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Large Language Models (LLMs) have demonstrated remarkable in-context learning (ICL) capabilities. In this study, we explore a surprising phenomenon related to ICL: LLMs can perform multiple, computationally distinct ICL tasks simultaneously, during a single inference call, a capability we term "task superposition". We provide empirical evidence of this phenomenon across various LLM families and scales and show that this phenomenon emerges even if we train the model to in-context learn one task at a time. We offer theoretical explanations that this capability is well within the expressive power of transformers. We also explore how LLMs internally compose task vectors during superposition. Furthermore, we show that larger models can solve more ICL tasks in parallel, and better calibrate their output distribution. Our findings offer insights into the latent capabilities of LLMs, further substantiate the perspective of "LLMs as superposition of simulators", and raise questions about the mechanisms enabling simultaneous task execution.

Random Feature Model (RFM) with a nonlinear activation function is instrumental in understanding training and generalization performance in high-dimensional learning. While existing research has established an asymptotic equivalence in performance between the RFM and noisy linear models under isotropic data assumptions, empirical observations indicate that the RFM frequently surpasses linear models in practical applications. To address this gap, we ask, "When and how does the RFM outperform linear models?" In practice, inputs often have additional structures that significantly influence learning. Therefore, we explore the RFM under anisotropic input data characterized by spiked covariance in the proportional asymptotic limit, where dimensions diverge jointly while maintaining finite ratios. Our analysis reveals that a high correlation between inputs and labels is a critical factor enabling the RFM to outperform linear models. Moreover, we show that the RFM performs equivalent to noisy polynomial models, where the polynomial degree depends on the strength of the correlation between inputs and labels. Our numerical simulations validate these theoretical insights, confirming the performance-wise superiority of RFM in scenarios characterized by strong input-label correlation., Comment: 29 pages, 5 figures

Annotating lidar point clouds for autonomous driving is a notoriously expensive and time-consuming task. In this work, we show that the quality of recent self-supervised lidar scan representations allows a great reduction of the annotation cost. Our method has two main steps. First, we show that self-supervised representations allow a simple and direct selection of highly informative lidar scans to annotate: training a network on these selected scans leads to much better results than a random selection of scans and, more interestingly, to results on par with selections made by SOTA active learning methods. In a second step, we leverage the same self-supervised representations to cluster points in our selected scans. Asking the annotator to classify each cluster, with a single click per cluster, then permits us to close the gap with fully-annotated training sets, while only requiring one thousandth of the point labels.

We introduce a novel approach for 3D whole-body pose estimation, addressing the challenge of scale- and deformability- variance across body parts brought by the challenge of extending the 17 major joints on the human body to fine-grained keypoints on the face and hands. In addition to addressing the challenge of exploiting motion in unevenly sampled data, we combine stable diffusion to a hierarchical part representation which predicts the relative locations of fine-grained keypoints within each part (e.g., face) with respect to the part's local reference frame. On the H3WB dataset, our method greatly outperforms the current state of the art, which fails to exploit the temporal information. We also show considerable improvements compared to other spatiotemporal 3D human-pose estimation approaches that fail to account for the body part specificities. Code is available at https://github.com/valeoai/PAFUSE.

Recent research has shown that Transformers with linear attention are capable of in-context learning (ICL) by implementing a linear estimator through gradient descent steps. However, the existing results on the optimization landscape apply under stylized settings where task and feature vectors are assumed to be IID and the attention weights are fully parameterized. In this work, we develop a stronger characterization of the optimization and generalization landscape of ICL through contributions on architectures, low-rank parameterization, and correlated designs: (1) We study the landscape of 1-layer linear attention and 1-layer H3, a state-space model. Under a suitable correlated design assumption, we prove that both implement 1-step preconditioned gradient descent. We show that thanks to its native convolution filters, H3 also has the advantage of implementing sample weighting and outperforming linear attention in suitable settings. (2) By studying correlated designs, we provide new risk bounds for retrieval augmented generation (RAG) and task-feature alignment which reveal how ICL sample complexity benefits from distributional alignment. (3) We derive the optimal risk for low-rank parameterized attention weights in terms of covariance spectrum. Through this, we also shed light on how LoRA can adapt to a new distribution by capturing the shift between task covariances. Experimental results corroborate our theoretical findings. Overall, this work explores the optimization and risk landscape of ICL in practically meaningful settings and contributes to a more thorough understanding of its mechanics.

