Pratik Chaudhari

Rongguang Wang, Pratik Chaudhari, Christos Davatzikos

Despite the great promise that machine learning has offered in many fields of medicine, it has also raised concerns about potential biases and poor generalization across genders, age distributions, races and ethnicities, hospitals, and data acquisition equipment and protocols. In the current study, and in the context of three brain diseases, we provide evidence which suggests that when properly trained, machine learning models can generalize well across diverse conditions and do not necessarily suffer from bias. Specifically, by using multi-study magnetic resonance imaging consortia for diagnosing Alzheimer's disease, schizophrenia, and autism spectrum disorder, we find that well-trained models have a high area-under-the-curve (AUC) on subjects across different subgroups pertaining to attributes such as gender, age, racial groups, and different clinical studies and are unbiased under multiple fairness metrics such as demographic parity difference, equalized odds difference, equal opportunity difference etc. We find that models that incorporate multi-source data from demographic, clinical, genetic factors and cognitive scores are also unbiased. These models have better predictive AUC across subgroups than those trained only with imaging features but there are also situations when these additional features do not help.

Yao Liu, Pratik Chaudhari, Rasool Fakoor · stanford

The main challenge of offline reinforcement learning, where data is limited, arises from a sequence of counterfactual reasoning dilemmas within the realm of potential actions: What if we were to choose a different course of action? These circumstances frequently give rise to extrapolation errors, which tend to accumulate exponentially with the problem horizon. Hence, it becomes crucial to acknowledge that not all decision steps are equally important to the final outcome, and to budget the number of counterfactual decisions a policy make in order to control the extrapolation. Contrary to existing approaches that use regularization on either the policy or value function, we propose an approach to explicitly bound the amount of out-of-distribution actions during training. Specifically, our method utilizes dynamic programming to decide where to extrapolate and where not to, with an upper bound on the decisions different from behavior policy. It balances between the potential for improvement from taking out-of-distribution actions and the risk of making errors due to extrapolation. Theoretically, we justify our method by the constrained optimality of the fixed point solution to our $Q$ updating rules. Empirically, we show that the overall performance of our method is better than the state-of-the-art offline RL methods on tasks in the widely-used D4RL benchmarks.

Rongguang Wang, Guray Erus, Pratik Chaudhari et al.

Machine learning (ML) has shown great promise for revolutionizing a number of areas, including healthcare. However, it is also facing a reproducibility crisis, especially in medicine. ML models that are carefully constructed from and evaluated on a training set might not generalize well on data from different patient populations or acquisition instrument settings and protocols. We tackle this problem in the context of neuroimaging of Alzheimer's disease (AD), schizophrenia (SZ) and brain aging. We develop a weighted empirical risk minimization approach that optimally combines data from a source group, e.g., subjects are stratified by attributes such as sex, age group, race and clinical cohort to make predictions on a target group, e.g., other sex, age group, etc. using a small fraction (10%) of data from the target group. We apply this method to multi-source data of 15,363 individuals from 20 neuroimaging studies to build ML models for diagnosis of AD and SZ, and estimation of brain age. We found that this approach achieves substantially better accuracy than existing domain adaptation techniques: it obtains area under curve greater than 0.95 for AD classification, area under curve greater than 0.7 for SZ classification and mean absolute error less than 5 years for brain age prediction on all target groups, achieving robustness to variations of scanners, protocols, and demographic or clinical characteristics. In some cases, it is even better than training on all data from the target group, because it leverages the diversity and size of a larger training set. We also demonstrate the utility of our models for prognostic tasks such as predicting disease progression in individuals with mild cognitive impairment. Critically, our brain age prediction models lead to new clinical insights regarding correlations with neurophysiological tests.

Ashwin De Silva, Rahul Ramesh, Carey E. Priebe et al.

We expect the generalization error to improve with more samples from a similar task, and to deteriorate with more samples from an out-of-distribution (OOD) task. In this work, we show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the number of OOD samples. As the number of OOD samples increases, the generalization error on the target task improves before deteriorating beyond a threshold. In other words, there is value in training on small amounts of OOD data. We use Fisher's Linear Discriminant on synthetic datasets and deep networks on computer vision benchmarks such as MNIST, CIFAR-10, CINIC-10, PACS and DomainNet to demonstrate and analyze this phenomenon. In the idealistic setting where we know which samples are OOD, we show that these non-monotonic trends can be exploited using an appropriately weighted objective of the target and OOD empirical risk. While its practical utility is limited, this does suggest that if we can detect OOD samples, then there may be ways to benefit from them. When we do not know which samples are OOD, we show how a number of go-to strategies such as data-augmentation, hyper-parameter optimization, and pre-training are not enough to ensure that the target generalization error does not deteriorate with the number of OOD samples in the dataset.

Ramya Muthukrishnan, Angelina Heyler, Keshava Katti et al.

In this study, we automate quantitative mammographic breast density estimation with neural networks and show that this tool is a strong use case for federated learning on multi-institutional datasets. Our dataset included bilateral CC-view and MLO-view mammographic images from two separate institutions. Two U-Nets were separately trained on algorithm-generated labels to perform segmentation of the breast and dense tissue from these images and subsequently calculate breast percent density (PD). The networks were trained with federated learning and compared to three non-federated baselines, one trained on each single-institution dataset and one trained on the aggregated multi-institution dataset. We demonstrate that training on multi-institution datasets is critical to algorithm generalizability. We further show that federated learning on multi-institutional datasets improves model generalization to unseen data at nearly the same level as centralized training on multi-institutional datasets, indicating that federated learning can be applied to our method to improve algorithm generalizability while maintaining patient privacy.

Rahul Ramesh, Jialin Mao, Itay Griniasty et al.

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress even on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.

Rasool Fakoor, Jonas Mueller, Zachary C. Lipton et al.

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a time-varying propensity score that can detect gradual shifts in the distribution of data which allows us to selectively sample past data to update the model -- not just similar data from the past like that of a standard propensity score but also data that evolved in a similar fashion in the past. The time-varying propensity score is quite general: we demonstrate different ways of implementing it and evaluate it on a variety of problems ranging from supervised learning (e.g., image classification problems) where data undergoes a sequence of gradual shifts, to reinforcement learning tasks (e.g., robotic manipulation and continuous control) where data shifts as the policy or the task changes.

