Computing with Living Neurons: Chaos-Controlled Reservoir Computing with Knowledge Transplant
Authors: Seung Hyun Kim, Zhi Dou, Gaurav Upadhyay, Anay Pattanaik, Leo Maslov, Lav Varshney, John Beggs, Howard Gritton, Mattia Gazzola
Organizations: Mechanical Science and Engineering, University of Illinois Urbana-Champaign · Electrical and Computer Engineering, University of Illinois Urbana-Champaign · Coordinated Science Laboratory, University of Illinois Urbana-Champaign · Department of Physics, University of Illinois Urbana-Champaign · Department of Physics, Indiana University Bloomington · Carl R. Woese Institute for Genomic Biology, University of Illinois Urbana-Champaign · Department of Comparative Biosciences, University of Illinois Urbana-Champaign · Beckman Institute for Advanced Science and Technology, University of Illinois Urbana-Champaign · National Center for Supercomputing Applications, University of Illinois Urbana-Champaign
We introduce chaos-controlled Reservoir Computing (cc-RC) for living neural cultures: dynamically rich substrates of unique potential for adaptive computation. To account for intrinsic biological variability, cc-RC combines: (i) pre-training identification of each culture's dynamical signature and phase-portrait attractor; (ii) low-power optical chaos control to stabilize spontaneous and stimulus-evoked activity; (iii) readout training within this controlled regime. Across hundreds of neural samples, cc-RC enables robust learning and pattern classification, improving both accuracy and model longevity by approximately 300% over standard RC. We further propose Knowledge Transplant (KT), for which the reservoir map learned by an expert culture is transplanted to an attractor-equivalent student culture, reducing training time to minutes while improving performance. By enabling cross-substrate, reusable learned models, KT paves the way for knowledge accumulation and sharing across neural populations, transcending biological lifespan limits.
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Figure 1: Overview of cc-RC setup. (a) ChR2-transfected mESCs are expanded, formed into embryoid body (EB) in suspension culture, and differentiated into motoneurons. On day 7, differentiated EBs are dissociated and plated on the MEA at a density of 5,000cells per mm2 . Cultures mature by day 14. See SI for details. (b) Living neural networks plated on 128 -electrodes MEAs realize integrated neural chips. (c) MiV platforms enable the recording of electric local field potentials (LFPs) via PCB-MEA interfaces connected to Intan-RHS2116 chips. Optical inputs are delivered by a 473nm laser (Doric). MiV platform and hosted cultures sit in an incubator for environmental control (temperature, humidity, CO2 ) and Faraday shielding. Acquisition system is placed outside to reduce degradation and signal noise. (d) LFPs show rich spatiotemporal dynamics: global avalanches, local bursts, and individual spikes. Neural activities are interpreted through state-space embedding to identify attractors and transitions, enabling cc-RC and comparison across preparations/conditions. (e) Neural cultures serve as a reservoirs driven by temporally encoded light pulses. Evoked firing rates are measured and processed through a readout map (linear vector) for task-specific operations.
Figure 2: Pre-flight characterization of reservoir type and quality. (a) Representative raster plots for spontaneous activity classes. Type A: Poisson-like incoherent activity. Type B/C: partially synchronized activity with individual spikes and global bursts, separated by burst rate (B: <0.5Hz , C: >0.5Hz ). Type D: strongly synchronized activity with narrow, regular bursts and minimal inter-burst spiking. (b) Representative latent trajectories for each type. Type A shows compact and aperiodic dynamics. Type B/C span larger latent volumes with variable-period structure. Type D displays highly uniform laminar trajectories. (c) Representative streamline fields from latent-state velocity estimates. (d) Diagnostics across 500+ spontaneous recordings: Type occurrences, branching ratio, kernel rank, spectral radius, and connectivity correlation. Red bands indicate preferred operating ranges per metric. Avalanche criticality analysis is not reported for Type A due to absent coherent bursts. Each data point is determined using at least 5min of spontaneous activity. Details on metrics and experimental measurements can be found in the SI.
Figure 3: Performance of ( naive ) reservoir computing. (a) Ten temporally encoded input patterns. Pattern N contains N light pulses ( 15ms each) within 900ms , followed by 100ms rest ( 1 s total pattern window). Firing rates are measured at the end of each pattern window. (b) Training protocol. During 1 hour, patterns are presented in random order and multichannel firing rates are recorded. A ridge-classification readout Wout is fit with 10 -fold cross-validation. (c) Test protocol. After 15 minutes rest, each round presents patterns over 3 minutes ( 180 patterns), followed by 12 minutes rest. The fixed readout Wout is evaluated over 12 hours ( 47 rounds). (d) Accuracy by culture Type (A–D): first hour (left) and full 12 -hour test (right). Accuracy declines over time, after the first 1 – 2 hours. Black line indicates best performing samples (95th percentile). Insets show early and late latent trajectories corresponding to pattern 1, 2, 3: trajectories are initially well-separates, then collapse into overlapping clusters.