The transformer architecture has catalyzed revolutionary advances in language modeling. However, recent architectural recipes, such as state-space models, have bridged the performance gap. Motivated by this, we examine the benefits of Convolution-Augmented Transformer (CAT) for recall, copying, and length generalization tasks. CAT incorporates convolutional filters in the K/Q/V embeddings of an attention layer. Through CAT, we show that the locality of the convolution synergizes with the global view of the attention. Unlike comparable architectures, such as Mamba or transformer, CAT can provably solve the associative recall (AR) and copying tasks using a single layer while also enjoying guaranteed length generalization. We also establish computational tradeoffs between convolution and attention by characterizing how convolution can mitigate the need for full attention by summarizing the context window and creating salient summary tokens to attend. Evaluations on real datasets corroborate our findings and demonstrate that CAT and its variations indeed enhance the language modeling performance.

We study a natural birational invariant for varieties over finite fields and show that its vanishing on projective space is equivalent to the Tate conjecture, the Beilinson conjecture, and the Grothendieck--Serre semi-simplicity conjecture for all smooth projective varieties over finite fields. We further show that the Tate, Beilinson, and 1-semi-simplicity conjecture in half of the degrees implies those conjectures in all degrees., Comment: 33 pages

Motion forecasting is crucial in autonomous driving systems to anticipate the future trajectories of surrounding agents such as pedestrians, vehicles, and traffic signals. In end-to-end forecasting, the model must jointly detect and track from sensor data (cameras or LiDARs) the past trajectories of the different elements of the scene and predict their future locations. We depart from the current trend of tackling this task via end-to-end training from perception to forecasting, and instead use a modular approach. We individually build and train detection, tracking and forecasting modules. We then only use consecutive finetuning steps to integrate the modules better and alleviate compounding errors. We conduct an in-depth study on the finetuning strategies and it reveals that our simple yet effective approach significantly improves performance on the end-to-end forecasting benchmark. Consequently, our solution ranks first in the Argoverse 2 End-to-end Forecasting Challenge, with 63.82 mAPf. We surpass forecasting results by +17.1 points over last year's winner and by +13.3 points over this year's runner-up. This remarkable performance in forecasting can be explained by our modular paradigm, which integrates finetuning strategies and significantly outperforms the end-to-end-trained counterparts. The code, model weights and results are made available https://github.com/valeoai/valeo4cast., Comment: Winning solution of the Argoverse 2 "Unified Detection, Tracking, and Forecasting" challenge; work accepted at Road++ ECCVW 2024

We introduce two new classes of single-valued contractions of polynomial type defined on a metric space. For the first one, called the class of polynomial contractions, we establish two fixed point theorems. Namely, we first consider the case when the mapping is continuous. Next, we weaken the continuity condition. In particular, we recover Banach's fixed point theorem. The second class, called the class of almost polynomial contractions, includes the class of almost contractions introduced by Berinde [Nonlinear Analysis Forum. 9(1) (2004) 43--53]. A fixed point theorem is established for almost polynomial contractions. The obtained result generalizes that derived by Berinde in the above reference. Several examples showing that our generalizations are significant, are provided.

