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Inferring Multi-Timescale Neural Dynamics with Switching Linear Dynamical Systems

Lulu Gong, Yongxu Zhang, Shreya Saxena

arXiv:2610.01786v1cs.LGeess.SPq-bio.NCstat.ML

TL;DR

Recovering latent neural timescales is difficult when autocorrelation summaries or fitted dynamics do not identify the underlying temporal structure. MTS-SLDS combines multi-lag moment initialization with regime-conditioned inference. It recovers timescales and switching structure in simulations and neural recordings, with limits from model assumptions and data conditions.

  • Problem

    Autocorrelation estimates depend on noise, population projection, and decay assumptions, while limited data can leave fitted transition eigenvalues and switching structure unidentified.

    Source: §1 · p. 2

  • Method

    MTS-SLDS initializes latent dynamics from multiple observation lags and refines them with regime-conditioned Laplace EM for Gaussian or Poisson observations.

    Source: §1 · p. 2

  • Results

    Across simulations and neural recordings, MTS-SLDS recovers timescales and switching structure; area 2 regimes align with movement onset and timescales agree with behavioral decay times.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The learned transition eigenvalues provide a direct biological interpretation of regime-specific timescales that can be compared across behavioral states.

    Source: §1 · p. 2, §5 · p. 9

    MTS-SLDS estimates effective timescales under its assumed model and cannot separate intrinsic circuit dynamics from temporally structured inputs.

    Source: §5 · p. 9

Abstract

from arXiv · show

Neural activity often exhibits multiple timescales that can vary with behavioral states and task conditions. Identifying these timescales from neural recordings is important for better understanding neural computation and function. However, traditional approaches based on autocorrelation fitting are difficult to scale to high-dimensional population recordings and can become unreliable when neural dynamics change with behavior. State-space models have been a powerful framework for modeling high-dimensional neural population activity through latent dynamical systems, but standard formulations and inference methods do not explicitly account for multiple timescales and therefore do not guarantee accurate recovery of the underlying temporal structure. Motivated by these questions, we introduce the Multi-Timescale Switching Linear Dynamical System (MTS-SLDS), a framework for identifying regime-specific latent timescales from continuous or spiking neural observations. MTS-SLDS combines a multi-lag moment initialization, which captures temporal structure across multiple observation lags, with \textit{regime-conditioned} Laplace-EM inference, which reduces mixing of dynamical statistics across uncertain regimes. Characteristic timescales can then be extracted directly from the eigenvalues of the learned latent transition matrices. In synthetic and neural experiments with Gaussian and Poisson spike observations, MTS-SLDS accurately recovers timescales and switching structure over multiple datasets.

1 INTRODUCTION

Neural timescales matter for understanding temporal organization, but recovering them from population recordings is difficult when methods summarize correlations or fitted dynamics are not identifiable. MTS-SLDS combines multi-lag initialization with regime-conditioned inference to recover regime-specific timescales.

1 INTRODUCTION

  • Autocorrelation-based estimates depend on noise, the measured population projection, and the assumed decay form, while latent models describe the dynamics generating observed activity.Latent models also support model-based prediction and held-out validation.Source: §1 · p. 2
  • Different transition matrices can produce similar observation likelihoods yet imply different decay rates or switching structure, limiting interpretation of fitted eigenvalues as timescales.This identifiability problem matters when the goal is to interpret the learned system, not only predict observations.Source: §1 · p. 2
  • MTS-SLDS combines multi-lag moment initialization with regime-conditioned Laplace EM to recover regime-specific latent timescales from Gaussian or Poisson observations.The inference method retains regime-specific state moments so uncertain assignments do not mix dynamical statistics across regimes.Source: §1 · p. 2
  • Across simulations and neural recordings, MTS-SLDS recovers timescales and switching structure, with V4 and area 2 analyses relating inferred dynamics to autocorrelation estimates and behavior.In V4, the single-regime model has higher held-out likelihood and closer simulated autocorrelations than the SLDS baseline; in area 2, regimes align with movement onset.Source: §1 · p. 2

1.1 RELATED WORK

  • Prior methods include autocorrelation fitting, spectral approaches, autoregressive models, and switching state-space methods, but flexibility or a posterior approximation alone does not ensure spectral recovery.MTS-SLDS combines regime-local multi-lag initialization with regime-conditioned learning and explicitly tests recovery of underlying timescales.Source: §1.1 · pp. 2–3

2 MULTI-TIMESCALE MODELING AND INFERENCE

MTS-SLDS models neural observations through latent dynamics selected by discrete regimes, with timescales read from transition eigenvalues. It initializes dynamics from multi-lag moments and refines them with regime-conditioned inference.

