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Researcher profile

Georgia Koppe

Georgia Koppe contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningArtificial IntelligenceComputation and Languagemath.DSNeurons and Cognitionnlin.CDphysics.comp-phQuantitative Methods

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Published work

4 published item(s)

preprint2026arXiv

Teacher Forcing as Generalized Bayes: Optimization Geometry Mismatch in Switching Surrogates for Chaotic Dynamics

Identity teacher forcing (ITF) enables stable training of deterministic recurrent surrogates for chaotic dynamical systems and has been highly effective for dynamical systems reconstruction (DSR) with recurrent neural networks (RNNs), including interpretable almost-linear RNNs (AL-RNNs). However, as an intervention-based prediction loss (and thus a generalized Bayes update), teacher forcing need not match the free-running model's marginal likelihood geometry. We compare the objective-induced curvatures of ITF and marginal likelihood in a probabilistic switching augmentation of AL-RNNs, estimating ambiguity-aware observed information via Louis' identity. In the switching setting studied here, conditioning on a single forced regime path (as ITF does) inflates curvature, while marginal likelihood curvature is reduced by a missing-information correction when multiple switching explanations remain plausible. In Lorenz-63 experiments, windowed evidence fine-tuning improves held-out evidence but can degrade dynamical quantities of interest (QoIs) relative to ITF-pretrained models.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Uncovering the Computational Roles of Nonlinearity in Sequence Modeling Using Almost-Linear RNNs

Sequence modeling tasks across domains such as natural language processing, time series forecasting, and control require learning complex input-output mappings. Nonlinear recurrence is theoretically required for universal approximation of sequence-to-sequence functions, yet linear recurrent models often prove surprisingly effective. This raises the question of when nonlinearity is truly required. We present a framework to systematically dissect the functional role of nonlinearity in recurrent networks, identifying when it is computationally necessary and what mechanisms it enables. We address this using Almost Linear Recurrent Neural Networks (AL-RNNs), which allow recurrence nonlinearity to be gradually attenuated and decompose network dynamics into analyzable linear regimes, making computational mechanisms explicit. We illustrate the framework across diverse synthetic and real-world tasks, including classic sequence modeling benchmarks, a neuroscientific stimulus-selection task, and a multi-task suite. We demonstrate how the AL-RNN's piecewise linear structure enables identification of computational primitives such as gating, rule-based integration, and memory-dependent transients, revealing that these operations emerge within predominantly linear backbones. Across tasks, sparse nonlinearity improves interpretability by reducing and localizing nonlinear computations, promotes shared representations in multi-task settings, and reduces computational cost. Moreover, sparse nonlinearity acts as a useful inductive bias: in low-data regimes or when tasks require discrete switching between linear regimes, sparsely nonlinear models often match or exceed fully nonlinear architectures. Our findings provide a principled approach for identifying where nonlinearity is functionally necessary, guiding the design of recurrent architectures that balance performance, efficiency, and interpretability.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Series

Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning methods to reconstruct this latent DS in a data-driven, unsupervised way. In many areas of science it is common to sample time series observations from many data modalities simultaneously, e.g. electrophysiological and behavioral time series in a typical neuroscience experiment. However, current machine learning tools for reconstructing DSs usually focus on just one data modality. Here we propose a general framework for multi-modal data integration for the purpose of nonlinear DS reconstruction and the analysis of cross-modal relations. This framework is based on dynamically interpretable recurrent neural networks as general approximators of nonlinear DSs, coupled to sets of modality-specific decoder models from the class of generalized linear models. Both an expectation-maximization and a variational inference algorithm for model training are advanced and compared. We show on nonlinear DS benchmarks that our algorithms can efficiently compensate for too noisy or missing information in one data channel by exploiting other channels, and demonstrate on experimental neuroscience data how the algorithm learns to link different data domains to the underlying dynamics.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI

A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. Here we advance a state space model (SSM) based on generative piecewise-linear recurrent neural networks (PLRNN) to assess dynamics from neuroimaging data. In contrast to many other nonlinear time series models which have been proposed for reconstructing latent dynamics, our model is easily interpretable in neural terms, amenable to systematic dynamical systems analysis of the resulting set of equations, and can straightforwardly be transformed into an equivalent continuous-time dynamical system. The major contributions of this paper are the introduction of a new observation model suitable for functional magnetic resonance imaging (fMRI) coupled to the latent PLRNN, an efficient stepwise training procedure that forces the latent model to capture the 'true' underlying dynamics rather than just fitting (or predicting) the observations, and of an empirical measure based on the Kullback-Leibler divergence to evaluate from empirical time series how well this goal of approximating the underlying dynamics has been achieved. We validate and illustrate the power of our approach on simulated 'ground-truth' dynamical (benchmark) systems as well as on actual experimental fMRI time series, and demonstrate that the latent dynamics harbors task-related nonlinear structure that a linear dynamical model fails to capture. Given that fMRI is one of the most common techniques for measuring brain activity non-invasively in human subjects, this approach may provide a novel step toward analyzing aberrant (nonlinear) dynamics for clinical assessment or neuroscientific research.

0 citations0 reviewsNo code linkedOpen access