Transformers have revolutionized deep learning across various tasks, including audio representation learning, due to their powerful modeling capabilities. However, they often suffer from quadratic complexity in both GPU memory usage and computational inference time, affecting their efficiency. Recently, state space models (SSMs) like Mamba have emerged as a promising alternative, offering a more efficient approach by avoiding these complexities. Given these advantages, we explore the potential of SSM-based models in audio tasks. In this paper, we introduce Self-Supervised Audio Mamba (SSAMBA), the first self-supervised, attention-free, and SSM-based model for audio representation learning. SSAMBA leverages the bidirectional Mamba to capture complex audio patterns effectively. We incorporate a self-supervised pretraining framework that optimizes both discriminative and generative objectives, enabling the model to learn robust audio representations from large-scale, unlabeled datasets. We evaluated SSAMBA on various tasks such as audio classification, keyword spotting, and speaker identification. Our results demonstrate that SSAMBA outperforms the Self-Supervised Audio Spectrogram Transformer (SSAST) in most tasks. Notably, SSAMBA is approximately 92.7% faster in batch inference speed and 95.4% more memory-efficient than SSAST for the tiny model size with an input token size of 22k. These efficiency gains, combined with superior performance, underscore the effectiveness of SSAMBA's architectural innovation, making it a compelling choice for a wide range of audio processing applications., Comment: Code at https://github.com/SiavashShams/ssamba

We are concerned with the study of fixed points for mappings $T: X\to X$, where $(X,G)$ is a $G$-metric space in the sense of Mustafa and Sims. After the publication of the paper [Journal of Nonlinear and Convex Analysis. 7(2) (2006) 289--297] by Mustafa and Sims, a great interest was devoted to the study of fixed points in $G$-metric spaces. In 2012, the first and third authors observed that several fixed point theorems established in $G$-metric spaces are immediate consequences of known fixed point theorems in standard metric spaces. This observation demotivated the investigation of fixed points in $G$-metric spaces. In this paper, we open new directions in fixed point theory in $G$-metric spaces. Namely, we establish new versions of the Banach, Kannan and Reich fixed point theorems in $G$-metric spaces. We point out that the approach used by the first and third authors [Fixed Point Theory Appl. 2012 (2012) 1--7] is inapplicable in the present study. We also provide some interesting applications related to mappings contracting perimeters of triangles.

This paper introduces a generalized mean-based C^1-smooth robustness measure over discrete-time signals (D-GMSR) for signal temporal logic (STL) specifications. In conjunction with its C1-smoothness, D-GMSR is proven to be both sound and complete. Furthermore, it demonstrates favorable gradient properties and addresses locality and masking problems, which are critical for numerical optimization. The C^1-smoothness of the proposed formulations enables the implementation of robust and efficient numerical optimization algorithms to solve problems with STL specifications while preserving their theoretical guarantees. The practical utility of the proposed robustness measure is demonstrated on two real-world trajectory optimization problems: i) quadrotor flight, and ii) autonomous rocket landing. A sequential convex programming (SCP) framework, incorporating a convergence-guaranteed optimization algorithm (the prox-linear method) is used to solve inherently non-convex trajectory optimization problems with STL specifications. The implementation is available at https://github.com/UW-ACL/D-GMSR

We propose a nonlinear model predictive control (NMPC) framework based on a direct optimal control method that ensures continuous-time constraint satisfaction and accurate evaluation of the running cost, without compromising computational efficiency. We leverage the recently proposed successive convexification framework for trajectory optimization, where: (1) the path constraints and running cost are equivalently reformulated by augmenting the system dynamics, (2) multiple shooting is used for exact discretization, and (3) a convergence-guaranteed sequential convex programming (SCP) algorithm, the prox-linear method, is used to solve the discretized receding-horizon optimal control problems. The resulting NMPC framework is computationally efficient, owing to its support for warm-starting and premature termination of SCP, and its reliance on first-order information only. We demonstrate the effectiveness of the proposed NMPC framework by means of a numerical example with reference-tracking and obstacle avoidance. The implementation is available at https://github.com/UW-ACL/nmpc-ctcs

