has to become an experimental and theoretical variable.

The 2018 multiscale theory of neural control argued that an intervention should be matched to the computational level one actually intends to control. Causal Scale of Rotors in a Cardiac System asked at what spatiotemporal scale a macroscopic rotor genuinely has causal explanatory power. Symmetry’s Edge in Cortical Dynamics asks which features of excitation/inhibition coordination survive coarse-graining and which broken symmetries distinguish physiological and pathological states.

The newer work pushes the same issue further. How long is the coast of a neuron? asks how apparent interaction order and computational capacity change with the ruler used to describe a neuron. When is there a manifold? treats temporal integration scale as a coordinate of neural population geometry rather than a hidden preprocessing choice.

The question is not “which scale is the correct one?” It is:

What survives when the ruler changes? What reorganizes? What disappears?

And then: at which scale does a new variable become sufficiently stable, predictive and causally useful to deserve its own effective theory?

Information processing is not yet computation

At some point, calling everything an information-processing system stopped being satisfying. The phrase is too cheap unless it makes exclusions.

A wave carries information. A tissue can preserve a pattern. A dynamical system can remember its past. A rock has state transitions. None of those statements, by itself, tells us that the system is computing.

This is where the cellular work and the work on foundations of physical computation meet. Systematizing Cellular Complexity asks what kinds of problems a cell must actually solve — control, reconfiguration, robustness, adaptation, noise management — and treats the formalization of the right problems as part of the scientific task. Physical Computing asks for a stricter bridge between physical processes and abstract computation, with compositional structure replacing an arbitrary labeling of physical states.

The hierarchy that has emerged from the newer work is deliberately demanding:

Physical memory is not yet physical computation, and physical computation is not yet autonomous computation.

A physical system can store a trace without computing with it. A system can implement a robust coarse-grained transition without internally choosing which transition comes next. Autonomous computation needs something stronger: an internal physical readout must participate in selecting the next physical operation.

That is closure. And increasingly, closure has become the word around which the rest of the program organizes itself.

Recurrence, recurrence, recurrence

Long before I had the word closure for it, I kept finding the same structure.

The thalamus does not simply relay cortical information; it participates in a loop that changes the effective computational regime of cortex according to context. Excitation and inhibition stabilize one another dynamically. A reservoir transforms an input because its present state contains its past. A bioelectric tissue persists because local state changes coupling, and coupling changes the future of local state. A neuron writes fields that act back on the neuron. A recurrent network carries state forward rather than reconstructing the past from scratch.

The common architecture is recurrence. Not merely a loop drawn on a circuit diagram, but a physical mechanism by which history becomes state, state becomes context, context changes the next transformation, and the consequences return to alter the future state.

That is why I keep coming back to it:

Recurrence is memory with consequences.

Feedback is recurrence used for control.

Closure is feedback that internalizes the choice of what happens next.

The forthcoming Computational Irreducibility of Time paper makes one part of this quantitative: for multiplicative temporal structure, persistent recurrent state can realize computations whose fixed-depth flattened implementations pay a growing resource cost. The point is not that every temporal computation requires recurrence. The point is to identify exactly what recurrence buys, and when it buys it.

Cells and tissues are not a detour

The brain is an extraordinary laboratory, but it is not always the easiest place to isolate first principles. It contains too many interacting cell types, scales, feedback loops and effective layers to make every conceptual distinction clean.

Cells and tissues provide a complementary laboratory. They let us ask stripped-down questions about memory, pattern, control and computation in systems where the components can sometimes be written explicitly enough to build mathematical frames around them. A cell has internal state, sensing, actuation and homeostatic control. A tissue adds coupling, collective states, spatial pattern and repair. These systems can expose the minimal ingredients of computation more cleanly than a whole brain, while still remaining genuinely biological.

That is why the bioelectric work matters to the same program. Self-insulating domains asks what physically holds a tissue-scale pattern memory. The Middle Way asks when a membrane-voltage pattern becomes a relatively autonomous mesoscopic computational layer rather than merely a coarse description of channels underneath it. Field closure, ice neurons, and when a dendrite is a motif asks what separates a branching object that looks neuronal from a biological neuron whose internal state and self-generated field participate in a dynamical loop.