Yansong Gao, Zhihong Pan, Xin Zhou et al.

Denoising diffusion probabilistic models (DDPMs) are a class of powerful generative models. The past few years have witnessed the great success of DDPMs in generating high-fidelity samples. A significant limitation of the DDPMs is the slow sampling procedure. DDPMs generally need hundreds or thousands of sequential function evaluations (steps) of neural networks to generate a sample. This paper aims to develop a fast sampling method for DDPMs requiring much fewer steps while retaining high sample quality. The inference process of DDPMs approximates solving the corresponding diffusion ordinary differential equations (diffusion ODEs) in the continuous limit. This work analyzes how the backward error affects the diffusion ODEs and the sample quality in DDPMs. We propose fast sampling through the \textbf{Restricting Backward Error schedule (RBE schedule)} based on dynamically moderating the long-time backward error. Our method accelerates DDPMs without any further training. Our experiments show that sampling with an RBE schedule generates high-quality samples within only 8 to 20 function evaluations on various benchmark datasets. We achieved 12.01 FID in 8 function evaluations on the ImageNet $128\times128$, and a $20\times$ speedup compared with previous baseline samplers.

Evangelos Sariyanidi, John D. Herrington, Lisa Yankowitz et al.

Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge or large datasets. We introduce a criterion for dependence, whereby two time series are deemed dependent if one can construct a classifier that distinguishes between temporally aligned vs. misaligned segments extracted from them. We show that this criterion, concurrence, is theoretically linked with dependence, and can become a standard approach for scientific analyses across disciplines, as it can expose relationships across a wide spectrum of signals (fMRI, physiological and behavioral data) without ad-hoc parameter tuning or large amounts of data.

Rohit Jena, Lukas Zhornyak, Nehal Doiphode et al.

Correctness of instance segmentation constitutes counting the number of objects, correctly localizing all predictions and classifying each localized prediction. Average Precision is the de-facto metric used to measure all these constituents of segmentation. However, this metric does not penalize duplicate predictions in the high-recall range, and cannot distinguish instances that are localized correctly but categorized incorrectly. This weakness has inadvertently led to network designs that achieve significant gains in AP but also introduce a large number of false positives. We therefore cannot rely on AP to choose a model that provides an optimal tradeoff between false positives and high recall. To resolve this dilemma, we review alternative metrics in the literature and propose two new measures to explicitly measure the amount of both spatial and categorical duplicate predictions. We also propose a Semantic Sorting and NMS module to remove these duplicates based on a pixel occupancy matching scheme. Experiments show that modern segmentation networks have significant gains in AP, but also contain a considerable amount of duplicates. Our Semantic Sorting and NMS can be added as a plug-and-play module to mitigate hedged predictions and preserve AP.

Rahul Ramesh, Anthony Bisulco, Ronald W. DiTullio et al.

We show that many perception tasks, from visual recognition, semantic segmentation, optical flow, depth estimation to vocalization discrimination, are highly redundant functions of their input data. Images or spectrograms, projected into different subspaces, formed by orthogonal bases in pixel, Fourier or wavelet domains, can be used to solve these tasks remarkably well regardless of whether it is the top subspace where data varies the most, some intermediate subspace with moderate variability--or the bottom subspace where data varies the least. This phenomenon occurs because different subspaces have a large degree of redundant information relevant to the task.

Rohit Jena, Ganesh Subramanian Iyer, Siddharth Choudhary et al.

We propose SplatArmor, a novel approach for recovering detailed and animatable human models by `armoring' a parameterized body model with 3D Gaussians. Our approach represents the human as a set of 3D Gaussians within a canonical space, whose articulation is defined by extending the skinning of the underlying SMPL geometry to arbitrary locations in the canonical space. To account for pose-dependent effects, we introduce a SE(3) field, which allows us to capture both the location and anisotropy of the Gaussians. Furthermore, we propose the use of a neural color field to provide color regularization and 3D supervision for the precise positioning of these Gaussians. We show that Gaussian splatting provides an interesting alternative to neural rendering based methods by leverging a rasterization primitive without facing any of the non-differentiability and optimization challenges typically faced in such approaches. The rasterization paradigms allows us to leverage forward skinning, and does not suffer from the ambiguities associated with inverse skinning and warping. We show compelling results on the ZJU MoCap and People Snapshot datasets, which underscore the effectiveness of our method for controllable human synthesis.

Rohit Jena, Pratik Chaudhari, James Gee et al.

Human reconstruction and synthesis from monocular RGB videos is a challenging problem due to clothing, occlusion, texture discontinuities and sharpness, and framespecific pose changes. Many methods employ deferred rendering, NeRFs and implicit methods to represent clothed humans, on the premise that mesh-based representations cannot capture complex clothing and textures from RGB, silhouettes, and keypoints alone. We provide a counter viewpoint to this fundamental premise by optimizing a SMPL+D mesh and an efficient, multi-resolution texture representation using only RGB images, binary silhouettes and sparse 2D keypoints. Experimental results demonstrate that our approach is more capable of capturing geometric details compared to visual hull, mesh-based methods. We show competitive novel view synthesis and improvements in novel pose synthesis compared to NeRF-based methods, which introduce noticeable, unwanted artifacts. By restricting the solution space to the SMPL+D model combined with differentiable rendering, we obtain dramatic speedups in compute, training times (up to 24x) and inference times (up to 192x). Our method therefore can be used as is or as a fast initialization to NeRF-based methods.

Yan Sun, Pratik Chaudhari, Ian J. Barnett et al.

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the $\ell_2$ Expected Calibration Error (ECE). We consider top-1-to-$k$ calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.

Rohit Jena, Deeksha Sethi, Pratik Chaudhari et al.

