Miracle-dz/UniFAR-FTUs huggingface dataset:
Mars Terrain Segmentation with Less Labels

Planetary rover systems need to perform terrain seg-mentation to identify drivable areas as well as identify specific types of soil for sample collection. The latest Martian terrain segmentation methods rely on supervised learning which is very data hungry and difficult to train where only a small number of labeled samples are available. Moreover, the semantic classes are defined differently for different applications (e.g., rover traversal vs. geological) and as a result the network has to be trained from scratch each time, which is an inefficient use of resources. This research proposes a semi-supervised learning framework for Mars terrain segmentation where a deep segmen-tation network trained in an unsupervised manner on unlabeled images is transferred to the task of terrain segmentation trained on few labeled images. The network incorporates a backbone module which is trained using a contrastive loss function and an output atrous convolution module which is trained using a pixel-wise cross-entropy loss function. Evaluation results using the metric of segmentation accuracy show that the proposed method with contrastive pretraining outperforms plain super-vised learning by 2%-10%. Moreover, the proposed model is able to achieve a segmentation accuracy of 91.1% using only 161 training images (1% of the original dataset) compared to 81.9% with plain supervised learning.
The Role of the Second Law of Thermodynamics in Continuum Physics: A Muschik and Ehrentraut Theorem Revisited

In continuum physics, constitutive equations model the material properties of physical systems. In those equations, material symmetry is taken into account by applying suitable representation theorems for symmetric and/or isotropic functions. Such mathematical representations must be in accordance with the second law of thermodynamics, which imposes that, in any thermodynamic process, the entropy production must be nonnegative. This requirement is fulfilled by assigning the constitutive equations in a form that guaranties that second law of thermodynamics is satisfied along arbitrary processes. Such an approach, in practice regards the second law of thermodynamics as a restriction on the constitutive equations, which must guarantee that any solution of the balance laws also satisfy the entropy inequality. This is a useful operative assumption, but not a consequence of general physical laws. Indeed, a different point of view, which regards the second law of thermodynamics as a restriction on the thermodynamic processes, i.e., on the solutions of the system of balance laws, is possible. This is tantamount to assuming that there are solutions of the balance laws that satisfy the entropy inequality, and solutions that do not satisfy it. In order to decide what is the correct approach, Muschik and Ehrentraut in 1996, postulated an amendment to the second law, which makes explicit the evident (but rather hidden) assumption that, in any point of the body, the entropy production is zero if, and only if, this point is a thermodynamic equilibrium. Then they proved that, given the amendment, the second law of thermodynamics is necessarily a restriction on the constitutive equations and not on the thermodynamic processes. In the present paper, we revisit their proof, lighting up some geometric aspects that were hidden in therein. Moreover, we propose an alternative formulation of the second law of thermodynamics, which incorporates the amendment. In this way we make this important result more intuitive and easily accessible to a wider audience.
On Regularizing Coordinate-MLPs

We show that typical implicit regularization assumptions for deep neural networks (for regression) do not hold for coordinate-MLPs, a family of MLPs that are now ubiquitous in computer vision for representing high-frequency signals. Lack of such implicit bias disrupts smooth interpolations between training samples, and hampers generalizing across signal regions with different spectra. We investigate this behavior through a Fourier lens and uncover that as the bandwidth of a coordinate-MLP is enhanced, lower frequencies tend to get suppressed unless a suitable prior is provided explicitly. Based on these insights, we propose a simple regularization technique that can mitigate the above problem, which can be incorporated into existing networks without any architectural modifications.
BICEP/Keck data and quadratic gravity

The recent results of the BICEP and Keck collaborations have put stringent bounds on many inflationary models, including some well-motivated ones. This is certainly the case when gravity remains described by Einstein's theory up to the inflationary scale, but can be avoided by introducing quadratic-in-curvature terms that are effective at that scale. Recently it has also been shown that these terms can UV complete gravity respecting stability and unitarity. Here the predictions of such quadratic gravity are computed and compared with the BICEP/Keck constraints by focusing on some of the inflationary scenarios that are best-motivated from the particle physics point of view and are already ruled out in Einstein gravity: (critical) Higgs inflation and natural inflation. The first scenario can be considered as the most economical option as the inflaton is identified with the only known elementary scalar field in the Standard Model and the near criticality of the Standard Model is used to remain in the perturbative regime. In the second one a pseudo-Nambu-Goldstone boson contributes to the inflationary dynamics and its potential is naturally flat. It is shown that in both scenarios one can restore the agreement with the observational constraints in quadratic gravity.
Algorithms for Efficiently Learning Low-Rank Neural Networks