2.2 MULTI-TIMESCALE SLDS MODEL

  • The SLDS uses a continuous latent state whose linear transition matrix is selected by a discrete regime, with Gaussian emissions for continuous signals and Poisson emissions for spike counts.Each regime has its own transition matrix, offset, and process-noise covariance.Source: §2.2 · p. 4

2.1 MULTIPLE TIMESCALES IN NEURAL DYNAMICS

  • For a stable latent mode, the transition eigenvalue determines its relaxation timescale; these within-regime timescales differ from regime dwell times governed by the transition matrix.Pooling channels in autocorrelation methods can suppress modal contributions that multichannel observations preserve.Source: §2.1 · p. 3, §2.2 · p. 4

2.3 LEARNING REGIME-SPECIFIC TIMESCALES

  • MTS-SLDS first estimates dynamics and provisional regimes from multi-lag observation moments, then refines the model with regime-conditioned Laplace EM before extracting timescales from each transition matrix.Ablations indicate that both stages contribute to regime identification and timescale estimation.Source: §2.3 · p. 5

2.3.1 MULTI-LAG MOMENT INITIALIZATION

  • Multi-lag initialization relates observation moments across positive lags to latent dynamics, using distinct moment constructions for Gaussian and Poisson observations.For Gaussian observations the moments are lagged observation covariances; for Poisson observations the method uses an element-wise conversion.Source: §2.3.1 · p. 5
  • The initialization projects pooled within-trial moments, assigns provisional regimes from windowed autocorrelation descriptors, and estimates transition operators from intervals assigned to a single regime.Because the stationary moment identities need not hold exactly after empirical segmentation, these operators serve as starting estimates for RC-L-EM.Source: §2.3.1 · p. 5

2.3.2 REGIME-CONDITIONED LAPLACE EM (RC-L-EM)

  • RC-L-EM maintains separate state approximations for candidate regimes and adjacent regime pairs, so each transition update uses moments conditioned on the regime generating it.Its moment matching and local Laplace updates make the procedure an approximate EM method.Source: §2.3.2 · pp. 5–6

3 SYNTHETIC DATA

In synthetic switching systems, MTS-SLDS improves timescale and regime recovery over standard SLDS for Poisson observations, while both methods show similar timescale errors under Gaussian noise. Stationary tests also recover the prescribed timescales.

3 SYNTHETIC DATA

  • The evaluation compared MTS-SLDS with standard SLDS across Gaussian and Poisson observations, using timescales matched to ground truth and median MAPE across datasets.Stationary Poisson comparisons also included two-exponential autocorrelation fitting and aABC.Source: §3 · pp. 6–7
  • 11% versus 44% timescale error and 0.95 versus 0.54 balanced regime accuracy favored MTS-SLDS over SLDS in an illustrative switching Poisson experiment, despite equal held-out latent R² of 0.82.The comparison shows that similar latent trajectory reconstruction can accompany different timescale and regime recovery.Source: §3 · p. 7
  • Both state-space methods recovered stationary timescales of 20 and 100 ms, and the switching tests prescribed spectra of {10, 40, 100} ms and {20, 80, 300} ms.The simulations used 128-channel observations from 10-dimensional latent systems, with Gaussian or Poisson emissions.Source: §3 · pp. 6–7
  • Approximately 6% median timescale error persisted for both methods across Gaussian SNR 0.5–5, while MTS-SLDS had 1.7–3.3-fold lower median error than SLDS across Poisson counts of 0.05–0.5 per bin per channel.Poisson errors increased as counts decreased.Source: §3 · p. 7

4 NEURAL DATA APPLICATIONS AND ANALYSES

In V4 fixation recordings, MTS-SLDS improves held-out prediction and captures a richer latent timescale spectrum than pooled autocorrelation fits. In Area 2, its movement-regime timescales distinguish active from passive reaching and closely match behavioral decay times.