We present successive convexification, a real-time-capable solution method for nonconvex trajectory optimization, with continuous-time constraint satisfaction and guaranteed convergence, that only requires first-order information. The proposed framework combines several key methods to solve a large class of nonlinear optimal control problems: (i) exterior penalty-based reformulation of the path constraints; (ii) generalized time-dilation; (iii) multiple-shooting discretization; (iv) $\ell_1$ exact penalization of the nonconvex constraints; and (v) the prox-linear method, a sequential convex programming (SCP) algorithm for convex-composite minimization. The reformulation of the path constraints enables continuous-time constraint satisfaction even on sparse discretization grids and obviates the need for mesh refinement heuristics. Through the prox-linear method, we guarantee convergence of the solution method to stationary points of the penalized problem and guarantee that the converged solutions that are feasible with respect to the discretized and control-parameterized optimal control problem are also Karush-Kuhn-Tucker (KKT) points. Furthermore, we highlight the specialization of this property to global minimizers of convex optimal control problems, wherein the reformulated path constraints cannot be represented by canonical cones, i.e., in the form required by existing convex optimization solvers. In addition to theoretical analysis, we demonstrate the effectiveness and real-time capability of the proposed framework with numerical examples based on popular optimal control applications: dynamic obstacle avoidance and rocket landing.

Recent successes in natural language processing have led to the proliferation of large language models (LLMs) by multiple providers. Each LLM offering has different inference accuracy, monetary cost, and latency, and their accuracy further depends on the exact wording of the question (i.e., the specific prompt). At the same time, users often have a limit on monetary budget and latency to answer all their questions, and they do not know which LLMs to choose for each question to meet their accuracy and long-term budget requirements. To navigate this rich design space, we propose TREACLE (Thrifty Reasoning via Context-Aware LLM and Prompt Selection), a reinforcement learning policy that jointly selects the model and prompting scheme while respecting the user's monetary cost and latency constraints. TREACLE uses the problem context, including question text embeddings (reflecting the type or difficulty of a query) and the response history (reflecting the consistency of previous responses) to make smart decisions. Our evaluations on standard reasoning datasets (GSM8K, CSQA, and LLC ) with various LLMs and prompts show that TREACLE enables cost savings of up to 85% compared to baselines while maintaining high accuracy. Importantly, it provides the user with the ability to gracefully trade off accuracy for cost.

In this study, we report a discovery from XMM-Newton, which involves the identification and subsequent examination of a newly discovered polar-type cataclysmic variable named XMM J152737.4-205305.9. The discovery was made by matching the XMM-Newton data archive with the cataclysmic variable candidate catalog provided by Gaia Data Release 3. The utilization of X-ray photometry has led to the identification of two distinct dips that exhibit a recurring pattern with a precise period of 112.4(1) minutes in two XMM-Newton observations that are one year apart. The data obtained from the photometry of Zwicky Transient Facility (ZTF) and ATLAS surveys consistently indicate the presence of the different mass accretion states of up to 2 mag. Following the optical data, the \textit{SRG}(Spectrum Roentgen Gamma)/eROSITA All Sky Survey observed the system in two different X-ray levels which may imply different accretion states. Following these observations, the low-resolution spectrum obtained using SALT spectroscopy exposes the prominent hydrogen Balmer and helium emission lines, strongly supporting that the system belongs to the category of polar-type magnetic cataclysmic variable. The XMM-Newton observations, conducted under various conditions of X-ray levels, reveal a consistent pattern of a deep dip-like feature with a width of $\approx 9.1$ min. This feature implies the presence of an eclipse in both observations. According to Gaia data, the object is located at a distance of $1156^{+720}_{-339}$,pc, and its X-ray luminosity lies within the $L_{\rm X}$= (3-6)$\times10^{31}$ \lergs range., Comment: 11 pages, 13 figures, 21 March 2024, accepted to Astronomy & Astrophysics

