Protein design often begins with knowledge of a desired function from a motif which motif-scaffolding aims to construct a functional protein around. Recently, generative models have achieved breakthrough success in designing scaffolds for a diverse range of motifs. However, the generated scaffolds tend to lack structural diversity, which can hinder success in wet-lab validation. In this work, we extend FrameFlow, an SE(3) flow matching model for protein backbone generation, to perform motif-scaffolding with two complementary approaches. The first is motif amortization, in which FrameFlow is trained with the motif as input using a data augmentation strategy. The second is motif guidance, which performs scaffolding using an estimate of the conditional score from FrameFlow, and requires no additional training. Both approaches achieve an equivalent or higher success rate than previous state-of-the-art methods, with 2.5 times more structurally diverse scaffolds. Code: //github.com/ microsoft/frame-flow.
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The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit representations in general. This paper introduces a novel series representation for this scale function, employing Laguerre polynomials to construct a uniformly convergent approximate sequence. Additionally, we derive statistical inference based on specific discrete observations, presenting estimators of scale functions that are asymptotically normal.
We introduce a fine-grained framework for uncertainty quantification of predictive models under distributional shifts. This framework distinguishes the shift in covariate distributions from that in the conditional relationship between the outcome (Y) and the covariates (X). We propose to reweight the training samples to adjust for an identifiable covariate shift while protecting against worst-case conditional distribution shift bounded in an $f$-divergence ball. Based on ideas from conformal inference and distributionally robust learning, we present an algorithm that outputs (approximately) valid and efficient prediction intervals in the presence of distributional shifts. As a use case, we apply the framework to sensitivity analysis of individual treatment effects with hidden confounding. The proposed methods are evaluated in simulation studies and three real data applications, demonstrating superior robustness and efficiency compared with existing benchmarks.
Pre-trained graph models (PGMs) aim to capture transferable inherent structural properties and apply them to different downstream tasks. Similar to pre-trained language models, PGMs also inherit biases from human society, resulting in discriminatory behavior in downstream applications. The debiasing process of existing fair methods is generally coupled with parameter optimization of GNNs. However, different downstream tasks may be associated with different sensitive attributes in reality, directly employing existing methods to improve the fairness of PGMs is inflexible and inefficient. Moreover, most of them lack a theoretical guarantee, i.e., provable lower bounds on the fairness of model predictions, which directly provides assurance in a practical scenario. To overcome these limitations, we propose a novel adapter-tuning framework that endows pre-trained graph models with provable fairness (called GraphPAR). GraphPAR freezes the parameters of PGMs and trains a parameter-efficient adapter to flexibly improve the fairness of PGMs in downstream tasks. Specifically, we design a sensitive semantic augmenter on node representations, to extend the node representations with different sensitive attribute semantics for each node. The extended representations will be used to further train an adapter, to prevent the propagation of sensitive attribute semantics from PGMs to task predictions. Furthermore, with GraphPAR, we quantify whether the fairness of each node is provable, i.e., predictions are always fair within a certain range of sensitive attribute semantics. Experimental evaluations on real-world datasets demonstrate that GraphPAR achieves state-of-the-art prediction performance and fairness on node classification task. Furthermore, based on our GraphPAR, around 90\% nodes have provable fairness.
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables (which are usually termed models) to express uncertainty about which variables are strongly linked to the response. This can be used to provide Bayesian model averaged predictions or inference, and to understand the relative importance of different variables. However, there has been little work on meaningful representations of this uncertainty beyond first order summaries. We introduce Cartesian credible sets to address this gap. The elements of these sets are formed by concatenating sub-models defined on each block of a partition of the variables. Investigating these sub-models allow us to understand whether the models in the Cartesian credible set always/never/sometimes include a particular variable or group of variables and provide a useful summary of model uncertainty. We introduce methods to find these sets that emphasize ease of understanding. The potential of the method is illustrated on regression problems with both small and large numbers of variables.
We develop a Markovian framework for load balancing that combines classical algorithms such as Power-of-$d$ with auto-scaling mechanisms that allow the net service capacity to scale up or down in response to the current load on the same timescale as job dynamics. Our framework is inspired by serverless platforms, such as Knative, where servers are software functions that can be flexibly instantiated in milliseconds according to scaling rules defined by the users of the serverless platform. The main question is how to design such scaling rules to minimize user-perceived delay performance while ensuring low energy consumption. For the first time, we investigate this problem when the auto-scaling and load balancing processes operate asynchronously (or proactively), as in Knative. In contrast to the synchronous (or reactive) paradigm, asynchronism brings the advantage that jobs do not necessarily need to wait any time a scale-up decision is taken. In our main result, we find a general condition on the structure of scaling rules able to drive mean-field dynamics to delay and relative energy optimality, i.e., a situation where both the user-perceived delay and the relative energy waste induced by idle servers vanish in the limit where the network demand grows to infinity in proportion to the nominal service capacity. The identified condition suggests to scale up the current net capacity if and only if the mean demand exceeds the rate at which servers become idle and active. Finally, we propose a family of scaling rules that satisfy our optimality condition. Numerical simulations demonstrate that these rules provide better delay performance than existing synchronous auto-scaling schemes while inducing almost the same power consumption.
