Enhancing Underwater Navigation through Cross-Correlation-Aware Deep INS/DVL Fusion

The accurate navigation of autonomous underwater vehicles critically depends on the precision of Doppler velocity log (DVL) velocity measurements. Recent advancements in deep learning have demonstrated significant potential in improving DVL outputs by leveraging spatiotemporal dependencies across multiple sensor modalities. However, integrating these estimates into model-based filters, such as the extended Kalman filter, introduces statistical inconsistencies, most notably, cross-correlations between process and measurement noise. This paper addresses this challenge by proposing a cross-correlation-aware deep INS/DVL fusion framework. Building upon BeamsNet, a convolutional neural network designed to estimate AUV velocity using DVL and inertial data, we integrate its output into a navigation filter that explicitly accounts for the cross-correlation induced between the noise sources. This approach improves filter consistency and better reflects the underlying sensor error structure. Evaluated on two real-world underwater trajectories, the proposed method outperforms both least squares and cross-correlation-neglecting approaches in terms of state uncertainty. Notably, improvements exceed 10% in velocity and misalignment angle confidence metrics. Beyond demonstrating empirical performance, this framework provides a theoretically principled mechanism for embedding deep learning outputs within stochastic filters.

Performance Analysis of Spatial and Temporal Learning Networks in the Presence of DVL Noise

Navigation is a critical aspect of autonomous underwater vehicles (AUVs) operating in complex underwater environments. Since global navigation satellite system (GNSS) signals are unavailable underwater, navigation relies on inertial sensing, which tends to accumulate errors over time. To mitigate this, the Doppler velocity log (DVL) plays a crucial role in determining navigation accuracy. In this paper, we compare two neural network models: an adapted version of BeamsNet, based on a one-dimensional convolutional neural network, and a Spectrally Normalized Memory Neural Network (SNMNN). The former focuses on extracting spatial features, while the latter leverages memory and temporal features to provide more accurate velocity estimates while handling biased and noisy DVL data. The proposed approaches were trained and tested on real AUV data collected in the Mediterranean Sea. Both models are evaluated in terms of accuracy and estimation certainty and are benchmarked against the least squares (LS) method, the current model-based approach. The results show that the neural network models achieve over a 50% improvement in RMSE for the estimation of the AUV velocity, with a smaller standard deviation.

Gaussian Process Regression for Improved Underwater Navigation

Accurate underwater navigation is a challenging task due to the absence of global navigation satellite system signals and the reliance on inertial navigation systems that suffer from drift over time. Doppler velocity logs (DVLs) are typically used to mitigate this drift through velocity measurements, which are commonly estimated using a parameter estimation approach such as least squares (LS). However, LS works under the assumption of ideal conditions and does not account for sensor biases, leading to suboptimal performance. This paper proposes a data-driven alternative based on multi-output Gaussian process regression (MOGPR) to improve DVL velocity estimation. MOGPR provides velocity estimates and associated measurement covariances, enabling an adaptive integration within an error-state Extended Kalman Filter (EKF). We evaluate our proposed approach using real-world AUV data and compare it against LS and a state-of-the-art deep learning model, BeamsNet. Results demonstrate that MOGPR reduces velocity estimation errors by approximately 20% while simultaneously enhancing overall navigation accuracy, particularly in the orientation states. Additionally, the incorporation of uncertainty estimates from MOGPR enables an adaptive EKF framework, improving navigation robustness in dynamic underwater environments.

Data-driven Coreference-based Ontology Building

While coreference resolution is traditionally used as a component in individual document understanding, in this work we take a more global view and explore what can we learn about a domain from the set of all document-level coreference relations that are present in a large corpus. We derive coreference chains from a corpus of 30 million biomedical abstracts and construct a graph based on the string phrases within these chains, establishing connections between phrases if they co-occur within the same coreference chain. We then use the graph structure and the betweeness centrality measure to distinguish between edges denoting hierarchy, identity and noise, assign directionality to edges denoting hierarchy, and split nodes (strings) that correspond to multiple distinct concepts. The result is a rich, data-driven ontology over concepts in the biomedical domain, parts of which overlaps significantly with human-authored ontologies. We release the coreference chains and resulting ontology under a creative-commons license, along with the code.

Provable Benefits of Complex Parameterizations for Structured State Space Models

Structured state space models (SSMs), the core engine behind prominent neural networks such as S4 and Mamba, are linear dynamical systems adhering to a specified structure, most notably diagonal. In contrast to typical neural network modules, whose parameterizations are real, SSMs often use complex parameterizations. Theoretically explaining the benefits of complex parameterizations for SSMs is an open problem. The current paper takes a step towards its resolution, by establishing formal gaps between real and complex diagonal SSMs. Firstly, we prove that while a moderate dimension suffices in order for a complex SSM to express all mappings of a real SSM, a much higher dimension is needed for a real SSM to express mappings of a complex SSM. Secondly, we prove that even if the dimension of a real SSM is high enough to express a given mapping, typically, doing so requires the parameters of the real SSM to hold exponentially large values, which cannot be learned in practice. In contrast, a complex SSM can express any given mapping with moderate parameter values. Experiments corroborate our theory, and suggest a potential extension of the theory that accounts for selectivity, a new architectural feature yielding state of the art performance.