Classical optimization and learning-based methods are the two reigning paradigms in deformable image registration. While optimization-based methods boast generalizability across modalities and robust performance, learning-based methods promise peak performance, incorporating weak supervision and amortized optimization. However, the exact conditions for either paradigm to perform well over the other are shrouded and not explicitly outlined in the existing literature. In this paper, we make an explicit correspondence between the mutual information of the distribution of per-pixel intensity and labels, and the performance of classical registration methods. This strong correlation hints to the fact that architectural designs in learning-based methods is unlikely to affect this correlation, and therefore, the performance of learning-based methods. This hypothesis is thoroughly validated with state-of-the-art classical and learning-based methods. However, learning-based methods with weak supervision can perform high-fidelity intensity and label registration, which is not possible with classical methods. Next, we show that this high-fidelity feature learning does not translate to invariance to domain shift, and learning-based methods are sensitive to such changes in the data distribution. Finally, we propose a general recipe to choose the best paradigm for a given registration problem, based on these observations.

Zhaoze Wang, Genela Morris, Dori Derdikman et al.

Grid cells in the medial entorhinal cortex (MEC) and place cells in the hippocampus (HC) both form spatial representations. Grid cells fire in triangular grid patterns, while place cells fire at specific locations and respond to contextual cues. How do these interacting systems support not only spatial encoding but also internally driven path planning, such as navigating to locations recalled from cues? Here, we propose a system-level theory of MEC-HC wiring that explains how grid and place cell patterns could be connected to enable cue-triggered goal retrieval, path planning, and reconstruction of sensory experience along planned routes. We suggest that place cells autoassociate sensory inputs with grid cell patterns, allowing sensory cues to trigger recall of goal-location grid patterns. We show analytically that grid-based planning permits shortcuts through unvisited locations and generalizes local transitions to long-range paths. During planning, intermediate grid states trigger place cell pattern completion, reconstructing sensory experiences along the route. Using a single-layer RNN modeling the HC-MEC loop with a planning subnetwork, we demonstrate these effects in both biologically grounded navigation simulations using RatatouGym and visually realistic navigation tasks using Habitat Sim.

Junyao Shi, Rujia Yang, Kaitian Chao et al.

Today's best-explored routes towards generalist robots center on collecting ever larger "observations-in actions-out" robotics datasets to train large end-to-end models, copying a recipe that has worked for vision-language models (VLMs). We pursue a road less traveled: building generalist policies directly around VLMs by augmenting their general capabilities with specific robot capabilities encapsulated in a carefully curated set of perception, planning, and control modules. In Maestro, a VLM coding agent dynamically composes these modules into a programmatic policy for the current task and scenario. Maestro's architecture benefits from a streamlined closed-loop interface without many manually imposed structural constraints, and a comprehensive and diverse tool repertoire. As a result, it largely surpasses today's VLA models for zero-shot performance on challenging manipulation skills. Further, Maestro is easily extensible to incorporate new modules, easily editable to suit new embodiments such as a quadruped-mounted arm, and even easily adapts from minimal real-world experiences through local code edits.

Siming He, Yuezhan Tao, Igor Spasojevic et al.

Active perception approaches select future viewpoints by using some estimate of the information gain. An inaccurate estimate can be detrimental in critical situations, e.g., locating a person in distress. However the true information gained can only be calculated post hoc, i.e., after the observation is realized. We present an approach to estimate the discrepancy between the estimated information gain (which is the expectation over putative future observations while neglecting correlations among them) and the true information gain. The key idea is to analyze the mathematical relationship between active perception and the estimation error of the information gain in a game-theoretic setting. Using this, we develop an online estimation approach that achieves sub-linear regret (in the number of time-steps) for the estimation of the true information gain and reduces the sub-optimality of active perception systems. We demonstrate our approach for active perception using a comprehensive set of experiments on: (a) different types of environments, including a quadrotor in a photorealistic simulation, real-world robotic data, and real-world experiments with ground robots exploring indoor and outdoor scenes; (b) different types of robotic perception data; and (c) different map representations. On average, our approach reduces information gain estimation errors by 42%, increases the information gain by 7%, PSNR by 5%, and semantic accuracy (measured as the number of objects that are localized correctly) by 6%. In real-world experiments with a Jackal ground robot, our approach demonstrated complex trajectories to explore occluded regions.

Ashwin De Silva, Rahul Ramesh, Rubing Yang et al.

In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a consequence, existing strategies to address the dynamic nature of data and goals exhibit poor real-world performance. This paper develops a theoretical framework called "Prospective Learning" that is tailored for situations when the optimal hypothesis changes over time. In PAC learning, empirical risk minimization (ERM) is known to be consistent. We develop a learner called Prospective ERM, which returns a sequence of predictors that make predictions on future data. We prove that the risk of prospective ERM converges to the Bayes risk under certain assumptions on the stochastic process generating the data. Prospective ERM, roughly speaking, incorporates time as an input in addition to the data. We show that standard ERM as done in PAC learning, without incorporating time, can result in failure to learn when distributions are dynamic. Numerical experiments illustrate that prospective ERM can learn synthetic and visual recognition problems constructed from MNIST and CIFAR-10. Code at https://github.com/neurodata/prolearn.

Rohit Jena, Pratik Chaudhari, James C. Gee

FireANTs introduced a novel Eulerian descent method for plug-and-play behavior with arbitrary optimizers adapted for diffeomorphic image registration as a test-time optimization problem, with a GPU-accelerated implementation. FireANTs uses Adam as its default optimizer for fast and more robust optimization. However, Adam requires storing state variables (i.e. momentum and squared-momentum estimates), each of which can consume significant memory, prohibiting its use for significantly large images. In this work, we propose a modified Levenberg-Marquardt (LM) optimizer that requires only a single scalar damping parameter as optimizer state, that is adaptively tuned using a trust region approach. The resulting optimizer reduces memory by up to 24.6% for large volumes, and retaining performance across all four datasets. A single hyperparameter configuration tuned on brain MRI transfers without modification to lung CT and cross-modal abdominal registration, matching or outperforming Adam on three of four benchmarks. We also perform ablations on the effectiveness of using Metropolis-Hastings style rejection step to prevent updates that worsen the loss function.

Yuxin Bai, Cecelia Shuai, Ashwin De Silva et al.