Ice can grow a dendritic silhouette. That is precisely why the distinction is useful. A shape is not a computation. Excitability is not yet autonomous computation. The interesting object appears when morphology, state, field, readout and feedback become part of the same causal architecture.

Cells and tissues are therefore not side projects away from neuroscience. They are simpler arenas in which to expose the basis of patterns, memory and computation — and then carry those principles back into the brain.

Prediction, internal models, agency

Control is future-oriented.

To control a changing system, an organism needs internal states that carry information about what is likely to happen next and about the consequences of possible actions. That is the sense in which I use internal model: not necessarily a symbolic representation, and not a little scientist hidden inside the organism, but a physical state whose structure is useful because it predicts enough of the world to guide control.

Prediction and internal model therefore go hand in hand. A cell uses them in the service of viability. A tissue uses them to maintain and repair a pattern. A nervous system extends the same logic over richer spaces — body, environment, other agents, possible actions, future consequences.

My view is that agency and intelligence grow out of this coupling between prediction and control. I would go further: I think consciousness belongs on the same physical continuum. I do not mean that as a spooky extra ingredient added above the biophysics. I mean that whatever effective layer we call consciousness has to sit on, and eventually be pinned back to, physical components, dynamics and causal organization. An effective theory is useful only if we can say what it is effective over and how it couples back to the machinery beneath it.

That is the wager running through this work: increasingly rich internal models, embedded in recurrent control loops, produce increasingly rich forms of agency.

Turn the arrow around

Then comes the part I care about just as much: build with the principles.

If biology has discovered useful computational organizations, the test is not whether we can describe them beautifully. The test is whether we can extract the operative principle, formalize it, and make it do work in another substrate.

That is the point of Bio-inspired AI. Biological intelligence is not interesting because neurons look like neural-network units. It is interesting because living systems are multiscale, context-dependent, recurrent, adaptive and organized around control.

The constructive work follows that line. In Cortical Blueprint RNNs, measured cortical geometry and functional organization become inductive biases for recurrent networks, and the biologically grounded models outperform weaker controls. In Adaptive Reservoir Computing, the recurrent substrate itself is placed under evolutionary selection for prediction of spatiotemporal chaos, exposing structural constraints rather than treating the reservoir as an arbitrary random matrix. All you need is recurrence! asks whether learning operations can live in recurrent state rather than in changing synaptic weights.

This is what I mean by true bio-inspired AI:

extract an organizing principle → formalize it → build with it → test it → bring the constructed system back to biology as a sharper probe.

The research program itself becomes recurrent: understand → build → use what was built to understand better → build again.

Circuits have to compose

There is still another missing level. Knowing what a primitive does does not tell us what happens when primitives are coupled.

Canonical neural motifs are usually assigned functional labels: this circuit normalizes, this one selects, this one gates. But a recurrent circuit exposed to sequences of inputs is not merely one function. It generates a repertoire of transformations.

“More Is Different” in Neural Circuits uses transition monoids, Krohn–Rhodes theory and holonomy decomposition to distinguish what is already present in a primitive update from what appears only under composition, and what belongs to one motif from what genuinely lives on the joint state space of coupled motifs.

This matters in both directions. For neuroscience, it gives us a way to move from saying that cortex contains motifs to asking what computations those motifs can generate together. For engineering, it points toward something closer to programming recurrent matter: choose primitives, interfaces and schedules so that the generated algebra has the repertoire you want.

The interface becomes part of the program. And that is also where effective theories become constructive rather than merely descriptive. A higher-level computational structure can belong to the composite even when no isolated part contains it.

More can genuinely be different.

The loop

The decade is therefore not a march from neuroscience toward AI. It is a loop.

  1. observe parts + function
  2. identify the relevant physical degrees of freedom
  3. ask what survives across scale
  4. find the effective state and what it predicts
  5. separate information, memory and computation
  6. find recurrence, feedback and closure
  7. formalize transformations and composition
  8. design new recurrent architectures and physical machines
  9. use them to ask sharper questions of biology
  10. back to the parts

The cortex, a cell collective, a wave-memory system, a reservoir computer and a recurrent circuit motif are obviously not the same object.

The point is to develop a language strong enough to say how they differ, while still asking the same physical question of each.

