In the matrix sensing problem, one wishes to reconstruct a matrix from (possibly noisy) observations of its linear projections along given directions. We consider this model in the high-dimensional limit: while previous works on this model primarily focused on the recovery of low-rank matrices, we consider in this work more general classes of structured signal matrices with potentially large rank, e.g. a product of two matrices of sizes proportional to the dimension. We provide rigorous asymptotic equations characterizing the Bayes-optimal learning performance from a number of samples which is proportional to the number of entries in the matrix. Our proof is composed of three key ingredients: $(i)$ we prove universality properties to handle structured sensing matrices, related to the ''Gaussian equivalence'' phenomenon in statistical learning, $(ii)$ we provide a sharp characterization of Bayes-optimal learning in generalized linear models with Gaussian data and structured matrix priors, generalizing previously studied settings, and $(iii)$ we leverage previous works on the problem of matrix denoising. The generality of our results allow for a variety of applications: notably, we mathematically establish predictions obtained via non-rigorous methods from statistical physics in [ETB+24] regarding Bilinear Sequence Regression, a benchmark model for learning from sequences of tokens, and in [MTM+24] on Bayes-optimal learning in neural networks with quadratic activation function, and width proportional to the dimension.

More and more phenomena that are virtually universal in the learning process have been discovered in contemporary AI systems. These phenomena are shared by models with different architectures, trained on different datasets, and with different training techniques. The existence of these universal phenomena calls for one or a few universal explanations. However, until today, most of the phenomena are instead described by narrow theories tailored to explain each phenomenon separately - often focusing on specific models trained on specific tasks or loss functions and in isolation from other interesting phenomena that are indispensable parts of the deep learning phenomenology. Certainly, it is desirable to have a universal perspective, if not a universal theory, that explains as many phenomena as possible. In the spirit of science, a universal perspective should be independent of system details such as variations in minor architecture definitions, choice of loss functions, training techniques, etc. A universal theory would give the field a simplified paradigm for thinking about and understanding AI systems and a potential design principle for a new generation of more efficient and capable models.

We identify and solve a hidden-layer model that is analytically tractable at any finite width and whose limits exhibit both the kernel phase and the feature learning phase. We analyze the phase diagram of this model in all possible limits of common hyperparameters including width, layer-wise learning rates, scale of output, and scale of initialization. We apply our result to analyze how and when feature learning happens in both infinite and finite-width models. Three prototype mechanisms of feature learning are identified: (1) learning by alignment, (2) learning by disalignment, and (3) learning by rescaling. In sharp contrast, neither of these mechanisms is present when the model is in the kernel regime. This discovery explains why large initialization often leads to worse performance. Lastly, we empirically demonstrate that discoveries we made for this analytical model also appear in nonlinear networks in real tasks.

The safety of autonomous vehicles (AV) has been a long-standing top concern, stemming from the absence of rare and safety-critical scenarios in the long-tail naturalistic driving distribution. To tackle this challenge, a surge of research in scenario-based autonomous driving has emerged, with a focus on generating high-risk driving scenarios and applying them to conduct safety-critical testing of AV models. However, limited work has been explored on the reuse of these extensive scenarios to iteratively improve AV models. Moreover, it remains intractable and challenging to filter through gigantic scenario libraries collected from other AV models with distinct behaviors, attempting to extract transferable information for current AV improvement. Therefore, we develop a continual driving policy optimization framework featuring Closed-Loop Individualized Curricula (CLIC), which we factorize into a set of standardized sub-modules for flexible implementation choices: AV Evaluation, Scenario Selection, and AV Training. CLIC frames AV Evaluation as a collision prediction task, where it estimates the chance of AV failures in these scenarios at each iteration. Subsequently, by re-sampling from historical scenarios based on these failure probabilities, CLIC tailors individualized curricula for downstream training, aligning them with the evaluated capability of AV. Accordingly, CLIC not only maximizes the utilization of the vast pre-collected scenario library for closed-loop driving policy optimization but also facilitates AV improvement by individualizing its training with more challenging cases out of those poorly organized scenarios. Experimental results clearly indicate that CLIC surpasses other curriculum-based training strategies, showing substantial improvement in managing risky scenarios, while still maintaining proficiency in handling simpler cases.

Autonomous driving and its widespread adoption have long held tremendous promise. Nevertheless, without a trustworthy and thorough testing procedure, not only does the industry struggle to mass-produce autonomous vehicles (AV), but neither the general public nor policymakers are convinced to accept the innovations. Generating safety-critical scenarios that present significant challenges to AV is an essential first step in testing. Real-world datasets include naturalistic but overly safe driving behaviors, whereas simulation would allow for unrestricted exploration of diverse and aggressive traffic scenarios. Conversely, higher-dimensional searching space in simulation disables efficient scenario generation without real-world data distribution as implicit constraints. In order to marry the benefits of both, it seems appealing to learn to generate scenarios from both offline real-world and online simulation data simultaneously. Therefore, we tailor a Reversely Regularized Hybrid Offline-and-Online ((Re)$^2$H2O) Reinforcement Learning recipe to additionally penalize Q-values on real-world data and reward Q-values on simulated data, which ensures the generated scenarios are both varied and adversarial. Through extensive experiments, our solution proves to produce more risky scenarios than competitive baselines and it can generalize to work with various autonomous driving models. In addition, these generated scenarios are also corroborated to be capable of fine-tuning AV performance.

We consider the problem of reconstructing the signal and the hidden variables from observations coming from a multi-layer network with rotationally invariant weight matrices. The multi-layer structure models inference from deep generative priors, and the rotational invariance imposed on the weights generalizes the i.i.d.\ Gaussian assumption by allowing for a complex correlation structure, which is typical in applications. In this work, we present a new class of approximate message passing (AMP) algorithms and give a state evolution recursion which precisely characterizes their performance in the large system limit. In contrast with the existing multi-layer VAMP (ML-VAMP) approach, our proposed AMP -- dubbed multi-layer rotationally invariant generalized AMP (ML-RI-GAMP) -- provides a natural generalization beyond Gaussian designs, in the sense that it recovers the existing Gaussian AMP as a special case. Furthermore, ML-RI-GAMP exhibits a significantly lower complexity than ML-VAMP, as the computationally intensive singular value decomposition is replaced by an estimation of the moments of the design matrices. Finally, our numerical results show that this complexity gain comes at little to no cost in the performance of the algorithm.