Transformer-based language models are trained on large datasets to predict the next token given an input sequence. Despite this simple training objective, they have led to revolutionary advances in natural language processing. Underlying this success is the self-attention mechanism. In this work, we ask: $\textit{What}$ $\textit{does}$ $\textit{a}$ $\textit{single}$ $\textit{self-attention}$ $\textit{layer}$ $\textit{learn}$ $\textit{from}$ $\textit{next-token}$ $\textit{prediction?}$ We show that training self-attention with gradient descent learns an automaton which generates the next token in two distinct steps: $\textbf{(1)}$ $\textbf{Hard}$ $\textbf{retrieval:}$ Given input sequence, self-attention precisely selects the $\textit{high-priority}$ $\textit{input}$ $\textit{tokens}$ associated with the last input token. $\textbf{(2)}$ $\textbf{Soft}$ $\textbf{composition:}$ It then creates a convex combination of the high-priority tokens from which the next token can be sampled. Under suitable conditions, we rigorously characterize these mechanics through a directed graph over tokens extracted from the training data. We prove that gradient descent implicitly discovers the strongly-connected components (SCC) of this graph and self-attention learns to retrieve the tokens that belong to the highest-priority SCC available in the context window. Our theory relies on decomposing the model weights into a directional component and a finite component that correspond to hard retrieval and soft composition steps respectively. This also formalizes a related implicit bias formula conjectured in [Tarzanagh et al. 2023]. We hope that these findings shed light on how self-attention processes sequential data and pave the path toward demystifying more complex architectures., Comment: Accepted to AISTATS 2024

Industrial anomaly detection is an important task within computer vision with a wide range of practical use cases. The small size of anomalous regions in many real-world datasets necessitates processing the images at a high resolution. This frequently poses significant challenges concerning memory consumption during the model training and inference stages, leaving some existing methods impractical for widespread adoption. To overcome this challenge, we present the tiled ensemble approach, which reduces memory consumption by dividing the input images into a grid of tiles and training a dedicated model for each tile location. The tiled ensemble is compatible with any existing anomaly detection model without the need for any modification of the underlying architecture. By introducing overlapping tiles, we utilize the benefits of traditional stacking ensembles, leading to further improvements in anomaly detection capabilities beyond high resolution alone. We perform a comprehensive analysis using diverse underlying architectures, including Padim, PatchCore, FastFlow, and Reverse Distillation, on two standard anomaly detection datasets: MVTec and VisA. Our method demonstrates a notable improvement across setups while remaining within GPU memory constraints, consuming only as much GPU memory as a single model needs to process a single tile., Comment: To appear at CVPR 24 Visual Anomaly Detection Workshop. Research conducted during Google Summer of Code 2023 at OpenVINO (Intel). GSoC 2023 page: https://summerofcode.withgoogle.com/archive/2023/projects/WUSjdxGl

Efficiently pricing multi-asset options poses a significant challenge in quantitative finance. The Monte Carlo (MC) method remains the prevalent choice for pricing engines; however, its slow convergence rate impedes its practical application. Fourier methods leverage the knowledge of the characteristic function to accurately and rapidly value options with up to two assets. Nevertheless, they face hurdles in the high-dimensional settings due to the tensor product (TP) structure of commonly employed quadrature techniques. This work advocates using the randomized quasi-MC (RQMC) quadrature to improve the scalability of Fourier methods with high dimensions. The RQMC technique benefits from the smoothness of the integrand and alleviates the curse of dimensionality while providing practical error estimates. Nonetheless, the applicability of RQMC on the unbounded domain, $\mathbb{R}^d$, requires a domain transformation to $[0,1]^d$, which may result in singularities of the transformed integrand at the corners of the hypercube, and deteriorate the rate of convergence of RQMC. To circumvent this difficulty, we design an efficient domain transformation procedure based on the derived boundary growth conditions of the integrand. This transformation preserves the sufficient regularity of the integrand and hence improves the rate of convergence of RQMC. To validate this analysis, we demonstrate the efficiency of employing RQMC with an appropriate transformation to evaluate options in the Fourier space for various pricing models, payoffs, and dimensions. Finally, we highlight the computational advantage of applying RQMC over MC or TP in the Fourier domain, and over MC in the physical domain for options with up to 15 assets.