Figure 4: Chaos-controlled reservoir computing. (a) Chaos control strategy: a low-amplitude triangular modulation ( 1\penaltyHz , 100% duty cycle, 10% of input intensity) is superimposed during training and testing. Modulation starts 40 seconds before pattern onset to suppress initial transients. (b) Burst-timing regularization. Raster plots without (top) and with (bottom) modulation; orange dots indicate burst onset. Modulation aligns spontaneous bursting with input patterns, and entrains burst-interval variance within ±1.5ms over 60 minutes of training. (c) Representative latent trajectories without and with modulation (no pattern input). Modulation improves phase alignment and trajectory consistency. (d) cc-RC accuracy over 12 hours for Type C and D. Stabilized dynamics preserve separable pattern trajectories and extend useful performance, yielding 350% longer time above the 60% accuracy threshold, and 250% higher accuracy at 5 hours.
Figure 5: Knowledge Transplant. (a) KT workflow. An expert reservoir is fully trained to obtain Woute . Alignment via transformation T allows to transplant Woute to a student sample Wouts=T−1Woute (b) Attractors’ alignment. Student’s attractor in latent space (estimated via few input-evoked trajectories) is mapped onto the expert’s attractor (estimated via thousands of trajectories) via ridge-regularized regression to obtain the geometric transformation T . (c) Learning curves from-scratch versus KT. For both approaches, accuracy at each time point is computed using a 70% – 30% train–test split. For KT, the readout is updated over time using only the training partition, with evaluation on the held - out test set, ensuring fair comparison. Score values normalized to final from-scratch accuracy: * p<0.05 , ** p<0.01 , *** p<0.001 . (d) Representative KT cases. (top) KT sustained learning and drift-resistance vs. from-scratch learning where performance degrades after 15 minutes. (bottom) KT bootstrapping and performance ceiling enhancement vs. from-scratch learning.
Reservoir computing (RC) is a machine learning technique for data-driven modeling of dynamics for forecasting and control, primarily studied in computer science and physics literature with promising applications in neural network learning, physical computing, and neuroscience. Why reservoirs learn and how to choose good reservoir architectures are considered important open questions. We show that the RC problem is mathematically an extension of a classic problem in systems and control theory, the Kazantzis-Kravaris-Luenberger (KKL) observer design problem. As a consequence, many of the questions considered open for RC stand to benefit from a large body of theory in the mature KKL literature, non-exhaustively including on questions of embedding, transverse stability, local and global uniqueness guarantees, and effective data-driven solution constructions. Elaborating on this connection, we show that the surprising forecasting ability of reservoirs is in fact a direct consequence of the well-known observer internal model principle, derive an upper bound on the prediction error over a fixed forecast horizon, and provide a partial explanation for why linear readout training in RC works reasonably well. This work illustrates how classical ideas from systems and control can provide strong theoretical backing and open new questions for modern machine learning methods.
Anastasia Bizyaeva, Fernando Castaños, Jaime A. Moreno
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA · Department of Automatic Control, Cinvestav, Mexico · Instituto de Ingenier´ıa, Universidad Nacional Aut´onoma de M´exico, Mexico
Modern predictive modeling increasingly calls for a single learned dynamical substrate to operate across multiple regimes. From a dynamical-systems viewpoint, this capability decomposes into the storage of multiple attractors and the selection of the appropriate attractor in response to contextual cues. In reservoir computing (RC), multi-attractor learning has largely been pursued using large, randomly wired reservoirs, on the assumption that stochastic connectivity is required to generate sufficiently rich internal dynamics. At the same time, recent work shows that minimal deterministic reservoirs can match random designs for single-system chaotic forecasting. Under which conditions can minimal topologies learn multiple chaotic attractors? In this paper, we find that minimal architectures can successfully store multiple chaotic attractors. However, these same architectures struggle with task switching, in which the system must transition between attractors in response to external cues. We test storage and selection on all 28 unordered system pairs formed from eight three-dimensional chaotic systems. We do not observe a robust dependence of multi-attractor performance on reservoir topology. Over the ten topologies investigated, we find that no single one consistently outperforms the others for either storage or cue-dependent selection. Our results suggest that while minimal substrates possess the representational capacity to model coexisting attractors, they may lack the robust temporal memory required for cued transitions.
Francesco Martinuzzi, Holger Kantz
Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
Reservoir computing (RC) trains only a linear readout over a fixed recurrent layer, making it fast and data-efficient for online prediction. However, a static reservoir degrades under system drift, readout-only adaptation is then insufficient, and unconstrained reservoir adaptation can destroy the echo-state and incremental stability properties that make RC reliable. This paper proposes LoRA-RC, which adapts the recurrent matrix through a low-rank correction driven by streaming prediction errors. The base reservoir and adaptation bases are fixed offline; a small core matrix is adapted online, projected onto a spectral-norm ball, and low-pass filtered at each step. The projection guarantees that every applied recurrent matrix remains within a certified contraction set, and an incremental input-to-state stability bound is established for the reservoir along each online adaptation path, with path-independent rate and gain. On a Lorenz system with an abrupt parameter drift, LoRA-RC cuts post-drift prediction error by 56% versus a fixed RC and 51% versus readout-only adaptation; ablations over 20 seeds show that removing the projection inflates this error by more than a factor of 40.
Wenbin Wan
Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, USA