We study algorithms for learning low-rank neural networks – networks where the weight parameters are re-parameterized by products of two low-rank matrices. First, we present a provably efficient algorithm which learns an optimal low-rank approximation to a single-hidden-layer ReLU network up to additive error with probability ≥ 1 − δ, given access to noiseless samples with Gaussian marginals in polynomial time and samples. Thus, we provide the first example of an algorithm which can efficiently learn a neural network up to additive error without assuming the ground truth is realizable. To solve this problem, we introduce an efficient SVD-based Nonlinear Kernel Projection algorithm for solving a nonlinear low-rank approximation problem over Gaussian space. Inspired by the efficiency of our algorithm, we propose a novel low-rank initialization framework for training low-rank deep networks, and prove that for ReLU networks, the gap between our method and existing schemes widens as the desired rank of the approximating weights decreases, or as the dimension of the inputs increases (the latter point holds when network width is superlinear in dimension). Finally, we validate our theory by training ResNets and EfficientNets [He et al., 2016, Tan and Le, 2019] models on ImageNet [Russakovsky et al., 2015].
Unified Scaling Laws for Routed Language Models

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their parameters while processing an input. For these models, parameter count and computational requirement form two independent axes along which an increase leads to better performance. In this work we derive and justify scaling laws defined on these two variables which generalize those known for standard language models and describe the performance of a wide range of routing architectures trained via three different techniques. Afterwards we provide two applications of these laws: first deriving an Effective Parameter Count along which all models scale at the same rate, and then using the scaling coefficients to give a quantitative comparison of the three routing techniques considered. Our analysis derives from an extensive evaluation of Routing Networks across five orders of magnitude of size, including models with hundreds of experts and hundreds of billions of parameters.
Framework for Evaluating Faithfulness of Local Explanations

We study the faithfulness of an explanation system to the underlying prediction model. We show that this can be captured by two properties, consistency and sufficiency, and introduce quantitative measures of the extent to which these hold. Interestingly, these measures depend on the test-time data distribution. For a variety of existing explanation systems, such as anchors, we analytically study these quantities. We also provide estimators and sample complexity bounds for empirically determining the faithfulness of black-box explanation systems. Finally, we experimentally validate the new properties and estimators.
Achieving Fairness at No Utility Cost via Data Reweighing

With the fast development of algorithmic governance, fairness has become a compulsory property for machine learning models to suppress unintentional discrimination. In this paper, we focus on the pre-processing aspect for achieving fairness, and propose a data reweighing approach that only adjusts the weight for samples in the training phase. Different from most previous reweighing methods which usually assign a uniform weight for each (sub)group, we granularly model the influence of each training sample with regard to fairness-related quantity and predictive utility, and compute individual weights based on influence under the constraints from both fairness and utility. Experimental results reveal that previous methods achieve fairness at a non-negligible cost of utility, while as a significant advantage, our approach can empirically release the tradeoff and obtain cost-free fairness for equal opportunity. We demonstrate the cost-free fairness through vanilla classifiers and standard training processes, compared to baseline methods on multiple real-world tabular datasets. Code available at https://github.com/brandeis-machine-learning/influence-fairness.
Precoding and Decoding Schemes for Downlink MIMO-RSMA with Simultaneous Diagonalization and User Exclusion

In this paper, we consider the precoder design for downlink multiple-input multiple-output (MIMO) rate-splitting multiple access (RSMA) systems. The proposed scheme with simultaneous diagonalization (SD) decomposes the MIMO channel matrices of the users into scalar channels via higher-order generalized singular value decomposition for the common message (CM) and block diagonalization (BD) for the private messages, thereby enabling low-complexity element-by-element successive interference cancellation (SIC) and decoding at the receivers. Furthermore, the proposed SD MIMO-RSMA overcomes a critical limitation in RSMA systems, whereby the achievable rate of the CM is restricted by the users with weak effective MIMO channel for the CM, by excluding a subset of users from decoding the CM. We formulate a non-convex weighted sum rate (WSR) optimization problem for SD MIMO-RSMA and solve it via successive convex approximation to obtain a locally optimal solution. Our simulation results reveal that, for both perfect and imperfect CSI, the proposed SD MIMO-RSMA with user exclusion outperforms baseline MIMO-RSMA schemes and linear BD precoding.
Non-Stationary Dueling Bandits