Modern language models rely on the transformer architecture and attention mechanism to perform language understanding and text generation. In this work, we study learning a 1-layer self-attention model from a set of prompts and associated output data sampled from the model. We first establish a precise mapping between the self-attention mechanism and Markov models: Inputting a prompt to the model samples the output token according to a context-conditioned Markov chain (CCMC) which weights the transition matrix of a base Markov chain. Additionally, incorporating positional encoding results in position-dependent scaling of the transition probabilities. Building on this formalism, we develop identifiability/coverage conditions for the prompt distribution that guarantee consistent estimation and establish sample complexity guarantees under IID samples. Finally, we study the problem of learning from a single output trajectory generated from an initial prompt. We characterize an intriguing winner-takes-all phenomenon where the generative process implemented by self-attention collapses into sampling a limited subset of tokens due to its non-mixing nature. This provides a mathematical explanation to the tendency of modern LLMs to generate repetitive text. In summary, the equivalence to CCMC provides a simple but powerful framework to study self-attention and its properties., Comment: 30 pages

We consider a higher order in (time) semilinear evolution inequality posed on the Kor\'{a}nyi ball under an inhomogeneous Dirichlet-type boundary condition. The problem involves an inverse-square potential $\lambda/|\xi|_\mathbb{H}^2$, where $\lambda \geq -(Q-2)^2/4$ and a general weight function $V$ depending on the space variable in front of the power nonlinearity. We first establish a general nonexistence result for the considered problem. Next, in the special case $V(\xi):=|\xi|_\mathbb{H}^a$, $a\in \mathbb{R}$, we prove the sharpness of our nonexistence result and show that the problem admits three different critical behaviors according to the value of the parameter $\lambda$., Comment: 24 pages

The key premise of federated learning (FL) is to train ML models across a diverse set of data-owners (clients), without exchanging local data. An overarching challenge to this date is client heterogeneity, which may arise not only from variations in data distribution, but also in data quality, as well as compute/communication latency. An integrated view of these diverse and concurrent sources of heterogeneity is critical; for instance, low-latency clients may have poor data quality, and vice versa. In this work, we propose FLASH(Federated Learning Across Simultaneous Heterogeneities), a lightweight and flexible client selection algorithm that outperforms state-of-the-art FL frameworks under extensive sources of heterogeneity, by trading-off the statistical information associated with the client's data quality, data distribution, and latency. FLASH is the first method, to our knowledge, for handling all these heterogeneities in a unified manner. To do so, FLASH models the learning dynamics through contextual multi-armed bandits (CMAB) and dynamically selects the most promising clients. Through extensive experiments, we demonstrate that FLASH achieves substantial and consistent improvements over state-of-the-art baselines -- as much as 10% in absolute accuracy -- thanks to its unified approach. Importantly, FLASH also outperforms federated aggregation methods that are designed to handle highly heterogeneous settings and even enjoys a performance boost when integrated with them.

State-space models (SSMs), such as Mamba (Gu & Dao, 2023), have been proposed as alternatives to Transformer networks in language modeling, by incorporating gating, convolutions, and input-dependent token selection to mitigate the quadratic cost of multi-head attention. Although SSMs exhibit competitive performance, their in-context learning (ICL) capabilities, a remarkable emergent property of modern language models that enables task execution without parameter optimization, remain underexplored compared to Transformers. In this study, we evaluate the ICL performance of SSMs, focusing on Mamba, against Transformer models across various tasks. Our results show that SSMs perform comparably to Transformers in standard regression ICL tasks, while outperforming them in tasks like sparse parity learning. However, SSMs fall short in tasks involving non-standard retrieval functionality. To address these limitations, we introduce a hybrid model, MambaFormer, that combines Mamba with attention blocks, surpassing individual models in tasks where they struggle independently. Our findings suggest that hybrid architectures offer promising avenues for enhancing ICL in language models., Comment: Changes in v2: experiments on formal language ICL and explorations of width vs. depth on ICL; code repo available (24 pages, 10 figures)