4.1 INTERPRETABLE TEMPORAL STRUCTURE IN V4 POPULATION ACTIVITY

  • V4 analysis uses 2-ms spike-count bins during sustained fixation, fits a single-regime Poisson model, and focuses on H = 8 after prediction saturates near that dimension.The latent-dimension comparison uses five-fold cross-validation and multiple seeds.Source: §4.1 · p. 7
  • MTS-SLDS improves held-out log-likelihood by 52.4 ± 6.9 per trial and reproduces observed pooled autocorrelation more closely than SLDS.Both methods yield three reproducible timescales, while pooled-autocorrelation methods provide coarser descriptions.Source: §4.1 · p. 7, Figure 3 · p. 8
  • MTS-SLDS estimates V4 timescales of 26.4, 49.5, and 120.2 ms, versus SLDS estimates of 23.5, 36.1, and 110.9 ms.The figure contrasts state-space estimates with estimates from pooled population autocorrelation.Source: §4.1 · p. 7, Figure 3 · p. 8

4.2 TASK-RELATED TIMESCALES IN SOMATOSENSORY CORTEX AREA 2

  • Area 2 models use 20-ms bins, two regimes, and a common H = 6 for active reaches and passive perturbations; both methods identify comparable onset-associated regime-probability changes.The analysis spans 500 ms before to 500 ms after movement onset.Source: §4.2 · p. 8
  • MTS-SLDS movement-regime medians are 188 ms (active) and 99 ms (passive), near behavioral decay times of 168 and 86 ms; SLDS estimates 117 and 108 ms.The analysis compares slowest effective timescales within a 20–300-ms band.Source: §4.2 · p. 8, Figure 4 · p. 9
  • Time-shuffling produces much smaller timescales under both methods, while sPCF-EM shows no clear timescale distinction or relation to behavioral ordering.The shuffle analysis permutes time bins within trials.Source: §4.2 · p. 9

5 DISCUSSION

MTS-SLDS combines multi-lag moment initialization with regime-conditioned Laplace EM to estimate regime-specific latent timescales. Its estimates are effective timescales under the assumed model, with recovery constrained by data quality and modeling approximations.

5 DISCUSSION

  • MTS-SLDS combines multi-lag moment initialization with regime-conditioned Laplace EM to recover regime-specific latent timescales from neural population recordings.The learned transition eigenvalues provide the timescales; ablations indicate both components contribute to recovery.Source: §5 · p. 9
  • Regime-conditioned inference recovers much regime information from baseline parameters, while multi-lag initialization accounts for the remaining gap in timescale error.Source: §5 · p. 9
  • The model estimates effective timescales and cannot separate intrinsic circuit dynamics from temporally structured inputs, including persistent drive from unobserved regions or behavioral variables.Source: §5 · p. 9
  • Weakly observed modes, closely spaced decay rates, short regime visits, and limited recording duration can restrict recovery; approximations mean estimates are not guaranteed globally optimal or unbiased.The authors identify quantifying spectrum uncertainty and sensitivity to model choices as future work.Source: §5 · p. 10

6 STATEMENTS

The appendix explains how latent transition spectra relate to observed temporal correlations and details a multi-lag initializer that segments regimes before estimating their dynamics. These links have limits: observation mappings and switching history can obscure modes, and the initializer’s stationary identities need not hold exactly under estimated segmentation or switching transients.

