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What distinguishes robust models from non-robust ones? While for ImageNet distribution shifts it has been shown that such differences in robustness can be traced back predominantly to differences in training data, so far it is not known what that translates to in terms of what the model has learned. In this work, we bridge this gap by probing the representation spaces of 16 robust zero-shot CLIP vision encoders with various backbones (ResNets and ViTs) and pretraining sets (OpenAI, LAION-400M, LAION-2B, YFCC15M, CC12M and {DataComp}), and comparing them to the representation spaces of less robust models with identical backbones, but different (pre)training sets or objectives (CLIP pretraining on ImageNet-Captions, and supervised training or finetuning on ImageNet).Through this analysis, we generate three novel insights. Firstly, we detect the presence of outlier features in robust zero-shot CLIP vision encoders, which to the best of our knowledge is the first time these are observed in non-language and non-transformer models. Secondly, we find the existence of outlier features to be an indication of ImageNet shift robustness in models, since we only find them in robust models in our analysis. Lastly, we also investigate the number of unique encoded concepts in the representation space and find zero-shot CLIP models to encode a higher number of unique concepts in their representation space. However, we do not find this to be an indicator of ImageNet shift robustness and hypothesize that it is rather related to the language supervision. Since the presence of outlier features can be detected without access to any data from shifted datasets, we believe that they could be a useful tool for practitioners to get a feeling for the distribution shift robustness of a pretrained model during deployment.

Robustness is a fundamental aspect for developing safe and trustworthy models, particularly when they are deployed in the open world. In this work we analyze the inherent capability of one-stage object detectors to robustly operate in the presence of out-of-distribution (OoD) data. Specifically, we propose a novel detection algorithm for detecting unknown objects in image data, which leverages the features extracted by the model from each sample. Differently from other recent approaches in the literature, our proposal does not require retraining the object detector, thereby allowing for the use of pretrained models. Our proposed OoD detector exploits the application of supervised dimensionality reduction techniques to mitigate the effects of the curse of dimensionality on the features extracted by the model. Furthermore, it utilizes high-resolution feature maps to identify potential unknown objects in an unsupervised fashion. Our experiments analyze the Pareto trade-off between the performance detecting known and unknown objects resulting from different algorithmic configurations and inference confidence thresholds. We also compare the performance of our proposed algorithm to that of logits-based post-hoc OoD methods, as well as possible fusion strategies. Finally, we discuss on the competitiveness of all tested methods against state-of-the-art OoD approaches for object detection models over the recently published Unknown Object Detection benchmark. The obtained results verify that the performance of avant-garde post-hoc OoD detectors can be further improved when combined with our proposed algorithm.

We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the problem arising in demography of estimating the covariance matrix of the total fertility rate (TFR) of 195 different countries when only 11 observations are available. We construct an estimator for high-dimensional covariance matrices by exploiting information about pairwise covariates, such as whether pairs of variables belong to the same cluster, or spatial structure of the variables, and interactions between the covariates. We reformulate the problem in terms of a mixed effects model. This requires the estimation of only a small number of parameters, which are easy to interpret and which can be selected using standard procedures. The estimator is consistent under general conditions, and asymptotically normal. It works if the mean and variance structure of the data is already specified or if some of the data are missing. We assess its performance under our model assumptions, as well as under model misspecification, using simulations. We find that it outperforms several popular alternatives. We apply it to the TFR dataset and draw some conclusions.

We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game theory, we specifically focus on two key concepts: resilient Nash equilibrium, and multi-leader-follower games -- domains traditionally known for the absence of general solutions. In the presence of standard assumptions and relaxation techniques, we formulate problem versions for such games that are expressible in terms of variational inequalities, ultimately leading to proofs of PPAD-completeness.

In-memory computing (IMC) has been shown to be a promising approach for solving binary optimization problems while significantly reducing energy and latency. Building on the advantages of parallel computation, we propose an IMC-compatible parallelism framework inspired by parallel tempering (PT), enabling cross-replica communication to improve the performance of IMC solvers. This framework enables an IMC solver not only to improve performance beyond what can be achieved through parallelization, but also affords greater flexibility for the search process with low hardware overhead. We justify that the framework can be applied to almost any IMC solver. We demonstrate the effectiveness of the framework for the Boolean satisfiability (SAT) problem, using the WalkSAT heuristic as a proxy for existing IMC solvers. The resulting PT-inspired cooperative WalkSAT (PTIC-WalkSAT) algorithm outperforms the traditional WalkSAT heuristic in terms of the iterations-to-solution in 76.3% of the tested problem instances and its na\"ive parallel variant (PA-WalkSAT) does so in 68.4% of the instances. An estimate of the energy overhead of the PTIC framework for two hardware accelerator architectures indicates that in both cases the overhead of running the PTIC framework would be less than 1% of the total energy required to run each accelerator.

