RiteeshGrandhi/sciclaimeval-shared-task huggingface dataset:
E.2 Reaching Task
For each model, we visualize the trial-averaged dynamic regime activity of each reach direction (Fig. 7 ). In SLDS, this is visualized by considering the discrete states as a one hot vector over time. When a dynamic regime is active, that state will have a value of 1 while the unactive states will have a value of 0. Thus the trial averaged value of each state must have a value in the interval [0,1] . In dLDS, we plot the inferred coefficient value without any modification.

Although SLDS correctly identifies preparatory and movement phases using states 4 and 3 respectively, it fails to differentiate dynamics occurring outside of these expected phases, incorrectly grouping unrelated regions together. Furthermore, the discrete formulation produces very similar activity patterns across all reach angles, obscuring any differences that are present. In dLDS, we observe that the features change smoothly and cyclically with the reach angle. However, the dynamic operator activity do not localize to the preparatory and movement phases due to a limited inference procedure.
F.1 Hyperparameter Settings
For switching models, we rely on the ssm package which allows for efficient Bayesian inference for a variety of state space models [ 21 ] .
We set the variational posterior to structured_meanfield , and the fitting procedure to laplace_em as recommended by the developers. Additionally, we set the distributional form of the dynamics and emissions matrices to Gaussian.

The hyperparameters of dLDS primarily consists of the lagrange multipliers in the BPDN-DF objective including \lambda_{0} , \lambda_{1} , \lambda_{2} . We find the optimal value of these hyperparameters using a random search with a fixed budget of 1000 evaluations. For each hyperparameter, we uniformly sample over the log of the interval [10^{-3},10^{3}] and evaluate it against the BPDN-DF objective. For the NASCAR experiment, we found that \lambda_{0}=1.044,\lambda_{1}=0.254, and \lambda_{2}=0.023 resulted in the best performance. For the Lorenz experiment, we found that \lambda_{0}=0.628,\lambda_{1}=2.010, and \lambda_{2}=0.0124 yielded the best performance.