A.1 FIXED-REGIME DYNAMICS AND GAUSSIAN OBSERVATIONS

  • Under a fixed stable regime, latent transition eigenvalues determine modal relaxation times, but observed ACF coefficients can hide modes or make the ACF unlike a nonnegative exponential mixture.Finite positive relaxation times are reported only for eigenvalues with 0 < |λ| < 1; defective or nonnormal dynamics can add effects beyond modal exponential decay.Source: §A.1 · p. 12

A.2 POISSON OBSERVATIONS AND MOMENT CONVERSION

  • For Poisson observations, moment conversion recovers log-intensity covariance at positive lags under jointly Gaussian latent states and an exponential link, but not for arbitrary switching mixtures or links.Raw count correlations can combine latent decay components into additional apparent timescales.Source: §A.2 · p. 13

A.3 SWITCHING AND COORDINATE INVARIANCE

  • In switching systems, observed correlations depend on regime paths, means, and emission mappings; regime dwell times differ from latent relaxation times, and stable individual regimes do not ensure process stability.Independent latent-coordinate choices across regimes do not determine the relative coordinates required by the initializer.Source: §A.3 · p. 13

B MULTI-LAG MOMENT INITIALIZATION

  • The multi-lag initializer pools training data for temporal features, provisionally segments regimes, then estimates dynamics from regime-local moments without crossing trial boundaries.Its stationary identities motivate the procedure but need not hold exactly under estimated segmentation or switching transients.Source: B MULTI-LAG MOMENT INITIALIZATION · p. 13

B.1 EMPIRICAL MOMENTS AND OBSERVATION-MODEL CONVERSION

  • For Poisson data the initializer converts regularized observation moments, requiring positive means and logarithm arguments; at zero lag it subtracts the Poisson mean-count diagonal before conversion.Gaussian zero-lag moments instead separate the observation-loading contribution from latent covariance.Source: §B.1 · p. 14

B.2 WINDOWED TEMPORAL SEGMENTATION

  • Windowed segmentation projects pooled positive-lag moments onto leading singular vectors, selects a lag band against shuffled null moments, then clusters standardized decay descriptors with sticky Viterbi labeling.The positive-floor descriptor discards negative ACF values and summarizes aggregate decay rather than resolving modes or fully representing oscillations.Source: §B.2 · p. 14

B.3 REGIME-LOCAL MULTI-LAG REGRESSION

  • For each regime, multi-lag regression recomputes observation moments from starts whose labels remain in that regime across the maximum lag, then fits covariance-shift relations across adjacent lags.Regimes with too few admissible starts fall back to the pooled operator; preconditioning changes weighting but does not remove empirical-moment errors.Source: §B.3 · pp. 14–15

B.4 EMISSION PARAMETERS, COORDINATES, AND COVARIANCE INITIALIZATION

This appendix specifies how the initializer sets emission parameters, latent coordinates, and covariance references, then describes regime-conditioned approximate inference and learning. It also distinguishes these procedures from ACF fitting, aABC, autoregressive models, and variational Laplace EM.

B.4 EMISSION PARAMETERS, COORDINATES, AND COVARIANCE INITIALIZATION

  • Within-regime moments determine spectra but not relative latent coordinates, so the initializer uses a common coordinate convention and compatible covariance reference before refining with RC-L-EM.Independent factorizations do not resolve cross-regime coordinate ambiguity, and some positive-definite corrections need not preserve the chosen emission reference.Source: §B.4 · p. 15

C.1 POSTERIOR APPROXIMATION AND DYNAMICAL STATISTICS

  • RC-L-EM retains regime- and transition-pair-conditioned state moments for dynamical updates, unlike a global Gaussian trajectory approximation independent of the candidate regime.It uses single-time moments for emissions and pair moments for dynamics; these local approximations need not define one globally consistent trajectory posterior.Source: C REGIME-CONDITIONED INFERENCE AND… · p. 15, §C.1 · p. 16, §C.3 · p. 17

C.2 FORWARD FILTERING

  • The forward pass moment-matches incoming state mixtures; Gaussian prediction updates are exact for that prediction, but not generally for the uncollapsed SLDS posterior.For a single Gaussian regime, filtering reduces to Kalman filtering; Poisson observations still use local Laplace approximations.Source: §C.2 · pp. 16–17

C.3 BACKWARD SMOOTHING AND PAIR MOMENTS

  • Backward smoothing supplies regime probabilities and pair-specific state moments that preserve predecessor information for dynamics learning, which a collapsed destination prediction loses.Regime weights or products of state means alone do not provide the required cross-covariances.Source: §C.3 · p. 17