In semantic segmentation, training data down-sampling is commonly performed due to limited resources, the need to adapt image size to the model input, or improve data augmentation. This down-sampling typically employs different strategies for the image data and the annotated labels. Such discrepancy leads to mismatches between the down-sampled color and label images. Hence, the training performance significantly decreases as the down-sampling factor increases. In this paper, we bring together the down-sampling strategies for the image data and the training labels. To that aim, we propose a novel framework for label down-sampling via soft-labeling that better conserves label information after down-sampling. Therefore, fully aligning soft-labels with image data to keep the distribution of the sampled pixels. This proposal also produces reliable annotations for under-represented semantic classes. Altogether, it allows training competitive models at lower resolutions. Experiments show that the proposal outperforms other down-sampling strategies. Moreover, state-of-the-art performance is achieved for reference benchmarks, but employing significantly less computational resources than foremost approaches. This proposal enables competitive research for semantic segmentation under resource constraints.
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using these methods, and to compare/relate them with other measures based on the decision tree. We explore the value of these lower bounds on quantum query complexity and their relation with other decision tree based complexity measures for the class of symmetric functions, arguably one of the most natural and basic sets of Boolean functions. We show an explicit construction for the dual of the positive adversary method and also of the square root of private coin certificate game complexity for any total symmetric function. This shows that the two values can't be distinguished for any symmetric function. Additionally, we show that the recently introduced measure of spectral sensitivity gives the same value as both positive adversary and approximate degree for every total symmetric Boolean function. Further, we look at the quantum query complexity of Gap Majority, a partial symmetric function. It has gained importance recently in regard to understanding the composition of randomized query complexity. We characterize the quantum query complexity of Gap Majority and show a lower bound on noisy randomized query complexity (Ben-David and Blais, FOCS 2020) in terms of quantum query complexity. Finally, we study how large certificate complexity and block sensitivity can be as compared to sensitivity for symmetric functions (even up to constant factors). We show tight separations, i.e., give upper bounds on possible separations and construct functions achieving the same.
With increasing data requirements of users, cellular operators are finding new ways to fulfil these requirements. These attempts involve the practice of deploying Wi-Fi access points nearer to the user and backhauling it to the nearest eNB (in case of LTE and LTE-A). The paper studies LTE-U, an extension of LTE which works in the unlicensed spectrum, as a potential solution to this problem. It is based on the idea of densification. Network deployments incorporating LTE-U will be able to better cater to the growing data rate demand of voice and video, thus reducing the load on eNB. Further we explore the possibility of LTE-U as an alternative to Wi-Fi or co-existing with Wi-Fi deployments and issues revolving around this idea. We show that LTE-U deployment solves the problem of capacity in both cases.
The presence of faulty or underactuated manipulators can disrupt the end-effector formation keeping of a team of manipulators. Based on two-link planar manipulators, we investigate this end-effector formation keeping problem for mixed fully- and under-actuated manipulators with flexible joints. In this case, the underactuated manipulators can comprise of active-passive (AP) manipulators, passive-active (PA) manipulators, or a combination thereof. We propose distributed control laws for the different types of manipulators to achieve and maintain the desired formation shape of the end-effectors. It is achieved by assigning virtual springs to the end-effectors for the fully-actuated ones and to the virtual end-effectors for the under-actuated ones. We study further the set of all desired and reachable shapes for the networked manipulators' end-effectors. Finally, we validate our analysis via numerical simulations.
This paper presents a general framework to integrate prior knowledge in the form of logic constraints among a set of task functions into kernel machines. The logic propositions provide a partial representation of the environment, in which the learner operates, that is exploited by the learning algorithm together with the information available in the supervised examples. In particular, we consider a multi-task learning scheme, where multiple unary predicates on the feature space are to be learned by kernel machines and a higher level abstract representation consists of logic clauses on these predicates, known to hold for any input. A general approach is presented to convert the logic clauses into a continuous implementation, that processes the outputs computed by the kernel-based predicates. The learning task is formulated as a primal optimization problem of a loss function that combines a term measuring the fitting of the supervised examples, a regularization term, and a penalty term that enforces the constraints on both supervised and unsupervised examples. The proposed semi-supervised learning framework is particularly suited for learning in high dimensionality feature spaces, where the supervised training examples tend to be sparse and generalization difficult. Unlike for standard kernel machines, the cost function to optimize is not generally guaranteed to be convex. However, the experimental results show that it is still possible to find good solutions using a two stage learning schema, in which first the supervised examples are learned until convergence and then the logic constraints are forced. Some promising experimental results on artificial multi-task learning tasks are reported, showing how the classification accuracy can be effectively improved by exploiting the a priori rules and the unsupervised examples.
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