For p-dLDS, the relevant hyperparameters consists of the SBL-DF dynamics tradeoff \xi , and the offset window size S . In the NASCAR experiment, we isolate the effect of the probabilistic inference procedure by setting S=T , removing the influence of the time-varying offset term. For \xi , we perform a random search by uniformly sample over the log of the interval [10^{-3},10^{3}] and found that \xi=0.945 was optimal. For the Lorenz experiment, we also optimize for the window size S by uniformly sample a discrete index on the interval \{2,\dots,T\} . For the Lorenz experiment, the optimized hyperparameters are S=85 and \xi=8.928 .
F.2 Hardware Specification
We perform hyperparameter sweep on our institution’s HPC cluster using small-scale CPU resources which consists of Dual Intel Xeon Gold 6226 CPUs. Once hyperparameters have been optimized, it is possible to run each experiment within approximately 2 hours on the 2020 edition of the M1 Macbook Pro.
Figure 1: (A) Graphical model of dLDS. (B) p-dLDS includes hierarchical variables for probabilistic sparse inference and reparameterizes the latent space to include a time-varying offset term.; (A) Graphical model of dLDS. (B) p-dLDS includes hierarchical variables for probabilistic sparse inference and reparameterizes the latent space to include a time-varying offset term.
Figure 2: Probabilistic model and offset term reduce estimation errors. (A) Example trial from the NASCAR experiment colored by the true switching labels (not provided during training). Each track segment has a random speed \tau . (B) Inferred state space, colored by discrete state or dominant coefficients. p-dLDS identifies correct track segments. (C) Example trial from the Lorenz experiment. The speed ramps according to the time intervals \Delta\tau in an ODE solver. (D) Inferred state space, colored by the dominant coefficients. The time-varying offset term allows p-dLDS coefficients to switch according to the true speed and accurately model the two fixed points in the opposing lobes.; Probabilistic model and offset term reduce estimation errors. (A) Example trial from the NASCAR experiment colored by the true switching labels (not provided during training). Each track segment has a random speed \tau . (B) Inferred state space, colored by discrete state or dominant coefficients. p-dLDS identifies correct track segments. (C) Example trial from the Lorenz experiment. The speed ramps according to the time intervals \Delta\tau in an ODE solver. (D) Inferred state space, colored by the dominant coefficients. The time-varying offset term allows p-dLDS coefficients to switch according to the true speed and accurately model the two fixed points in the opposing lobes.
Figure 3: p-dLDS efficiently captures changes in dynamics. (A) Latent factors are computed from empirical EMG of the reaching experiment in [ 7 ] .
Dynamics are characterized by a preparatory and movement phase. (B) Synthetic spikes and LFPs are generated using the wslfp package [ 15 , 14 ] (C) The trial-averaged coefficients for p-dLDS smoothly vary with reaching angle. DO 1 captures preparatory dynamics while DO 3 captures movement dynamics. (D) Confusion matrix for linear classification of reach directions. p-dLDS predictions closely align to true diagonal.; p-dLDS efficiently captures changes in dynamics. (A) Latent factors are computed from empirical EMG of the reaching experiment in [ 7 ] .
Dynamics are characterized by a preparatory and movement phase. (B) Synthetic spikes and LFPs are generated using the wslfp package [ 15 , 14 ] (C) The trial-averaged coefficients for p-dLDS smoothly vary with reaching angle. DO 1 captures preparatory dynamics while DO 3 captures movement dynamics. (D) Confusion matrix for linear classification of reach directions. p-dLDS predictions closely align to true diagonal.
Figure 4: Learned system discovers coherent structure in clinical data. (A, D) LFP data was collected on patients watching videos with different emotional content. (B, E) LFP spectrograms are 40-dimensional signals where each channel represents a particular frequency. (C, F) Inferred states and coefficients shows that rSLDS and dLDS exhibit unpredictable switching behavior. In contrast, p-dLDS captures smooth coefficients and identifies DOs that align with the trial’s emotional content.
The learned patterns broadly generalize to the held-out data.; Learned system discovers coherent structure in clinical data. (A, D) LFP data was collected on patients watching videos with different emotional content. (B, E) LFP spectrograms are 40-dimensional signals where each channel represents a particular frequency. (C, F) Inferred states and coefficients shows that rSLDS and dLDS exhibit unpredictable switching behavior. In contrast, p-dLDS captures smooth coefficients and identifies DOs that align with the trial’s emotional content.
The learned patterns broadly generalize to the held-out data.
Figure 5: Empirically-Derived Reach Experiment. (A) 1,200 neurons are randomly placed into a 5 mm by 10 mm by 1 mm region. Electrodes are placed in a grid centered in this region (B) Spiking activity for a subset of neurons in an example trial produced from a factor-based spiking network. (C) First 15 channels in a simulated multi-channel LFP recording. Preparatory and Movement phases are marked by the dotted lines.; Empirically-Derived Reach Experiment. (A) 1,200 neurons are randomly placed into a 5 mm by 10 mm by 1 mm region. Electrodes are placed in a grid centered in this region (B) Spiking activity for a subset of neurons in an example trial produced from a factor-based spiking network. (C) First 15 channels in a simulated multi-channel LFP recording. Preparatory and Movement phases are marked by the dotted lines.
Figure 6: (A) ELBO converges in both synthetic dynamical systems. (B) Multi-step inference where k represents the number of steps. Tables 3 and 4 report the final values.; (A) ELBO converges in both synthetic dynamical systems. (B) Multi-step inference where k represents the number of steps. Tables 3 and 4 report the final values.
Figure 7: Trial-averaged activity for (A) SLDS discrete states and (B) dLDS DO coefficients for each reach angle. The preparatory and movement phases occur between the dashed lines similar to Figure 3 . Time 0 represents the onset of the stimulus.; Trial-averaged activity for (A) SLDS discrete states and (B) dLDS DO coefficients for each reach angle. The preparatory and movement phases occur between the dashed lines similar to Figure 3 . Time 0 represents the onset of the stimulus.
Metrics for synthetic dynamical systems. Bold means best performance. (\uparrow) indicates higher score is better while (\downarrow) indicates that lower is better. ✗ indicates that value diverged towards -\infty . Switch events for decomposed models are defined as times where the active set of DOs change from the previous time step.
Inference performance for the reaching experiment (see Figure 3 ) on a held-out test set.
Top-1 and Top-3 accuracies
are obtained by predicting reach directions from latent variable features using linear classifiers.
State and Dynamics MSE are computed with respect to true latent variables.
Metrics for NASCAR. Bold means best performance. (\uparrow) indicates higher score is better while (\downarrow) indicates that lower is better. ✗ indicates that value diverged towards -\infty . All MSE values are \times 10^{-3} while R^{2} values are not scaled. We report means across 5 seeds and include standard deviation in parenthesis.
Metrics for Lorenz. Bold means best performance. (\uparrow) indicates higher score is better while (\downarrow) indicates that lower is better. ✗ indicates that value diverged towards -\infty . We report means across 5 seeds and include standard deviation in parenthesis.
Inference performance for the reaching experiment (see Figure 3 ) on a held-out test set.
Top-1 and Top-3 accuracies
are obtained by predicting reach directions from latent variable features using linear classifiers.
State and Dynamics MSE are computed with respect to true latent variables. We report standard deviations in parenthesis across 5 seeds.