We study the non-stationary dueling bandits problem with $K$ arms, where the time horizon $T$ consists of $M$ stationary segments, each of which is associated with its own preference matrix. The learner repeatedly selects a pair of arms and observes a binary preference between them as feedback. To minimize the accumulated regret, the learner needs to pick the Condorcet winner of each stationary segment as often as possible, despite preference matrices and segment lengths being unknown. We propose the $\mathrm{Beat\, the\, Winner\, Reset}$ algorithm and prove a bound on its expected binary weak regret in the stationary case, which tightens the bound of current state-of-art algorithms. We also show a regret bound for the non-stationary case, without requiring knowledge of $M$ or $T$. We further propose and analyze two meta-algorithms, $\mathrm{DETECT}$ for weak regret and $\mathrm{Monitored\, Dueling\, Bandits}$ for strong regret, both based on a detection-window approach that can incorporate any dueling bandit algorithm as a black-box algorithm. Finally, we prove a worst-case lower bound for expected weak regret in the non-stationary case.
On Lyapunov Stability of Positive and Conservative Time Integrators and Application to Second Order Modified Patankar-Runge-Kutta Schemes

Since almost twenty years, modified Patankar–Runge–Kutta (MPRK) methods have proven to be efficient and robust numerical schemes that preserve positivity and conservativity of the production-destruction system irrespectively of the time step size chosen. Due to these advantageous properties they are used for a wide variety of applications. Nevertheless, until now, an analytic investigation of the stability of MPRK schemes is still missing, since the usual approach by means of Dahlquist’s equation is not feasible. Therefore, we consider a positive and conservative 2D test problem and provide statements usable for a stability analysis of general positive and conservative time integrator schemes based on the center manifold theory. We use this approach to investigate the Lyapunov stability of the second order MPRK22(α) and MPRK22ncs(α) schemes. We prove that MPRK22(α) schemes are unconditionally stable and derive the stability regions of MPRK22ncs(α) schemes. Finally, numerical experiments are presented, which confirm the theoretical results.
Probabilistically Robust Learning: Balancing Average- and Worst-case Performance

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues are often addressed by training against worst-case perturbations of data, a technique known as adversarial training. Although empirically effective, adversarial training can be overly conservative, leading to unfavorable trade-offs between nominal performance and robustness. To this end, in this paper we propose a framework called probabilistic robustness that bridges the gap between the accurate, yet brittle average case and the robust, yet conservative worst case by enforcing robustness to most rather than to all perturbations. From a theoretical point of view, this framework overcomes the trade-offs between the performance and the sample-complexity of worst-case and average-case learning. From a practical point of view, we propose a novel algorithm based on risk-aware optimization that effectively balances average- and worst-case performance at a considerably lower computational cost relative to adversarial training. Our results on MNIST, CIFAR-10, and SVHN illustrate the advantages of this framework on the spectrum from average- to worst-case robustness.
Global Riemannian Acceleration in Hyperbolic and Spherical Spaces

We further research on the accelerated optimization phenomenon on Riemannian manifolds by introducing accelerated global first-order methods for the optimization of L-smooth and geodesically convex (g-convex) or μ-strongly g-convex functions defined on the hyperbolic space or a subset of the sphere. For a manifold other than the Euclidean space, these are the first methods to globally achieve the same rates as accelerated gradient descent in the Euclidean space with respect to L and ε (and μ if it applies), up to log factors. Due to the geometric deformations, our rates have an extra factor, depending on the initial distance R to a minimizer and the curvature K, with respect to Euclidean accelerated algorithms.1 As a proxy for our solution, we solve a constrained non-convex Euclidean problem, under a condition between convexity and quasar-convexity, of independent interest. Additionally, for any Riemannian manifold of bounded sectional curvature, we provide reductions from optimization methods for smooth and g-convex functions to methods for smooth and strongly g-convex functions and vice versa. We also reduce global optimization to optimization over bounded balls where the effect of the curvature is reduced.
The Cold Interstellar Medium of Galaxies in the Local Universe

The cold interstellar medium (ISM) plays a central role in the galaxy evolution process. It is the reservoir that fuels galaxy growth via star formation, the repository of material formed by these stars, and a sensitive tracer of internal and external processes that affect entire galaxies. Consequently, significant efforts have gone into systematic surveys of the cold ISM of the galaxies in the local Universe. This review discusses the resulting network of scaling relations connecting the atomic and molecular gas masses of galaxies with their other global properties (stellar masses, morphologies, metallicities, star-formation activity…) and their implications for our understanding of galaxy evolution. Key take-home messages are as follows: ▪ From a gas perspective, there are three main factors that determine the star-formation rate of a galaxy: the total mass of its cold ISM, how much of that gas is molecular, and the rate at which any molecular gas is converted into stars. All three of these factors vary systematically across the local galaxy population. ▪ The shape and scatter of both the star-formation main sequence and the mass–metallicity relation are deeply linked to the availability of atomic and molecular gas. ▪ Future progress will come from expanding our exploration of scaling relations into new parameter space (in particular, the regime of dwarf galaxies), better connecting the cold ISM of large samples of galaxies with the environment that feeds them (the circumgalactic medium, in particular), and understanding the impact of these large scales on the efficiency of the star-formation process on molecular cloud scales. Expected final online publication date for the Annual Review of Astronomy and Astrophysics Volume 60 is August 2022. Please see http://www.annualreviews. org/page/journal/pubdates for revised estimates.
Using Ballistocardiography for Sleep Stage Classification