In most real-world applications of artificial intelligence, the distributions of the data and the goals of the learners tend to change over time. The Probably Approximately Correct (PAC) learning framework, which underpins most machine learning algorithms, fails to account for dynamic data distributions and evolving objectives, often resulting in suboptimal performance. Prospective learning is a recently introduced mathematical framework that overcomes some of these limitations. We build on this framework to present preliminary results that improve the algorithm and numerical results, and extend prospective learning to sequential decision-making scenarios, specifically foraging. Code is available at: https://github.com/neurodata/prolearn2.

Richeek Das, Pratik Chaudhari

Neurosim is a fast, real-time, high-performance library for simulating sensors such as dynamic vision sensors, RGB cameras, depth sensors, and inertial sensors. It can also simulate agile dynamics of multi-rotor vehicles in complex and dynamic environments. Neurosim can achieve frame rates as high as ~2700 FPS on a desktop GPU. Neurosim integrates with a ZeroMQ-based communication library called Cortex to facilitate seamless integration with machine learning and robotics workflows. Cortex provides a high-throughput, low-latency message-passing system for Python and C++ applications, with native support for NumPy arrays and PyTorch tensors. This paper discusses the design philosophy behind Neurosim and Cortex. It demonstrates how they can be used to (i) train neuromorphic perception and control algorithms, e.g., using self-supervised learning on time-synchronized multi-modal data, and (ii) test real-time implementations of these algorithms in closed-loop. Neurosim and Cortex are available at https://github.com/grasp-lyrl/neurosim .

Rohit Jena, Pratik Chaudhari, James C. Gee

The LUMIR challenge represents an important benchmark for evaluating deformable image registration methods on large-scale neuroimaging data. While the challenge demonstrates that modern deep learning methods achieve competitive accuracy on T1-weighted MRI, it also claims exceptional zero-shot generalization to unseen contrasts and resolutions, assertions that contradict established understanding of domain shift in deep learning. In this paper, we perform an independent re-evaluation of these zero-shot claims using rigorous evaluation protocols while addressing potential sources of instrumentation bias. Our findings reveal a more nuanced picture: (1) deep learning methods perform comparably to iterative optimization on in-distribution T1w images and even on human-adjacent species (macaque), demonstrating improved task understanding; (2) however, performance degrades significantly on out-of-distribution contrasts (T2, T2*, FLAIR), with Cohen's d scores ranging from 0.7-1.5, indicating substantial practical impact on downstream clinical workflows; (3) deep learning methods face scalability limitations on high-resolution data, failing to run on 0.6 mm isotropic images, while iterative methods benefit from increased resolution; and (4) deep methods exhibit high sensitivity to preprocessing choices. These results align with the well-established literature on domain shift and suggest that claims of universal zero-shot superiority require careful scrutiny. We advocate for evaluation protocols that reflect practical clinical and research workflows rather than conditions that may inadvertently favor particular method classes.

Christopher D. Hsu, Pratik Chaudhari

We study pursuit-evasion games in highly occluded urban environments, e.g. tall buildings in a city, where a scout (quadrotor) tracks multiple dynamic targets on the ground. We show that we can build a neural radiance field (NeRF) representation of the city -- online -- using RGB and depth images from different vantage points. This representation is used to calculate the information gain to both explore unknown parts of the city and track the targets -- thereby giving a completely first-principles approach to actively tracking dynamic targets. We demonstrate, using a custom-built simulator using Open Street Maps data of Philadelphia and New York City, that we can explore and locate 20 stationary targets within 300 steps. This is slower than a greedy baseline, which does not use active perception. But for dynamic targets that actively hide behind occlusions, we show that our approach maintains, at worst, a tracking error of 200m; the greedy baseline can have a tracking error as large as 600m. We observe a number of interesting properties in the scout's policies, e.g., it switches its attention to track a different target periodically, as the quality of the NeRF representation improves over time, the scout also becomes better in terms of target tracking. Code is available at https://github.com/grasp-lyrl/ActiveScout.

Yansong Gao, Rahul Ramesh, Pratik Chaudhari

What is the best way to exploit extra data -- be it unlabeled data from the same task, or labeled data from a related task -- to learn a given task? This paper formalizes the question using the theory of reference priors. Reference priors are objective, uninformative Bayesian priors that maximize the mutual information between the task and the weights of the model. Such priors enable the task to maximally affect the Bayesian posterior, e.g., reference priors depend upon the number of samples available for learning the task and for very small sample sizes, the prior puts more probability mass on low-complexity models in the hypothesis space. This paper presents the first demonstration of reference priors for medium-scale deep networks and image-based data. We develop generalizations of reference priors and demonstrate applications to two problems. First, by using unlabeled data to compute the reference prior, we develop new Bayesian semi-supervised learning methods that remain effective even with very few samples per class. Second, by using labeled data from the source task to compute the reference prior, we develop a new pretraining method for transfer learning that allows data from the target task to maximally affect the Bayesian posterior. Empirical validation of these methods is conducted on image classification datasets. Code is available at https://github.com/grasp-lyrl/deep_reference_priors.

Rahul Ramesh, Pratik Chaudhari

This paper argues that continual learning methods can benefit by splitting the capacity of the learner across multiple models. We use statistical learning theory and experimental analysis to show how multiple tasks can interact with each other in a non-trivial fashion when a single model is trained on them. The generalization error on a particular task can improve when it is trained with synergistic tasks, but can also deteriorate when trained with competing tasks. This theory motivates our method named Model Zoo which, inspired from the boosting literature, grows an ensemble of small models, each of which is trained during one episode of continual learning. We demonstrate that Model Zoo obtains large gains in accuracy on a variety of continual learning benchmark problems. Code is available at https://github.com/grasp-lyrl/modelzoo_continual.