In this paper, we explore a new domain for video-to-video translation. Motivated by the availability of animation movies that are adopted from illustrated books for children, we aim to stylize these videos with the style of the original illustrations. Current state-of-the-art video-to-video translation models rely on having a video sequence or a single style image to stylize an input video. We introduce a new problem for video stylizing where an unordered set of images are used. This is a challenging task for two reasons: i) we do not have the advantage of temporal consistency as in video sequences; ii) it is more difficult to obtain consistent styles for video frames from a set of unordered images compared to using a single image. Most of the video-to-video translation methods are built on an image-to-image translation model, and integrate additional networks such as optical flow, or temporal predictors to capture temporal relations. These additional networks make the model training and inference complicated and slow down the process. To ensure temporal coherency in video-to-video style transfer, we propose a new generator network with feature warping layers which overcomes the limitations of the previous methods. We show the effectiveness of our method on three datasets both qualitatively and quantitatively. Code and pretrained models are available at https://github.com/giddyyupp/wait., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Modern classification problems exhibit heterogeneities across individual classes: Each class may have unique attributes, such as sample size, label quality, or predictability (easy vs difficult), and variable importance at test-time. Without care, these heterogeneities impede the learning process, most notably, when optimizing fairness objectives. Confirming this, under a gaussian mixture setting, we show that the optimal SVM classifier for balanced accuracy needs to be adaptive to the class attributes. This motivates us to propose CAP: An effective and general method that generates a class-specific learning strategy (e.g. hyperparameter) based on the attributes of that class. This way, optimization process better adapts to heterogeneities. CAP leads to substantial improvements over the naive approach of assigning separate hyperparameters to each class. We instantiate CAP for loss function design and post-hoc logit adjustment, with emphasis on label-imbalanced problems. We show that CAP is competitive with prior art and its flexibility unlocks clear benefits for fairness objectives beyond balanced accuracy. Finally, we evaluate CAP on problems with label noise as well as weighted test objectives to showcase how CAP can jointly adapt to different heterogeneities., Comment: 15 pages, 8 figures

Parameter-efficient tuning (PET) methods such as LoRA, Adapter, and Visual Prompt Tuning (VPT) have found success in enabling adaptation to new domains by tuning small modules within a transformer model. However, the number of domains encountered during test time can be very large, and the data is usually unlabeled. Thus, adaptation to new domains is challenging; it is also impractical to generate customized tuned modules for each such domain. Toward addressing these challenges, this work introduces PLUTO: a Plug-and-pLay modUlar Test-time domain adaptatiOn strategy. We pre-train a large set of modules, each specialized for different source domains, effectively creating a ``module store''. Given a target domain with few-shot unlabeled data, we introduce an unsupervised test-time adaptation (TTA) method to (1) select a sparse subset of relevant modules from this store and (2) create a weighted combination of selected modules without tuning their weights. This plug-and-play nature enables us to harness multiple most-relevant source domains in a single inference call. Comprehensive evaluations demonstrate that PLUTO uniformly outperforms alternative TTA methods and that selecting $\leq$5 modules suffice to extract most of the benefit. At a high level, our method equips pre-trained transformers with the capability to dynamically adapt to new domains, motivating a new paradigm for efficient and scalable domain adaptation.