A practical way of detecting sleep stages has become more necessary as we begin to learn about the vast effects that sleep has on people's lives. The current methods of sleep stage detection are expensive, invasive to a person's sleep, and not practical in a modern home setting. While the method of detecting sleep stages via the monitoring of brain activity, muscle activity, and eye movement, through electroencephalogram in a lab setting, provide the gold standard for detection, this paper aims to investigate a new method that will allow a person to gain similar insight and results with no obtrusion to their normal sleeping habits. Ballistocardiography (BCG) is a non-invasive sensing technology that collects information by measuring the ballistic forces generated by the heart. Using features extracted from BCG such as time of usage, heart rate, respiration rate, relative stroke volume, and heart rate variability, we propose to implement a sleep stage detection algorithm and compare it against sleep stages extracted from a Fitbit Sense Smart Watch. The accessibility, ease of use, and relatively-low cost of the BCG offers many applications and advantages for using this device. By standardizing this device, people will be able to benefit from the BCG in analyzing their own sleep patterns and draw conclusions on their sleep efficiency. This work demonstrates the feasibility of using BCG for an accurate and non-invasive sleep monitoring method that can be set up in the comfort of a one's personal sleep environment.
Should I take a walk? Estimating Energy Expenditure from Video Data

We explore the problem of automatically inferring the amount of kilocalories used by human during physical activity from his/her video observation. To study this under-researched task, we introduce Vid2Burn – an omni-source benchmark for estimating caloric expenditure from video data featuring both, high- and low-intensity activities for which we derive energy expenditure annotations based on models established in medical literature.In practice, a training set would only cover a certain amount of activity types, and it is important to validate, if the model indeed captures the essence of energy expenditure, (e.g., how many and which muscles are involved and how intense they work) instead of memorizing fixed values of specific activity categories seen during training. Ideally, the models should look beyond such category-specific biases and regress the caloric cost in videos depicting activity categories not explicitly present during training. With this property in mind, Vid2Burn is accompanied with a cross-category benchmark, where the task is to regress caloric expenditure for types of physical activities not present during training. An extensive evaluation of state-of-the-art approaches for video recognition modified for the energy expenditure estimation task demonstrates the difficulty of this problem, especially for new activity types at test-time, marking a new research direction. Dataset and code are available at https://github.com/KPeng9510/Vid2Burn 1.
Team Belief DAG: Generalizing the Sequence Form to Team Games for Fast Computation of Correlated Team Max-Min Equilibria via Regret Minimization

A classic result in the theory of extensive-form games asserts that the set of strategies available to any perfect-recall player is strategically equivalent to a low-dimensional convex polytope, called the sequence-form polytope. Online convex optimization tools operating on this polytope are the current state-of-the-art for computing several notions of equilibria in games, and have been crucial in landmark applications of computational game theory. However, when optimizing over the joint strategy space of a team of players, one cannot use the sequence form to obtain a strategically-equivalent convex description of the strategy set of the team. In this paper, we provide new complexity results on the computation of optimal strategies for teams, and propose a new representation, coined team belief DAG (TB-DAG), that describes team strategies as a convex set. The TB-DAG enjoys state-of-the-art parameterized complexity bounds, while at the same time enjoying the advantages of efficient regret minimization techniques. We show that TB-DAG can be exponentially smaller and can be computed exponentially faster than all other known representations, and that the converse is never true. Experimentally, we show that the TB-DAG, when paired with learning techniques, yields state of the art on a wide variety of benchmark team games.
HTS-AT: A Hierarchical Token-Semantic Audio Transformer for Sound Classification and Detection

Audio classification is an important task of mapping audio samples into their corresponding labels. Recently, the transformer model with self-attention mechanisms has been adopted in this field. However, existing audio transformers require large GPU memories and long training time, meanwhile relying on pretrained vision models to achieve high performance, which limits the model’s scalability in audio tasks. To combat these problems, we introduce HTS-AT: an audio transformer with a hierarchical structure to reduce the model size and training time. It is further combined with a token-semantic module to map final outputs into class featuremaps, thus enabling the model for the audio event detection (i.e. localization in time). We evaluate HTS-AT on three datasets of audio classification where it achieves new state-of-the-art (SOTA) results on AudioSet and ESC50, and equals the SOTA on Speech Command V2. It also achieves better performance in event localization than the previous CNN-based models. Moreover, HTS-AT requires only 35% model parameters and 15% training time of the previous audio transformer. These results demonstrate the high performance and high efficiency of HTS-AT.