Approximating the action of a matrix function $f(\mathbf{A})$ on a vector $\mathbf{b}$ is an increasingly important primitive in machine learning, data science, and statistics, with applications such as sampling high dimensional Gaussians, Gaussian process regression and Bayesian inference, principle component analysis, and approximating Hessian spectral densities. Over the past decade, a number of algorithms enjoying strong theoretical guarantees have been proposed for this task. Many of the most successful belong to a family of algorithms called Krylov subspace methods. Remarkably, a classic Krylov subspace method, called the Lanczos method for matrix functions (Lanczos-FA), frequently outperforms newer methods in practice. Our main result is a theoretical justification for this finding: we show that, for a natural class of rational functions, Lanczos-FA matches the error of the best possible Krylov subspace method up to a multiplicative approximation factor. The approximation factor depends on the degree of $f(x)$'s denominator and the condition number of $\mathbf{A}$, but not on the number of iterations $k$. Our result provides a strong justification for the excellent performance of Lanczos-FA, especially on functions that are well approximated by rationals, such as the matrix square root.

All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that determines how incorrect outputs are penalized and can be tuned to improve performance. This paper shows that training speed and final accuracy of neural networks can significantly depend on the loss function used to train neural networks. In particular derivative values can be significantly different with different loss functions leading to significantly different performance after gradient descent based Backpropagation (BP) training. This paper explores the effect on performance of using new loss functions that are also convex but penalize errors differently compared to the popular Cross-entropy loss. Two new classification loss functions that significantly improve performance on a wide variety of benchmark tasks are proposed. A new loss function call smooth absolute error that outperforms the Squared error, Huber and Log-Cosh losses on datasets with significantly many outliers is proposed. This smooth absolute error loss function is infinitely differentiable and more closely approximates the absolute error loss compared to the Huber and Log-Cosh losses used for robust regression.

We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity information among observations. This graph-based statistic is applicable to datasets of any dimension, is computationally efficient to obtain, and can be paired with any kind of clustering technique. Asymptotic theory is developed to establish the selection consistency of the proposed approach. Simulation studies demonstrate that the graph-based statistic outperforms existing methods for estimating k, especially in the high-dimensional setting. We illustrate its utility on an imaging dataset and an RNA-seq dataset.

Quantum no-cloning theorem gives rise to the intriguing possibility of quantum copy protection where we encode a program or functionality in a quantum state such that a user in possession of k copies cannot create k+1 copies, for any k. Introduced by Aaronson (CCC'09) over a decade ago, copy protection has proven to be notoriously hard to achieve. Previous work has been able to achieve copy-protection for various functionalities only in restricted models: (i) in the bounded collusion setting where k -> k+1 security is achieved for a-priori fixed collusion bound k (in the plain model with the same computational assumptions as ours, by Liu, Liu, Qian, Zhandry [TCC'22]), or, (ii) only k -> 2k security is achieved (relative to a structured quantum oracle, by Aaronson [CCC'09]). In this work, we give the first unbounded collusion-resistant (i.e. multiple-copy secure) copy-protection schemes, answering the long-standing open question of constructing such schemes, raised by multiple previous works starting with Aaronson (CCC'09). More specifically, we obtain the following results. - We construct (i) public-key encryption, (ii) public-key functional encryption, (iii) signature and (iv) pseudorandom function schemes whose keys are copy-protected against unbounded collusions in the plain model (i.e. without any idealized oracles), assuming (post-quantum) subexponentially secure iO and LWE. - We show that any unlearnable functionality can be copy-protected against unbounded collusions, relative to a classical oracle. - As a corollary of our results, we rule out the existence of hyperefficient quantum shadow tomography, * even given non-black-box access to the measurements, assuming subexponentially secure iO and LWE, or, * unconditionally relative to a quantumly accessible classical oracle, and hence answer an open question by Aaronson (STOC'18).

We construct a polynomial-time classical algorithm that samples from the output distribution of low-depth noisy Clifford circuits with any product-state inputs and final single-qubit measurements in any basis. This class of circuits includes Clifford-magic circuits and Conjugated-Clifford circuits, which are important candidates for demonstrating quantum advantage using non-universal gates. Additionally, our results generalize a simulation algorithm for IQP circuits [Rajakumar et. al, SODA'25] to the case of IQP circuits augmented with CNOT gates, which is another class of non-universal circuits that are relevant to current experiments. Importantly, our results do not require randomness assumptions over the circuit families considered (such as anticoncentration properties) and instead hold for \textit{every} circuit in each class. This allows us to place tight limitations on the robustness of these circuits to noise. In particular, we show that there is no quantum advantage at large depths with realistically noisy Clifford circuits, even with perfect magic state inputs, or IQP circuits with CNOT gates, even with arbitrary diagonal non-Clifford gates. The key insight behind the algorithm is that interspersed noise causes a decay of long-range entanglement, and at depths beyond a critical threshold, the noise builds up to an extent that most correlations can be classically simulated. To prove our results, we merge techniques from percolation theory with tools from Pauli path analysis.