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David G. Clark

@david-g-clark.bsky.social

410 followers 460 following 130 posts

Theoretical neuroscientist Research fellow @ Kempner Institute, Harvard dclark.io

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David G. Clark @david-g-clark.bsky.social · Aug 25

(1/26) Excited to share a new preprint led by grad student Albert Wakhloo, with me and Larry Abbott: "Associative synaptic plasticity creates dynamic persistent activity."
www.biorxiv.org/content/10.1...

Associative synaptic plasticity creates dynamic persistent activity

In biological neural circuits, the dynamics of neurons and synapses are tightly coupled. We study the consequences of this coupling and show that it enables a novel form of working memory. In recurren...

www.biorxiv.org

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Reposted by David G. Clark

Naomi Saphra @nsaphra.bsky.social · 14d

I did a QA with Quanta about interpretability and training dynamics! I got to talk about a bunch of research hobby horses and how I got into them.

Ben Brubaker @benbenbrubaker.bsky.social · 14d

I really enjoyed talking to @nsaphra.bsky.social about her thoughts on what much language model interpretability research misses. My latest in @quantamagazine.bsky.social:

To Understand AI, Watch How It Evolves | Quanta Magazine

Naomi Saphra thinks that most research into language models focuses too much on the finished product. She’s mining the history of their training for insights into why these systems work the way they d...

www.quantamagazine.org

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Reposted by David G. Clark

Kris Jensen @kristorpjensen.bsky.social · 14d

I’m super excited to finally put my recent work with @behrenstimb.bsky.social on bioRxiv, where we develop a new mechanistic theory of how PFC structures adaptive behaviour using attractor dynamics in space and time!

www.biorxiv.org/content/10.1...

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Reposted by David G. Clark

Valentin Schmutz @bio-emergent.bsky.social · 19d

🎉 "High-dimensional neuronal activity from low-dimensional latent dynamics: a solvable model" will be presented as an oral at #NeurIPS2025 🎉

Feeling very grateful that reviewers and chairs appreciated concise mathematical explanations, in this age of big models.

www.biorxiv.org/content/10.1...
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David G. Clark @david-g-clark.bsky.social · 23d

A great reading list for historical+recent RNN theory

Alessandro Ingrosso @aingrosso.bsky.social · 23d

Just got back from a great summer school at Sapienza University sites.google.com/view/math-hi... where I gave a short course on Dynamics and Learning in RNNs. I compiled a (very biased) list of recommended readings on the subject, for anyone interested: aleingrosso.github.io/_pages/2025_...

Home

The school will open the thematic period on Data Science and will be dedicated to the mathematical foundations and methods for high-dimensional data analysis. It will provide an in-depth introduction ...

sites.google.com

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David G. Clark @david-g-clark.bsky.social · Sep 8

One for the books

bioRxiv Neuroscience @biorxiv-neursci.bsky.social · Sep 8

Motor cortex flexibly deploys a high-dimensional repertoire of subskills https://www.biorxiv.org/content/10.1101/2025.09.07.674717v1

Reposted by David G. Clark

Sreejan Kumar @sreejan.bsky.social · Sep 6

I'm excited to share that my new postdoctoral position is going so well that I submitted a new paper at the end of my first week! www.biorxiv.org/content/10.1... A thread below

Sensory Compression as a Unifying Principle for Action Chunking and Time Coding in the Brain

The brain seamlessly transforms sensory information into precisely-timed movements, enabling us to type familiar words, play musical instruments, or perform complex motor routines with millisecond pre...

www.biorxiv.org

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David G. Clark @david-g-clark.bsky.social · Aug 25

(26/26) Finally, one more HUGE shoutout to Albert Wakhloo for conceiving, calculating, and charting our way through this fascinating project.

(Link, again: www.biorxiv.org/content/10.1...)

David G. Clark @david-g-clark.bsky.social · Aug 25

(25/26) This work emphasizes that understanding memory-related neural activity requires modeling synaptic and neuronal dynamics together. Separating these processes, while convenient, can obscure circuit functions. Coupling enables new forms of computation beyond what either process achieves alone.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(24/26) This mechanism is evocative of experimental findings in motor cortex and sensory areas that reveal apparent constraints on neural activity patterns during learning (e.g., from Yu, Batista, Chase, et al.).