Rasool Fakoor, Pratik Chaudhari, Alexander J. Smola

On-policy reinforcement learning (RL) algorithms have high sample complexity while off-policy algorithms are difficult to tune. Merging the two holds the promise to develop efficient algorithms that generalize across diverse environments. It is however challenging in practice to find suitable hyper-parameters that govern this trade off. This paper develops a simple algorithm named P3O that interleaves off-policy updates with on-policy updates. P3O uses the effective sample size between the behavior policy and the target policy to control how far they can be from each other and does not introduce any additional hyper-parameters. Extensive experiments on the Atari-2600 and MuJoCo benchmark suites show that this simple technique is effective in reducing the sample complexity of state-of-the-art algorithms. Code to reproduce experiments in this paper is at https://github.com/rasoolfa/P3O.

Amrut Nadgir, Vijay Balasubramanian, Pratik Chaudhari

Many language tasks can be modeled as classification problems where a large language model (LLM) is given a prompt and selects one among many possible answers. We show that the classification error in such problems scales as a power law in the number of classes. This has a dramatic consequence: the prediction error can be reduced substantially by splitting the overall task into a sequence of smaller classification problems, each with the same number of classes ("degree"). This tree-structured decomposition models chain-of-thought (CoT). It has been observed that CoT-based predictors perform better when they "think'", i.e., when they develop a deeper tree, thus decomposing the problem into a larger number of steps. We identify a critical threshold for the degree, below which thinking is detrimental, and above which there exists an optimal depth that minimizes the error. It is impossible to surpass this minimal error by increasing the depth of thinking.

Ke Yang, Yao Liu, Sapana Chaudhary et al.

Autonomy via agents using large language models (LLMs) for personalized, standardized tasks boosts human efficiency. Automating web tasks (like booking hotels within a budget) is increasingly sought after. Fulfilling practical needs, the web agent also serves as an important proof-of-concept example for various agent grounding scenarios, with its success promising advancements in many future applications. Prior research often handcrafts web agent strategies (e.g., prompting templates, multi-agent systems, search methods, etc.) and the corresponding in-context examples, which may not generalize well across all real-world scenarios. On the other hand, there has been limited study on the misalignment between a web agent's observation/action representation and the pre-training data of the LLM it's based on. This discrepancy is especially notable when LLMs are primarily trained for language completion rather than tasks involving embodied navigation actions and symbolic web elements. Our study enhances an LLM-based web agent by simply refining its observation and action space to better align with the LLM's capabilities. This approach enables our base agent to significantly outperform previous methods on a wide variety of web tasks. Specifically, on WebArena, a benchmark featuring general-purpose web interaction tasks, our agent AgentOccam surpasses the previous state-of-the-art and concurrent work by 9.8 (+29.4%) and 5.9 (+15.8%) absolute points respectively, and boosts the success rate by 26.6 points (+161%) over similar plain web agents with its observation and action space alignment. We achieve this without using in-context examples, new agent roles, online feedback or search strategies. AgentOccam's simple design highlights LLMs' impressive zero-shot performance on web tasks, and underlines the critical role of carefully tuning observation and action spaces for LLM-based agents.

Matteo Marchi, Stefano Soatto, Pratik Chaudhari et al.

Improvement and adoption of generative machine learning models is rapidly accelerating, as exemplified by the popularity of LLMs (Large Language Models) for text, and diffusion models for image generation. As generative models become widespread, data they generate is incorporated into shared content through the public web. This opens the question of what happens when data generated by a model is fed back to the model in subsequent training campaigns. This is a question about the stability of the training process, whether the distribution of publicly accessible content, which we refer to as "knowledge", remains stable or collapses. Small scale empirical experiments reported in the literature show that this closed-loop training process is prone to degenerating. Models may start producing gibberish data, or sample from only a small subset of the desired data distribution (a phenomenon referred to as mode collapse). So far there has been only limited theoretical understanding of this process, in part due to the complexity of the deep networks underlying these generative models. The aim of this paper is to provide insights into this process (that we refer to as "generative closed-loop learning") by studying the learning dynamics of generative models that are fed back their own produced content in addition to their original training dataset. The sampling of many of these models can be controlled via a "temperature" parameter. Using dynamical systems tools, we show that, unless a sufficient amount of external data is introduced at each iteration, any non-trivial temperature leads the model to asymptotically degenerate. In fact, either the generative distribution collapses to a small set of outputs or becomes uniform over a large set of outputs.

Zhepeng Cen, Yao Liu, Siliang Zeng et al.

Language models are often trained to maximize the likelihood of the next token given past tokens in the training dataset. However, during inference time, they are utilized differently, generating text sequentially and auto-regressively by using previously generated tokens as input to predict the next one. Marginal differences in predictions at each step can cascade over successive steps, resulting in different distributions from what the models were trained for and potentially leading to unpredictable behavior. This paper proposes two simple approaches based on model own generation to address this discrepancy between the training and inference time. Our first approach is Batch-Scheduled Sampling, where, during training, we stochastically choose between the ground-truth token from the dataset and the model's own generated token as input to predict the next token. This is done in an offline manner, modifying the context window by interleaving ground-truth tokens with those generated by the model. Our second approach is Reference-Answer-based Correction, where we explicitly incorporate a self-correction capability into the model during training. This enables the model to effectively self-correct the gaps between the generated sequences and the ground truth data without relying on an external oracle model. By incorporating our proposed strategies during training, we have observed an overall improvement in performance compared to baseline methods, as demonstrated by our extensive experiments using summarization, general question-answering, and math question-answering tasks.

Siming He, Zach Osman, Pratik Chaudhari

For robotics applications where there is a limited number of (typically ego-centric) views, parametric representations such as neural radiance fields (NeRFs) generalize better than non-parametric ones such as Gaussian splatting (GS) to views that are very different from those in the training data; GS however can render much faster than NeRFs. We develop a procedure to convert back and forth between the two. Our approach achieves the best of both NeRFs (superior PSNR, SSIM, and LPIPS on dissimilar views, and a compact representation) and GS (real-time rendering and ability for easily modifying the representation); the computational cost of these conversions is minor compared to training the two from scratch.