C.4 DYNAMICS AND TRANSITION UPDATES

  • Dynamics and transition parameters are updated from expected moments and counts; priors, covariance restrictions, and stability constraints can modify the unconstrained updates.A real Schur representation alone does not enforce stable transition matrices.Source: §C.4 · pp. 17–18

C.5 OBSERVATION PARAMETERS AND FIXED PARAMETER BLOCKS

  • Observation parameters use expected moments, with a fixed-moment Poisson objective whose variance term accounts for continuous-state uncertainty; initialized fixed blocks remain unchanged.RC-L-EM is approximate: moment matching and Laplace approximations do not guarantee monotonic marginal-likelihood ascent or improved timescales at each iteration.Source: §C.5 · p. 18

D BASELINE TIMESCALE ESTIMATORS AND SLDS INFERENCE

  • ACF-exponential fitting estimates decay components by nonlinear least squares, while aABC compares simulated and observed summaries; neither directly models latent multivariate dynamics.ACF estimates depend on lag window and finite-sample distortion and do not explicitly model oscillations; aABC estimates describe simulator timescales and need not be unbiased under misspecification.Source: D BASELINE TIMESCALE ESTIMATORS AND… · p. 18, §D.1 · p. 19, §D.3 · p. 19

D.2 RELATION TO AUTOREGRESSIVE MODELS

  • AR/VAR models can represent multiple timescales in observations, whereas SLDS places autoregressive dynamics in a shared latent process; variational Laplace EM factorizes continuous and discrete trajectories.For Gaussian emissions its Gaussian coordinate update is exact, but the joint factorization remains approximate; Poisson updates are approximate, and RC-L-EM differs in its regime-conditioned moments.Source: §D.2 · p. 19, §D.4 · p. 20, §D.5 · p. 20

E SPATIAL POOLING OBSCURES TIMESCALES

Pooling can increase counts while reducing the visibility of latent timescales because spatial projection reweights their contributions to the scalar ACF. In the reported simulation, full pooling favors fewer exponential components than the three generating timescales, while multichannel state-space models retain spatial and cross-channel information.

E SPATIAL POOLING OBSCURES TIMESCALES

  • A pooled scalar projection preserves decay constants of contributing modes but reweights their amplitudes, so a mode orthogonal to the pooling vector disappears and a weakly projected mode can be hard to resolve.Thus a scalar ACF may contain multiple timescales, but their visibility depends on their relative contributions.Source: E SPATIAL POOLING OBSCURES TIMESCALES · pp. 20–21
  • Channel summation can make coherent modes grow quadratically with pooled channel count, while modes with canceling loadings receive less weight and can lose relative visibility.Increasing total count level therefore need not make every latent timescale easier to detect.Source: E SPATIAL POOLING OBSCURES TIMESCALES · p. 21
  • The experiment uses three independent modes with timescales of 10, 40, and 150 ms and compares dense and sparse Poisson count settings across pooling levels.It uses a fixed 300-channel loading matrix and the same latent trajectories in both count settings.Source: E SPATIAL POOLING OBSCURES TIMESCALES · p. 21
  • At full pooling, BIC favors two exponentials in both count settings although the generator has three timescales; fewer-component fits can omit a weak mode or summarize mixtures with effective timescales.The figure compares per-mode recovery, selected exponential order, and full-pooling one- and two-component fits; dotted lines mark the true order or timescales.Source: E SPATIAL POOLING OBSCURES TIMESCALES · pp. 21–22, Figure 5 · p. 22
  • Multichannel state-space models retain channel-specific loadings and cross-channel temporal dependencies, providing information about modes that may contribute weakly to the population sum.The study evaluates ACF-fit recovery fractions and BIC-selected order using channel draws from a fixed recording; full-pooling repetitions vary only optimization.Source: E SPATIAL POOLING OBSCURES TIMESCALES · pp. 21–22

F.1 ABLATION TESTS

The ablations test how initialization, fitting configuration, inference, and transition priors affect timescale recovery and regime identification. Results show that these outcomes can respond differently to each choice.

