LatentTrack: Sequential Weight Generation via Latent Filtering

TL;DR

LatentTrack (LT) treats online probabilistic prediction under nonstationary dynamics as a filter over predictive functions rather than observations. A low-dimensional latent state $z_t$ evolves to generate predictor weights $\theta_t$ via a hypernetwork, with online amortized inference yielding a predict--generate--update cycle and constant-time test-time updates. LT supports both structured and unstructured latent dynamics through a streaming ELBO bound, and uses Monte Carlo mixtures over latent trajectories to form calibrated predictive distributions with fixed per-step cost. Evaluations on long-horizon climate data show that LT achieves lower $\text{NLL}$ and $\text{MSE}$ and better calibration than stateful and static baselines, illustrating that function-space adaptation can be more robust to distribution shift than traditional latent-state modeling.

Abstract

We introduce LatentTrack (LT), a sequential neural architecture for online probabilistic prediction under nonstationary dynamics. LT performs causal Bayesian filtering in a low-dimensional latent space and uses a lightweight hypernetwork to generate predictive model parameters at each time step, enabling constant-time online adaptation without per-step gradient updates. At each time step, a learned latent model predicts the next latent distribution, which is updated via amortized inference using new observations, yielding a predict--generate--update filtering framework in function space. The formulation supports both structured (Markovian) and unstructured latent dynamics within a unified objective, while Monte Carlo inference over latent trajectories produces calibrated predictive mixtures with fixed per-step cost. Evaluated on long-horizon online regression using the Jena Climate benchmark, LT consistently achieves lower negative log-likelihood and mean squared error than stateful sequential and static uncertainty-aware baselines, with competitive calibration, demonstrating that latent-conditioned function evolution is an effective alternative to traditional latent-state modeling under distribution shift.

Figures (18)

• Figure 1: LT predict--generate--update loop (supervised setting). A latent belief $z_t$ is propagated via a causal prior/transition conditioned on a running summary of past observations, mapped to predictor parameters $\theta_t$ by the hypernetwork $g_\eta$, and used to define the predictive model $p_\vartheta(y_t \mid x_t;\theta_t)$. Incoming observations then amortize a posterior update over $z_t$, enabling temporally causal belief filtering over predictor parameters.
• Figure 2: Predictive mean over time for the representative seed. LT tracks the signal more accurately than stateful baselines, but exhibits occasional instability consistent with the failure-rate statistics.
• Figure 3: Ranking stability across time. Colors indicate the top-3 models at each time step. (a) Per-time-step negative log-likelihood (NLL) ranking. (b) Per-time-step mean squared error (MSE) ranking. Lower ranks indicate better performance. LT-Structured appears more frequently among the top-ranked methods across time, indicating greater ranking stability under both metrics.
• Figure 4: Temporal stability and catastrophic failure under distribution shift. (a) Complementary cumulative distribution function (CCDF) of the maximum per-time-step negative log-likelihood, $\max_t \mathrm{NLL}(t)$, computed per run and aggregated across seeds, characterizing the tail behavior of rare but severe prediction failures. (b) Fraction of runs whose peak NLL exceeds a fixed threshold $\tau = 10^6$, corresponding to a vertical slice of the CCDF in (a). LT variants exhibit lighter tails and lower failure rates than stateful baselines, indicating improved robustness to transient instability while maintaining competitive predictive accuracy.
• Figure 5: Predictive mean trajectories for a representative seed. (a) Unclipped predictive mean $\mathbb{E}[y_t \mid x_t, \mathcal{D}_{1:t-1}]$ over the full time horizon, illustrating a single isolated divergence event for LT-Structured. (b) Clipped view of the same trajectories to highlight typical predictive behavior across methods. The isolated spike in (a) corresponds to a rare catastrophic failure and dominates untrimmed temporal mean statistics, while the clipped view in (b) shows that LT-Structured otherwise tracks the signal accurately over time.