Rohit Jena, Pratik Chaudhari, James C. Gee

The paper proposes FireANTs, a multi-scale Adaptive Riemannian Optimization algorithm for dense diffeomorphic image matching. Existing state-of-the-art methods for diffeomorphic image matching are slow due to inefficient implementations and slow convergence due to the ill-conditioned nature of the optimization problem. Deep learning methods offer fast inference but require extensive training time, substantial inference memory, and fail to generalize across long-tailed distributions or diverse image modalities, necessitating costly retraining. We address these challenges by proposing a training-free, GPU-accelerated multi-scale Adaptive Riemannian Optimization algorithm for fast and accurate dense diffeomorphic image matching. FireANTs runs about 2.5x faster than ANTs on a CPU, and upto 1200x faster on a GPU. On a single GPU, FireANTs performs competitively with deep learning methods on inference runtime while consuming upto 10x less memory. FireANTs shows remarkable robustness to a wide variety of matching problems across modalities, species, and organs without any domain-specific training or tuning. Our framework allows hyperparameter grid search studies with significantly less resources and time compared to traditional and deep learning registration algorithms alike.

Haoran Tang, Jieren Deng, Zhihong Pan et al.

Diffusion-based methods have demonstrated remarkable capabilities in generating a diverse array of high-quality images, sparking interests for styled avatars, virtual try-on, and more. Previous methods use the same reference image as the target. An overlooked aspect is the leakage of the target's spatial information, style, etc. from the reference, harming the generated diversity and causing shortcuts. However, this approach continues as widely available datasets usually consist of single images not grouped by identities, and it is expensive to recollect large-scale same-identity data. Moreover, existing metrics adopt decoupled evaluation on text alignment and identity preservation, which fail at distinguishing between balanced outputs and those that over-fit to one aspect. In this paper, we propose a multi-level, same-identity dataset RetriBooru, which groups anime characters by both face and cloth identities. RetriBooru enables adopting reference images of the same character and outfits as the target, while keeping flexible gestures and actions. We benchmark previous methods on our dataset, and demonstrate the effectiveness of training with a reference image different from target (but same identity). We introduce a new concept composition task, where the conditioning encoder learns to retrieve different concepts from several reference images, and modify a baseline network RetriNet for the new task. Finally, we introduce a novel class of metrics named Similarity Weighted Diversity (SWD), to measure the overlooked diversity and better evaluate the alignment between similarity and diversity.

Rubing Yang, Pratik Chaudhari

We derive a differential equation that governs the evolution of the generalization gap when a deep network is trained by gradient descent. This differential equation is controlled by two quantities, a contraction factor that brings together trajectories corresponding to slightly different datasets, and a perturbation factor that accounts for them training on different datasets. We analyze this differential equation to compute an ``effective Gram matrix'' that characterizes the generalization gap in terms of the alignment between this Gram matrix and a certain initial ``residual''. Empirical evaluations on image classification datasets indicate that this analysis can predict the test loss accurately. Further, during training, the residual predominantly lies in the subspace of the effective Gram matrix with the smallest eigenvalues. This indicates that the generalization gap accumulates slowly along the direction of training, charactering a benign training process. We provide novel perspectives for explaining the generalization ability of neural network training with different datasets and architectures through the alignment pattern of the ``residual" and the ``effective Gram matrix".

Tian Yu Liu, Stefano Soatto, Matteo Marchi et al.

We tackle the question of whether Large Language Models (LLMs), viewed as dynamical systems with state evolving in the embedding space of symbolic tokens, are observable. That is, whether there exist multiple 'mental' state trajectories that yield the same sequence of generated tokens, or sequences that belong to the same Nerode equivalence class ('meaning'). If not observable, mental state trajectories ('experiences') evoked by an input ('perception') or by feedback from the model's own state ('thoughts') could remain self-contained and evolve unbeknown to the user while being potentially accessible to the model provider. Such "self-contained experiences evoked by perception or thought" are akin to what the American Psychological Association (APA) defines as 'feelings'. Beyond the lexical curiosity, we show that current LLMs implemented by autoregressive Transformers cannot have 'feelings' according to this definition: The set of state trajectories indistinguishable from the tokenized output is a singleton. But if there are 'system prompts' not visible to the user, then the set of indistinguishable trajectories becomes non-trivial, and there can be multiple state trajectories that yield the same verbalized output. We prove these claims analytically, and show examples of modifications to standard LLMs that engender such 'feelings.' Our analysis sheds light on possible designs that would enable a model to perform non-trivial computation that is not visible to the user, as well as on controls that the provider of services using the model could take to prevent unintended behavior.

Keshava Katti, Pratik Chaudhari, Deep Jariwala

Classical computing is beginning to encounter fundamental limits of energy efficiency. This presents a challenge that can no longer be solved by strategies such as increasing circuit density or refining standard semiconductor processes. The growing computational and memory demands of artificial intelligence (AI) require disruptive innovation in how information is represented, stored, communicated, and processed. By leveraging novel device modalities and compute-in-memory (CIM), in addition to analog dynamics and sparse communication inspired by the brain, neuromorphic computing offers a promising path toward improvements in the energy efficiency and scalability of current AI systems. But realizing this potential is not a matter of replacing one chip with another; rather, it requires a co-design effort, spanning new materials and non-volatile device structures, novel mixed-signal circuits and architectures, and learning algorithms tailored to the physics of these substrates. This article surveys the key limitations of classical complementary metal-oxide-semiconductor (CMOS) technology and outlines how such cross-layer neuromorphic approaches may overcome them.

Siming He, Zachary Osman, Fernando Cladera et al.

Forest inventories rely on accurate measurements of the diameter at breast height (DBH) for ecological monitoring, resource management, and carbon accounting. While LiDAR-based techniques can achieve centimeter-level precision, they are cost-prohibitive and operationally complex. We present a low-cost alternative that only needs a consumer-grade 360 video camera. Our semi-automated pipeline comprises of (i) a dense point cloud reconstruction using Structure from Motion (SfM) photogrammetry software called Agisoft Metashape, (ii) semantic trunk segmentation by projecting Grounded Segment Anything (SAM) masks onto the 3D cloud, and (iii) a robust RANSAC-based technique to estimate cross section shape and DBH. We introduce an interactive visualization tool for inspecting segmented trees and their estimated DBH. On 61 acquisitions of 43 trees under a variety of conditions, our method attains median absolute relative errors of 5-9% with respect to "ground-truth" manual measurements. This is only 2-4% higher than LiDAR-based estimates, while employing a single 360 camera that costs orders of magnitude less, requires minimal setup, and is widely available.

