Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics ofobservedsequence data.

A major problem in motor control is understanding how the brain plans and executes proper movements in the face of delayed and noisy stimuli. A prominent framework for addressing such control problems is Optimal Feedback Control (OFC). OFC generates control actions that optimize behaviorally relevant criteria by integrating noisy sensory stimuli and the predictions of an internal model using the Kalman filter or its extensions. However, a satisfactory neural model of Kalman filtering and control is lacking because existing proposals have the following limitations: not considering the delay of sensory feedback, training in alternating phases, requiring knowledge of the noise covariance matrices, as well as that of systems dynamics. Moreover, the majority of these studies considered Kalman filtering in isolation, and not jointly with control.

Transformers and linear state space models can be evaluated in parallel on modern hardware, but evaluating nonlinear RNNs appears to be an inherently sequential problem. Recently, however, Lim et al. '24 developed an approach called DEER, which evaluates nonlinear RNNs in parallel by posing the states as the solution to a fixed-point problem. They derived a parallel form of Newton's method to solve the fixed-point problem and achieved significant speedups over sequential evaluation. However, the computational complexity of DEER is cubic in the state size, and the algorithm can suffer from numerical instability. We address these limitations with two novel contributions. To reduce the computational complexity, we apply quasi-Newton approximations and show they converge comparably to Newton, use less memory, and are faster. To stabilize DEER, we leverage a connection between the Levenberg-Marquardt algorithm and Kalman smoothing, which we call ELK. This connection allows us to stabilize Newton's method while using efficient parallelized Kalman smoothing algorithms to retain performance. Through several experiments, we show that these innovations allow for parallel evaluation of nonlinear RNNs at larger scales and with greater stability.

There, demand is highly intermittent and bursty: long runs of zeros, with islands of high counts.

Achieving sub-10 m indoor ranging with LoRaWAN is difficult because multipath, human blockage, and micro-climate dynamics induce non-stationary attenuation in received signal strength indicator (RSSI) measurements. We present a lightweight, interpretable pipeline that couples an environment-aware multi-wall path loss model with a forward-only, innovation-driven Kalman prefilter for RSSI. The model augments distance and wall terms with frequency, signal-to-noise ratio (SNR), and co-located environmental covariates (temperature, relative humidity, carbon dioxide, particulate matter, and barometric pressure), and is inverted deterministically for distance estimation. On a one-year single-gateway office dataset comprising over 2 million uplinks, the approach attains a mean absolute error (MAE) of 4.74 m and a root mean square error (RMSE) of 6.76 m in distance estimation, improving over a COST-231 multi-wall baseline (12.07 m MAE) and its environment-augmented variant (7.76 m MAE. Filtering reduces RSSI volatility from 10.33 to 5.43 dB and halves path loss error to 5.35 dB while raising R-squared from 0.82 to 0.89. The result is a single-anchor LoRaWAN ranging method with constant per-packet cost that is accurate, robust, and interpretable, providing a strong building block for multi-gateway localization.

There, demand is highly intermittent and bursty: long runs of zeros, with islands of high counts.

A major problem in motor control is understanding how the brain plans and executes proper movements in the face of delayed and noisy stimuli. A prominent framework for addressing such control problems is Optimal Feedback Control (OFC). OFC generates control actions that optimize behaviorally relevant criteria by integrating noisy sensory stimuli and the predictions of an internal model using the Kalman filter or its extensions. However, a satisfactory neural model of Kalman filtering and control is lacking because existing proposals have the following limitations: not considering the delay of sensory feedback, training in alternating phases, requiring knowledge of the noise covariance matrices, as well as that of systems dynamics. Moreover, the majority of these studies considered Kalman filtering in isolation, and not jointly with control.

Transformers and linear state space models can be evaluated in parallel on modern hardware, but evaluating nonlinear RNNs appears to be an inherently sequential problem. Recently, however, Lim et al. '24 developed an approach called DEER, which evaluates nonlinear RNNs in parallel by posing the states as the solution to a fixed-point problem. They derived a parallel form of Newton's method to solve the fixed-point problem and achieved significant speedups over sequential evaluation. However, the computational complexity of DEER is cubic in the state size, and the algorithm can suffer from numerical instability. We address these limitations with two novel contributions.

We consider the problem of controlling a linear dynamical system from bilinear observations with minimal quadratic cost. Despite the similarity of this problem to standard linear quadratic Gaussian (LQG) control, we show that when the observation model is bilinear, neither does the Separation Principle hold, nor is the optimal controller affine in the estimated state. Moreover, the cost-to-go is non-convex in the control input. Hence, finding an analytical expression for the optimal feedback controller is difficult in general. Under certain settings, we show that the standard LQG controller locally maximizes the cost instead of minimizing it. Furthermore, the optimal controllers (derived analytically) are not unique and are nonlinear in the estimated state. We also introduce a notion of input-dependent observability and derive conditions under which the Kalman filter covariance remains bounded. We illustrate our theoretical results through numerical experiments in multiple synthetic settings.

A major problem in motor control is understanding how the brain plans and executes proper movements in the face of delayed and noisy stimuli. A prominent framework for addressing such control problems is Optimal Feedback Control (OFC). OFC generates control actions that optimize behaviorally relevant criteria by integrating noisy sensory stimuli and the predictions of an internal model using the Kalman filter or its extensions. However, a satisfactory neural model of Kalman filtering and control is lacking because existing proposals have the following limitations: not considering the delay of sensory feedback, training in alternating phases, requiring knowledge of the noise covariance matrices, as well as that of systems dynamics. Moreover, the majority of these studies considered Kalman filtering in isolation, and not jointly with control.