The papers in this arc

10 out · 8 forthcoming

This is intentionally not the full publication list. The older experimental and neurophysiology papers are linked where their ideas enter the story above. The papers below are the recent foundation and the current wave of work that makes the theoretical arc explicit.

out — PDF, room and blog post linked complete — released in sequence
01

Foundations · 2024–2025

5

These papers set the frame: systematize the questions, define physical computation more strictly, identify multiscale and contextual organization as the real target of bio-inspired design, and build the statistical-physics language for scale and effective structure.

  1. 2024 Systematizing cellular complexity: A Hilbertian approach to biological problems published · PLOS Complex Systems Frames cellular biology as a set of system-level problems that cells must solve — control, reconfiguration, robustness and noise management — and argues that choosing and formalizing the right questions is itself part of building a theory of biological computation. PDF Room Blog arXiv:2210.04627
  2. 2024 Physical Computing: A Category Theoretic Perspective on Physical Computation and System Compositionality published · J. Physics Complexity Builds a categorical bridge between physical processes and abstract computations, emphasizing functorial structure, composition, natural transformations and adjunctions rather than an arbitrary labelling of physical states. PDF Room Blog arXiv:2210.00392
  3. 2024 Bio-inspired AI: Integrating Biological Complexity into Artificial Intelligence arXiv Argues that the useful lessons of biology are not superficial neuronal imitation but multiscale organization, context, feedback, adaptive control and interaction with the environment — principles that should become architectural constraints in artificial systems. PDF Room Blog arXiv:2411.15243
  4. 2025 Compression, Regularity, Randomness and Emergent Structure: Rethinking Physical Complexity in the Data-Driven Era arXiv Organizes complexity measures around regularity, randomness and structure, and uses compression and learned representations as a bridge between classical complexity theory and data-driven effective descriptions. PDF Room Blog arXiv:2505.07222
  5. 2025 Symmetry’s Edge in Cortical Dynamics: Multiscale Dynamics of Ensemble Excitation and Inhibition arXiv Treats multiscale ensemble E/I coordination as a search for invariance, order parameters and broken symmetries, tying statistical-physics ideas directly to identified excitatory and inhibitory populations and their physiological states. PDF Room Blog arXiv:2306.11965
02

2026 · out

5

These are the papers already released from the current wave. Each has a room in the Paper Maze and a companion post in the blog.

  1. 2026 Morphoelectric properties of inhibitory neurons shift gradually and regardless of cell type along the depth of the cerebral cortex released · bioRxiv Decomposes cortical inhibitory-neuron diversity into two separable axes: molecular cell-type-specific morphoelectric structure that remains stable across depth, and a gradual depth-dependent modulation shared across types. The same organization generalizes across cortical areas and species, giving a cleaner map from inhibitory cell identity to the local cortical context in which that identity is expressed. PDF Room Blog bioRxiv
  2. 2026 Harnessing cortical geometry, wiring, and function as inductive biases for recurrent neural networks released · arXiv Uses measured MICrONS cortical geometry, wiring and function as recurrent-network priors. Function-derived initialization gives the largest learning gain, real spatial embedding adds a robust benefit, and the resulting networks move toward low-entropy, modular and small-world organization. PDF Room Blog arXiv:2606.14975
  3. 2026 Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaos released · arXiv Turns reservoir design into an evolutionary problem for prediction of Kuramoto–Sivashinsky chaos. Selection improves forecast horizon while revealing a constrained recurrent architecture: a conserved spectral envelope, refinement of slow modes, an intermediate modularity band and pruning of connection cost. PDF Room Blog arXiv:2606.22765
  4. 2026 Autonomous Physical Computation: A Categorical Closure Criterion for Physical and Neuromorphic Reservoirs released · arXiv Separates memory, feedback and physical state evolution from autonomous computation. Robust coarse-grained transition preservation gives the computation criterion; closure adds the requirement that an internal physical readout select the next physical operation. PDF Room Blog arXiv:2607.23902
  5. 2026 “More Is Different” in Neural Circuits: Algebraic Emergence of Effective Theories in Canonical Recurrent Motifs released · arXiv Treats canonical recurrent motifs as finite transformation systems. Individually aperiodic updates can generate local reversible structure under composition, and coupling normalization to selection produces genuinely composite group structure certified by holonomy — a route from circuit motifs to a compositional algebra of computation. PDF Room Blog arXiv:2608.30231
03

2026 · coming next

8

Written and complete, being released in sequence. Grouped by the question each one answers rather than by upload order.