Richeek Das, Kostas Daniilidis, Pratik Chaudhari

This paper develops a mathematical argument and algorithms for building representations of data from event-based cameras, that we call Fast Feature Field ($\text{F}^3$). We learn this representation by predicting future events from past events and show that it preserves scene structure and motion information. $\text{F}^3$ exploits the sparsity of event data and is robust to noise and variations in event rates. It can be computed efficiently using ideas from multi-resolution hash encoding and deep sets - achieving 120 Hz at HD and 440 Hz at VGA resolutions. $\text{F}^3$ represents events within a contiguous spatiotemporal volume as a multi-channel image, enabling a range of downstream tasks. We obtain state-of-the-art performance on optical flow estimation, semantic segmentation, and monocular metric depth estimation, on data from three robotic platforms (a car, a quadruped robot and a flying platform), across different lighting conditions (daytime, nighttime), environments (indoors, outdoors, urban, as well as off-road) and dynamic vision sensors (resolutions and event rates). Our implementations can predict these tasks at 25-75 Hz at HD resolution.

Rohit Jena, Vedant Zope, Pratik Chaudhari et al.

In this work, we propose FFDP, a set of IO-aware non-GEMM fused kernels supplemented with a distributed framework for image registration at unprecedented scales. Image registration is an inverse problem fundamental to biomedical and life sciences, but algorithms have not scaled in tandem with image acquisition capabilities. Our framework complements existing model parallelism techniques proposed for large-scale transformer training by optimizing non-GEMM bottlenecks and enabling convolution-aware tensor sharding. We demonstrate unprecedented capabilities by performing multimodal registration of a 100 micron ex-vivo human brain MRI volume at native resolution - an inverse problem more than 570x larger than a standard clinical datum in about a minute using only 8 A6000 GPUs. FFDP accelerates existing state-of-the-art optimization and deep learning registration pipelines by upto 6 - 7x while reducing peak memory consumption by 20 - 59%. Comparative analysis on a 250 micron dataset shows that FFDP can fit upto 64x larger problems than existing SOTA on a single GPU, and highlights both the performance and efficiency gains of FFDP compared to SOTA image registration methods.

Alok N. Shah, Khush Gupta, Keshav Ramji et al.

While modern Transformer-based language models (LMs) have achieved major success in multi-task generalization, they often struggle to capture long-range dependencies within their context window. This work introduces a novel approach using meta-tokens, special tokens injected during pre-training, along with a dedicated meta-attention mechanism to guide LMs to use these tokens. We pre-train a language model with a modified GPT-2 architecture equipped with meta-attention in addition to causal multi-head attention, and study the impact of these tokens on a suite of synthetic tasks. We find that data-efficient language model pre-training on fewer than 100B tokens utilizing meta-tokens and our meta-attention mechanism achieves strong performance on these tasks after fine-tuning. We suggest that these gains arise due to the meta-tokens sharpening the positional encoding. This enables them to operate as trainable, content-based landmarks, implicitly compressing preceding context and "caching" it in the meta-token. At inference-time, the meta-token points to relevant context, facilitating length generalization up to 2$\times$ its context window, even after extension with YaRN. We provide further evidence of these behaviors by visualizing model internals to study the residual stream, and assessing the compression quality by information-theoretic analysis on the rate-distortion tradeoff. Our findings suggest that pre-training LMs with meta-tokens offers a simple, data-efficient method to enhance long-context language modeling performance, while introducing new insights into the nature of their behavior towards length generalization.

Anthony Bisulco, Rahul Ramesh, Randall Balestriero et al.

Masked Autoencoders (MAEs) have emerged as a powerful pretraining technique for vision foundation models. Despite their effectiveness, they require extensive hyperparameter tuning (masking ratio, patch size, encoder/decoder layers) when applied to novel datasets. While prior theoretical works have analyzed MAEs in terms of their attention patterns and hierarchical latent variable models, the connection between MAE hyperparameters and performance on downstream tasks is relatively unexplored. This work investigates how MAEs learn spatial correlations in the input image. We analytically derive the features learned by a linear MAE and show that masking ratio and patch size can be used to select for features that capture short- and long-range spatial correlations. We extend this analysis to non-linear MAEs to show that MAE representations adapt to spatial correlations in the dataset, beyond second-order statistics. Finally, we discuss some insights on how to select MAE hyper-parameters in practice.

Evangelos Sariyanidi, John D. Herrington, Lisa Yankowitz et al.

Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge regarding the nature of dependence. We introduce a self-supervised approach, concurrence, which is inspired by the observation that if two signals are dependent, then one should be able to distinguish between temporally aligned vs. misaligned segments extracted from them. Experiments with fMRI, physiological and behavioral signals show that, to our knowledge, concurrence is the first approach that can expose relationships across such a wide spectrum of signals and extract scientifically relevant differences without ad-hoc parameter tuning or reliance on a priori information, providing a potent tool for scientific discoveries across fields. However, dependencies caused by extraneous factors remain an open problem, thus researchers should validate that exposed relationships truly pertain to the question(s) of interest.

Jialin Mao, Itay Griniasty, Yan Sun et al.

Recent experiments have shown that training trajectories of multiple deep neural networks with different architectures, optimization algorithms, hyper-parameter settings, and regularization methods evolve on a remarkably low-dimensional "hyper-ribbon-like" manifold in the space of probability distributions. Inspired by the similarities in the training trajectories of deep networks and linear networks, we analytically characterize this phenomenon for the latter. We show, using tools in dynamical systems theory, that the geometry of this low-dimensional manifold is controlled by (i) the decay rate of the eigenvalues of the input correlation matrix of the training data, (ii) the relative scale of the ground-truth output to the weights at the beginning of training, and (iii) the number of steps of gradient descent. By analytically computing and bounding the contributions of these quantities, we characterize phase boundaries of the region where hyper-ribbons are to be expected. We also extend our analysis to kernel machines and linear models that are trained with stochastic gradient descent.