F.1 ABLATION TESTS

  • The ablations assessed both timescale estimation and regime recovery in Poisson switching simulations, using medians and interquartile ranges unless otherwise stated.The setup varied K and mean count level; initialization comparisons used ten seeds and comparisons involving ssm fitting used five.Source: §F.1 · pp. 22–23
  • 10 iterations versus 130: for K = 2 runs crossing 15% MAPE, moment initialization reached the threshold sooner than ssm initialization, despite similar final errors of about 9.5%.All ten moment-initialized runs crossed the threshold, compared with nine of ten ssm-initialized runs; the median first-crossing iterations were 10 (IQR 10–10) and 130 (100–150).Source: §F.1 · p. 23, Figure 6 · p. 24
  • 14.9 percentage points: for K = 3, ssm initialization had higher timescale MAPE than moment initialization, and failed regime recovery in six of ten paired datasets.Moment initialization with the ridge descriptor had no regime-recovery failures; the failure threshold was minimum per-regime recall below 0.10.Source: §F.1 · p. 23, Figure 6 · p. 24
  • 9.5% to 56.2%: moment-start RC-Laplace-EM reduced median timescale MAPE, while the tested Laplace-EM configuration increased it and failed regime recovery on all five seeds.The fitting configurations also differed in starting parameters, iteration budgets, and whether emission loadings were updated, so the contrast does not isolate one factor.Source: §F.1 · p. 23, Figure 6 · p. 24
  • 0.770 versus 0.507: regime-conditioned inference improved held-out regime accuracy using the same fitted ssm parameters, while MTS-SLDS reached 0.949.The regime-conditioned result did not close the gap to MTS-SLDS.Source: §F.1 · p. 23, Figure 7 · p. 25
  • 9.5%: MTS-SLDS median timescale MAPE was below all six tested transition-prior settings; an oracle-matched prior reduced baseline MAPE from 31.2% to 15.2% but regime accuracy remained 0.507.Matching the MTS-SLDS prior to p_stay = 0.99 yielded 33.8% MAPE; transition regularization improved parameter estimation but did not explain the regime-recovery gap.Source: §F.1 · p. 23, Figure 7 · p. 25

F.2 RECOVERY OF OSCILLATORY AND DECAYING DYNAMICS

The experiments test whether MTS-SLDS can recover damped oscillations as well as multiple decay timescales. It estimated oscillation frequencies and decay times close to their generating values, while direct exponential ACF fitting overestimated slower components in a separate test.

F.2 RECOVERY OF OSCILLATORY AND DECAYING DYNAMICS

  • The experiments address oscillatory dynamics as a real-data-relevant case in addition to the synthetic timescale-recovery conditions reported in the main text.The tested oscillatory case evaluates recovery of both decay timescale and oscillation frequency.Source: §F.2 · p. 26
  • Across tested modes with 100–400 ms decay times and 2–10 Hz frequencies, MTS-SLDS estimates were close to ground truth.The estimates capture the decay envelope and oscillatory frequency as distinct properties of latent dynamics.Source: §F.2 · p. 26
  • For decay timescales of 10, 40, and 100 ms, MTS-SLDS and SLDS closely recovered the true values, while ACF-exp overestimated the two slower components.The overestimation was particularly marked for the 100-ms timescale.Source: §F.2 · p. 26

G V4 DATA ANALYSIS DETAILS

The V4 analysis uses held-out trials to assess prediction and compares effective timescale bands with autocorrelation-based fits. MTS-SLDS improved held-out predictive likelihood at matched latent dimension, while the analysis treats the exact number and separation of decay processes as dependent on model dimension and spectral resolution.