David G. Clark @david-g-clark.bsky.social · Aug 25

(23/26) Some concluding thoughts. In many models of synaptic plasticity-based learning, weight updates simply overwrite existing connectivity. Our model points out that plasticity can instead dramatically shape dynamics by manipulating the dynamic reservoir provided by static backbone connectivity.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(22/26) Furthermore, studies report persistent oscillations following periodic stimuli & phase-locking to LFP oscillations during WM tasks, interpreted as evidence for intrinsic oscillatory circuitry. Our results suggest this may arise via ongoing plasticity, without preexisting circuit structure.

David G. Clark @david-g-clark.bsky.social · Aug 25

(21/26) What about experimental links? Many working-memory (WM) studies report complex dynamic activity following stim. cessation, not aligning neatly with "sustained firing" WM theories. Our results suggest such activity could be generated by Hebbian plasticity, also underlying canonical WM models.

David G. Clark @david-g-clark.bsky.social · Aug 25

(20/26) In sum, we have arrived at a conceptual understanding of, and analytical solution to, the behavior of coupled neuronal-synaptic dynamics in a nonlinear, input-driven recurrent network. In particular, we have shown that this behavior enables a useful computational function: dynamic memory.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(19/26) Furthermore, we show that, while Ψ is not in general an eigenvector of J, it becomes an increasingly good approximate eigenvector as ν → g⁺. Thus, the mechanism is essentially the same as in the targeted case.

David G. Clark @david-g-clark.bsky.social · Aug 25

(18/26) Using this approximation, we derive exact large-N expressions for outlier eigenvalues λ = g²ν/|ν|² + α/(|ν|² - g²). This correctly predicts the full phenomenology of persistent oscillations, including amplitude and frequency dependence, preferred frequency bands, and regime transitions.

David G. Clark @david-g-clark.bsky.social · Aug 25

(17/26) Let us now return to the full, random-phase input case. We approximate A(0) ≈ 2α Re{ΨΨ†} where Ψ = (νI − J)⁻¹eⁱᶿ. Here, eⁱᶿ is a vector containing input phases θᵢ for each neuron; ν is a complex scalar that depends on the system parameters; and α = kI²/4.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(16/26) This leads to a dynamic analog of Hopfield networks: rather than evoking static patterns by aligning inputs to symmetric-connectivity eigenstructure, we evoke dynamic patterns by aligning inputs to asymmetric-connectivity eigenstructure.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(15/26) We show that, at large N, adding Â to J pulls eigenvalue η to λ = η + α, generating complex-conjugate outliers that can drive oscillations. Furthermore, A(0) ≈ Â can be generated using oscillatory inputs whose single-neuron phases are chosen based on the eigenvector ψ.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(14/26) To understand this alignment mechanism, we consider a toy scenario involving a "target" matrix Â = 2α Re{ψψ†} where ψ is an eigenvector of J with complex eigenvalue η and α is a real scalar (thus, Â is real, symmetric, and rank-two).

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David G. Clark @david-g-clark.bsky.social · Aug 25

(13/26) Thus, to create complex outliers, A(t) must become correlated with J. This can happen only if activity reflects both inputs and recurrence, explaining the significance of being in the "intermediate" regime. Indeed, A(t) aligns to eigenvector subspaces of J associated w/ complex eigenvalues.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(12/26) The emergence of these complex outliers is surprising! Hebbian plasticity produces symmetric weight updates where A(t) = A(t)ᵀ, and symmetric matrices have only real eigenvalues. Moreover, adding a fixed low-rank symmetric matrix to a random J can only create real outliers at large N.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(11/26) We now turn to mechanistic understanding. Persistent oscillations occur when J + A(t) has complex-conjugate outlier eigenvalues at stimulation offset (t=0). In particular, while networks in the persistent-oscillation regime develop complex outliers, other regimes develop only real outliers.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(10/26) The frequency of persistent oscillations tracks the input frequency (within a preferred band). That is, faster inputs generally produce faster persistent oscillations. Thus, the autonomous dynamics reflect the temporal structure of previously experienced stimuli, indicating a dynamic memory!

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David G. Clark @david-g-clark.bsky.social · Aug 25

(9/26) Persistent oscillations occur in an "intermediate" dynamic regime where activity expresses features of both external inputs and recurrent connectivity. In particular, too-strong inputs lead to neuronal activity being dominated by the input alone, preventing persistent oscillations.

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David G. Clark @david-g-clark.bsky.social · Aug 25

(8/26) These "persistent oscillations" require ongoing plasticity, exemplifying a self-renewing, coupled neuronal-synaptic process. In particular, persistent oscillations are thwarted if we prevent neurons from influencing synapses (i.e., if the closed neuronal-synaptic loop is opened) for t≥0.

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