  1. Scale as part of the theory
  2. 2026 How long is the coast of a neuron? Resolution-dependent interaction order and computational capacity Shows that interaction order is not invariant under coarse-graining: higher-order structure can become pairwise after projection, while resolving organized dendritic-like subunits expands approximation capacity and effective representational dimension. complete link on release
  3. 2026 When is there a manifold? Temporal scale as a missing coordinate of neural population geometry Promotes temporal integration scale to a coordinate of population geometry. Defines a finite manifold window, derives a band-limited SNR condition, identifies recurrence as the critical-scale condition, predicts period-dispersion smearing and rate scaling, and shows topological revival beyond the recurrence zero. complete link on release
  4. What recurrence buys
  5. 2026 The Computational Irreducibility of Time: Why Recurrence Cannot Be Flattened Prices the attempt to compile temporal multiplicative structure into fixed-depth parallel computation. Exact recurrent constructions retain persistent state at cost independent of sequence length in the relevant regimes, while flattening pays growing width or parameter cost; experiments probe the separation in synthetic functionals, physical dynamics and arithmetic. complete link on release
  6. 2026 All you need is “recurrence”! Learning without plasticity in fixed-weight neural networks Moves the variables of learning from synaptic weights into recurrent state. Fixed-weight motifs — Retentor, Multiplier, Derivative Latch and Batch Accumulator — compose into networks that implement first-order learning operations without rewriting connectivity. complete link on release
  7. Memory, pattern and closure in living matter
  8. 2026 Self-insulating domains: voltage-gated coupling as the read and hold mechanism of a bioelectric pattern memory Proves that junctional gating alone cannot hold a nonuniform pattern when residual conductance remains positive. Local bistability supplies admissible states; voltage-gated coupling pins the interfaces between them, producing a densely associative landscape with measurable basins and a sharp informational boundary of recall. complete link on release
  9. 2026 The Middle Way in Cellular Information Processing: Bioelectric Patterns as a Mesoscopic Computational Layer Asks when membrane voltage becomes a relatively autonomous mesoscopic computational variable. Conductance degeneracy protects the effective state, bistability gives it a discrete codomain, and voltage-dependent junctional coupling pins persistent domains; internal operation selection supplies the route to closure. complete link on release
  10. 2026 Field closure, ice neurons, and when a dendrite is a motif Uses the “ice neuron” as a deliberately cruel control: branching morphology alone is cheap. A biological neuron adds internal state and a field it helps generate. In the model, finite field-closure gain couples the moving-front instability to an interfacial excitable state and increases distal persistence even when morphology is frozen. complete link on release
  11. Toward a generative calculus
  12. 2026 A Generative Computational Calculus of Physical Complexity Inverts the usual complexity question: rather than assigning a measure to data, ask how difficult the data is to generate. A diffusion process yields coordinated readouts of randomness, regularity and complexity, with the complexity functional vanishing at both perfect order and perfect randomness and becoming a scale-resolved measure of non-Gaussian structure between them. complete link on release

The forthcoming manuscripts are written and complete; they are being released in sequence. The order below is conceptual rather than a promise of upload order — arXiv and PDF links are added to each entry as it goes out.

Reading routes

4 entrances

The page is a map, not a prescribed order. Four reasonable entrances — links open the room in the Paper Maze; unlinked steps are forthcoming.

⌥ fullmetal

If there is one idea I would keep from the whole decade, it is this:

Intelligence is not painted on top of dynamics.

Biological systems have to survive in a changing world. They retain state. They predict enough of what matters. They act. Their actions alter the world and themselves. The consequences return. Internal variables change what happens next.

  1. At sufficient depth, that loop becomes control
  2. With memory, it becomes context
  3. With prediction, it becomes agency
  4. With internal operation selection, it becomes closure

And with increasingly rich internal models embedded in those recurrent loops, I think we get the physical basis of learning, intelligence and consciousness — not as additions to matter, but as effective layers that have to be cashed out in biophysics, dynamics and components.

That is the object I have been circling for ten years.

Recurrence all the way down.

full speed

A decade is a convenient unit of time, not a stopping condition. The loop is still open: understand the machinery, formalize the computation, build from the principles, and bring what we learn back to biology.

Full metal. Full speed. Into the next decade.