Rohit Jena, Pratik Chaudhari, James C. Gee

Deep Learning in Image Registration (DLIR) methods have been tremendously successful in image registration due to their speed and ability to incorporate weak label supervision at training time. However, existing DLIR methods forego many of the benefits and invariances of optimization methods. The lack of a task-specific inductive bias in DLIR methods leads to suboptimal performance, especially in the presence of domain shift. Our method aims to bridge this gap between statistical learning and optimization by explicitly incorporating optimization as a layer in a deep network. A deep network is trained to predict multi-scale dense feature images that are registered using a black box iterative optimization solver. This optimal warp is then used to minimize image and label alignment errors. By implicitly differentiating end-to-end through an iterative optimization solver, we explicitly exploit invariances of the correspondence matching problem induced by the optimization, while learning registration and label-aware features, and guaranteeing the warp functions to be a local minima of the registration objective in the feature space. Our framework shows excellent performance on in-domain datasets, and is agnostic to domain shift such as anisotropy and varying intensity profiles. For the first time, our method allows switching between arbitrary transformation representations (free-form to diffeomorphic) at test time with zero retraining. End-to-end feature learning also facilitates interpretability of features and arbitrary test-time regularization, which is not possible with existing DLIR methods.

Stefano Soatto, Paulo Tabuada, Pratik Chaudhari et al.

We tackle the question of whether an agent can, by suitable choice of prompts, control an AI bot to any state. To that end, we first introduce a formal definition of ``meaning'' that is amenable to analysis. Then, we characterize ``meaningful data'' on which large language models (LLMs) are ostensibly trained, and ``well-trained LLMs'' through conditions that are largely met by today's LLMs. While a well-trained LLM constructs an embedding space of meanings that is Euclidean, meanings themselves do not form a vector (linear) subspace, but rather a quotient space within. We then characterize the subset of meanings that can be reached by the state of the LLMs for some input prompt, and show that a well-trained bot can reach any meaning albeit with small probability. We then introduce a stronger notion of controllability as {\em almost certain reachability}, and show that, when restricted to the space of meanings, an AI bot is controllable. We do so after introducing a functional characterization of attentive AI bots, and finally derive necessary and sufficient conditions for controllability. The fact that AI bots are controllable means that an adversary could steer them towards any state. However, the sampling process can be designed to counteract adverse actions and avoid reaching undesirable regions of state space before their boundary is crossed.

Daiwei Chen, Wei-Kai Chang, Pratik Chaudhari

We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective dimensionality of a model. We show that the learning capacity is a useful notion of the complexity because (a) it correlates well with the test loss and it is a tiny fraction of the number of parameters for many deep networks trained on typical datasets, (b) it depends upon the number of samples used for training, (c) it is numerically consistent with notions of capacity obtained from PAC-Bayes generalization bounds, and (d) the test loss as a function of the learning capacity does not exhibit double descent. We show that the learning capacity saturates at very small and very large sample sizes; the threshold that characterizes the transition between these two regimes provides guidelines as to when one should procure more data and when one should search for a different architecture to improve performance. We show how the learning capacity can be used to provide a quantitative notion of capacity even for non-parametric models such as random forests and nearest neighbor classifiers.

Jialin Mao, Itay Griniasty, Han Kheng Teoh et al.

We develop information-geometric techniques to analyze the trajectories of the predictions of deep networks during training. By examining the underlying high-dimensional probabilistic models, we reveal that the training process explores an effectively low-dimensional manifold. Networks with a wide range of architectures, sizes, trained using different optimization methods, regularization techniques, data augmentation techniques, and weight initializations lie on the same manifold in the prediction space. We study the details of this manifold to find that networks with different architectures follow distinguishable trajectories but other factors have a minimal influence; larger networks train along a similar manifold as that of smaller networks, just faster; and networks initialized at very different parts of the prediction space converge to the solution along a similar manifold.

Shiyun Xu, Zhiqi Bu, Pratik Chaudhari et al.

Interpretable machine learning has demonstrated impressive performance while preserving explainability. In particular, neural additive models (NAM) offer the interpretability to the black-box deep learning and achieve state-of-the-art accuracy among the large family of generalized additive models. In order to empower NAM with feature selection and improve the generalization, we propose the sparse neural additive models (SNAM) that employ the group sparsity regularization (e.g. Group LASSO), where each feature is learned by a sub-network whose trainable parameters are clustered as a group. We study the theoretical properties for SNAM with novel techniques to tackle the non-parametric truth, thus extending from classical sparse linear models such as the LASSO, which only works on the parametric truth. Specifically, we show that SNAM with subgradient and proximal gradient descents provably converges to zero training loss as $t\to\infty$, and that the estimation error of SNAM vanishes asymptotically as $n\to\infty$. We also prove that SNAM, similar to LASSO, can have exact support recovery, i.e. perfect feature selection, with appropriate regularization. Moreover, we show that the SNAM can generalize well and preserve the `identifiability', recovering each feature's effect. We validate our theories via extensive experiments and further testify to the good accuracy and efficiency of SNAM.

Ashwin De Silva, Rahul Ramesh, Lyle Ungar et al.

Learning is a process which can update decision rules, based on past experience, such that future performance improves. Traditionally, machine learning is often evaluated under the assumption that the future will be identical to the past in distribution or change adversarially. But these assumptions can be either too optimistic or pessimistic for many problems in the real world. Real world scenarios evolve over multiple spatiotemporal scales with partially predictable dynamics. Here we reformulate the learning problem to one that centers around this idea of dynamic futures that are partially learnable. We conjecture that certain sequences of tasks are not retrospectively learnable (in which the data distribution is fixed), but are prospectively learnable (in which distributions may be dynamic), suggesting that prospective learning is more difficult in kind than retrospective learning. We argue that prospective learning more accurately characterizes many real world problems that (1) currently stymie existing artificial intelligence solutions and/or (2) lack adequate explanations for how natural intelligences solve them. Thus, studying prospective learning will lead to deeper insights and solutions to currently vexing challenges in both natural and artificial intelligences.