The Implicit Bias of Structured State Space Models Can Be Poisoned With Clean Labels

Neural networks are powered by an implicit bias: a tendency of gradient descent to fit training data in a way that generalizes to unseen data. A recent class of neural network models gaining increasing popularity is structured state space models (SSMs), regarded as an efficient alternative to transformers. Prior work argued that the implicit bias of SSMs leads to generalization in a setting where data is generated by a low dimensional teacher. In this paper, we revisit the latter setting, and formally establish a phenomenon entirely undetected by prior work on the implicit bias of SSMs. Namely, we prove that while implicit bias leads to generalization under many choices of training data, there exist special examples whose inclusion in training completely distorts the implicit bias, to a point where generalization fails. This failure occurs despite the special training examples being labeled by the teacher, i.e. having clean labels! We empirically demonstrate the phenomenon, with SSMs trained independently and as part of non-linear neural networks. In the area of adversarial machine learning, disrupting generalization with cleanly labeled training examples is known as clean-label poisoning. Given the proliferation of SSMs, particularly in large language models, we believe significant efforts should be invested in further delineating their susceptibility to clean-label poisoning, and in developing methods for overcoming this susceptibility.

Lecture Notes on Linear Neural Networks: A Tale of Optimization and Generalization in Deep Learning

These notes are based on a lecture delivered by NC on March 2021, as part of an advanced course in Princeton University on the mathematical understanding of deep learning. They present a theory (developed by NC, NR and collaborators) of linear neural networks -- a fundamental model in the study of optimization and generalization in deep learning. Practical applications born from the presented theory are also discussed. The theory is based on mathematical tools that are dynamical in nature. It showcases the potential of such tools to push the envelope of our understanding of optimization and generalization in deep learning. The text assumes familiarity with the basics of statistical learning theory. Exercises (without solutions) are included.

Deep Learning Assisted Inertial Dead Reckoning and Fusion

The interest in mobile platforms across a variety of applications has increased significantly in recent years. One of the reasons is the ability to achieve accurate navigation by using low-cost sensors. To this end, inertial sensors are fused with global navigation satellite systems (GNSS) signals. GNSS outages during platform operation can result in pure inertial navigation, causing the navigation solution to drift. In such situations, periodic trajectories with dedicated algorithms were suggested to mitigate the drift. With periodic dynamics, inertial deep learning approaches can capture the motion more accurately and provide accurate dead-reckoning for drones and mobile robots. In this paper, we propose approaches to extend deep learning-assisted inertial sensing and fusion capabilities during periodic motion. We begin by demonstrating that fusion between GNSS and inertial sensors in periodic trajectories achieves better accuracy compared to straight-line trajectories. Next, we propose an empowered network architecture to accurately regress the change in distance of the platform. Utilizing this network, we drive a hybrid approach for a neural-inertial fusion filter. Finally, we utilize this approach for situations when GNSS is available and show its benefits. A dataset of 337 minutes of data collected from inertial sensors mounted on a mobile robot and a quadrotor is used to evaluate our approaches.

DeciMamba: Exploring the Length Extrapolation Potential of Mamba

Long-range sequence processing poses a significant challenge for Transformers due to their quadratic complexity in input length. A promising alternative is Mamba, which demonstrates high performance and achieves Transformer-level capabilities while requiring substantially fewer computational resources. In this paper we explore the length-generalization capabilities of Mamba, which we find to be relatively limited. Through a series of visualizations and analyses we identify that the limitations arise from a restricted effective receptive field, dictated by the sequence length used during training. To address this constraint, we introduce DeciMamba, a context-extension method specifically designed for Mamba. This mechanism, built on top of a hidden filtering mechanism embedded within the S6 layer, enables the trained model to extrapolate well even without additional training. Empirical experiments over real-world long-range NLP tasks show that DeciMamba can extrapolate to context lengths that are 25x times longer than the ones seen during training, and does so without utilizing additional computational resources. We will release our code and models.

Seamless Underwater Navigation with Limited Doppler Velocity Log Measurements

Autonomous Underwater Vehicles (AUVs) commonly utilize an inertial navigation system (INS) and a Doppler velocity log (DVL) for underwater navigation. To that end, their measurements are integrated through a nonlinear filter such as the extended Kalman filter (EKF). The DVL velocity vector estimate depends on retrieving reflections from the seabed, ensuring that at least three out of its four transmitted acoustic beams return successfully. When fewer than three beams are obtained, the DVL cannot provide a velocity update to bind the navigation solution drift. To cope with this challenge, in this paper, we propose a hybrid neural coupled (HNC) approach for seamless AUV navigation in situations of limited DVL measurements. First, we drive an approach to regress two or three missing DVL beams. Then, those beams, together with the measured beams, are incorporated into the EKF. We examined INS/DVL fusion both in loosely and tightly coupled approaches. Our method was trained and evaluated on recorded data from AUV experiments conducted in the Mediterranean Sea on two different occasions. The results illustrate that our proposed method outperforms the baseline loosely and tightly coupled model-based approaches by an average of 96.15%. It also demonstrates superior performance compared to a model-based beam estimator by an average of 12.41% in terms of velocity accuracy for scenarios involving two or three missing beams. Therefore, we demonstrate that our approach offers seamless AUV navigation in situations of limited beam measurements.