G V4 DATA ANALYSIS DETAILS

  • The comparison used 81 V4 fixation trials, 3-second epochs, 2-ms bins, a single dynamical regime, and a fixed split reserving 10 trials for final testing.The methods used five-fold cross-validation, three initialization seeds, and matched H = 8 for the main comparison; test trials were not used for fitting or model selection.Source: G V4 DATA ANALYSIS DETAILS · p. 26
  • 26.4, 49.5, and 120.2 ms: MTS-SLDS yielded three timescale-band centers across the 15 seed–fold fits, compared with 23.5, 36.1, and 110.9 ms for SSM-SLDS.The analysis reported one center per band rather than treating closely spaced eigenvalues as separate resolved processes; an additional MTS-SLDS mode varied between 69.7 and 101.9 ms and did not reach full occupancy.Source: G V4 DATA ANALYSIS DETAILS · pp. 26–27
  • State-space models had smaller pooled-ACF errors over 100–500 ms than the two- and three-timescale aABC fits, but aABC agreement over 0–100 ms measures fit to its objective rather than independent prediction.Increasing direct exponential-fit order introduced near-bin components and a boundary-limited 1-ms component across tested fitting windows.Source: G V4 DATA ANALYSIS DETAILS · p. 27
  • 52.37 nats per trial: at matched H = 8, MTS-SLDS improved held-out predictive likelihood over SLDS on all 10 reserved trials.The advantage was 44.14 nats per trial against SSM-SLDS at its development-optimal H = 4; the likelihood decomposition attributed the improvement primarily to predicted firing rates.Source: G V4 DATA ANALYSIS DETAILS · p. 27
  • The V4 analyses support multiple reproducible effective timescale bands and improved held-out prediction, while the exact number and separation of decay processes depend on model dimension and spectral resolution.The single-channel prediction in Figure 9 is a selected best-channel example, not a representative-channel summary.Source: G V4 DATA ANALYSIS DETAILS · p. 27
  • With H = 2, MTS-SLDS produced effective components in the tens-of-milliseconds and approximately 100-ms ranges, within the two-timescale aABC estimates.H = 2 limits the model to at most two distinct spectral decay times but does not prescribe their values; the later method showed broader posterior uncertainty, while ACF-exp tended toward faster timescales.Source: G V4 DATA ANALYSIS DETAILS · p. 27

H AREA 2: FITTING AND ANALYSIS

The Area 2 analysis compares MTS-SLDS and SLDS predictions and regime assignments around movement onset, then examines estimated timescales and their relation to behavior. Estimates were closer to behavioral magnitudes and ordering for MTS-SLDS, but the comparison does not establish neural-behavioral coupling.

H AREA 2: FITTING AND ANALYSIS

  • The analysis used 88 trials, 20-ms bins around movement onset, separate condition fits, five repeated 90/10 splits, and K = 2 regimes; H = 6 was used for displayed comparisons.Neither model used hand kinematics as inputs; subsequent increases in latent dimension beyond H = 6 gave inconsistent predictive gains.Source: H AREA 2: FITTING AND ANALYSIS · p. 27
  • The apparent pre-movement to movement timescale shifts at H = 6 did not remain consistent across band choices and latent dimensions.Numerical summaries were restricted to 20–300 ms as a practical range, not a formally established identifiability interval; the paired comparisons included three active and four passive splits.Source: H AREA 2: FITTING AND ANALYSIS · pp. 27–28
  • 1.9 versus 1.4: the median ratio of real to shuffled geometric-mean in-band timescales was 1.9 for MTS-SLDS and 1.4 for SLDS.The temporal control permuted population count vectors across time within each trial, preserving count distributions and within-bin cross-channel structure; ratios used five and four paired split summaries, respectively.Source: H AREA 2: FITTING AND ANALYSIS · p. 28
  • 168 versus 86 ms: median behavioral decay times were 168 ms for 19 active trials and 86 ms for 66 passive trials; MTS-SLDS slowest in-band movement timescales were 188 and 99 ms, compared with 117 and 108 ms for SLDS.MTS-SLDS estimates matched behavioral magnitudes and ordering more closely, but differing emission settings confound attribution to latent dynamics.Source: H AREA 2: FITTING AND ANALYSIS · pp. 28–29
  • Both methods showed changes in regime probability near movement onset, while MTS-SLDS assigned appreciable movement-regime probability before onset on some trials, particularly during passive perturbation.The displayed single-channel example was selected by MTS-SLDS predictive score and is a favorable example rather than typical single-channel performance.Source: H AREA 2: FITTING AND ANALYSIS · p. 27, Figure 11 · p. 30
  • The separate sPCF-EM analysis found timescale patterns different from MTS-SLDS and SLDS and less aligned with behavioral timescales.It used H = 6, K = 2, and three folds per condition.Source: H AREA 2: FITTING AND ANALYSIS · p. 29, Figure 12 · p. 30
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