Test time adaptation is the process of adapting, in an unsupervised manner, a pre-trained source model to each incoming batch of the test data (i.e., without requiring a substantial portion of the test data to be available, as in traditional domain adaptation) and without access to the source data. Since it works with each batch of test data, it is well-suited for dynamic environments where decisions need to be made as the data is streaming in. Current test time adaptation methods are primarily focused on a single source model. We propose the first completely unsupervised Multi-source Test Time Adaptation (MeTA) framework that handles multiple source models and optimally combines them to adapt to the test data. MeTA has two distinguishing features. First, it efficiently obtains the optimal combination weights to combine the source models to adapt to the test data distribution. Second, it identifies which of the source model parameters to update so that only the model which is most correlated to the target data is adapted, leaving the less correlated ones untouched; this mitigates the issue of "forgetting" the source model parameters by focusing only on the source model that exhibits the strongest correlation with the test batch distribution. Experiments on diverse datasets demonstrate that the combination of multiple source models does at least as well as the best source (with hindsight knowledge), and performance does not degrade as the test data distribution changes over time (robust to forgetting)., Comment: Under Review

Recent advances in visual anomaly detection research have seen AUROC and AUPRO scores on public benchmark datasets such as MVTec and VisA converge towards perfect recall, giving the impression that these benchmarks are near-solved. However, high AUROC and AUPRO scores do not always reflect qualitative performance, which limits the validity of these metrics in real-world applications. We argue that the artificial ceiling imposed by the lack of an adequate evaluation metric restrains progression of the field, and it is crucial that we revisit the evaluation metrics used to rate our algorithms. In response, we introduce Per-IMage Overlap (PIMO), a novel metric that addresses the shortcomings of AUROC and AUPRO. PIMO retains the recall-based nature of the existing metrics but introduces two distinctions: the assignment of curves (and respective area under the curve) is per-image, and its X-axis relies solely on normal images. Measuring recall per image simplifies instance score indexing and is more robust to noisy annotations. As we show, it also accelerates computation and enables the usage of statistical tests to compare models. By imposing low tolerance for false positives on normal images, PIMO provides an enhanced model validation procedure and highlights performance variations across datasets. Our experiments demonstrate that PIMO offers practical advantages and nuanced performance insights that redefine anomaly detection benchmarks -- notably challenging the perception that MVTec AD and VisA datasets have been solved by contemporary models. Available on GitHub: https://github.com/jpcbertoldo/aupimo., Comment: Accepted to BMVC 2024. Official implementation https://github.com/jpcbertoldo/aupimo and integrated in anomalib https://github.com/openvinotoolkit/anomalib This research has been conducted during Google Summer of Code 2023 (GSoC 2023) at OpenVINO (Intel)

In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterparts. This paper delves into the heart of this phenomenon, comparing neural ordinary differential equations (ODEs) and neural stochastic differential equations (SDEs) as reverse processes. We use a control theoretic perspective by posing the approximation of the reverse process as a trajectory tracking problem. We analyze the ability of neural SDEs to approximate trajectories of the Fokker-Planck equation, revealing the advantages of stochasticity. First, neural SDEs exhibit a powerful regularizing effect, enabling $L^2$ norm trajectory approximation surpassing the Wasserstein metric approximation achieved by neural ODEs under similar conditions, even when the reference vector field or score function is not Lipschitz. Applying this result, we establish the class of distributions that can be sampled using score matching in SGMs, relaxing the Lipschitz requirement on the gradient of the data distribution in existing literature. Second, we show that this approximation property is preserved when network width is limited to the input dimension of the network. In this limited width case, the weights act as control inputs, framing our analysis as a controllability problem for neural SDEs in probability density space. This sheds light on how noise helps to steer the system towards the desired solution and illuminates the empirical success of stochasticity in generative modeling., Comment: Extended preprint for submission to Learning for Dynamics & Control Conference

Monocular 3D human pose estimation (3D-HPE) is an inherently ambiguous task, as a 2D pose in an image might originate from different possible 3D poses. Yet, most 3D-HPE methods rely on regression models, which assume a one-to-one mapping between inputs and outputs. In this work, we provide theoretical and empirical evidence that, because of this ambiguity, common regression models are bound to predict topologically inconsistent poses, and that traditional evaluation metrics, such as the MPJPE, P-MPJPE and PCK, are insufficient to assess this aspect. As a solution, we propose ManiPose, a novel manifold-constrained multi-hypothesis model capable of proposing multiple candidate 3D poses for each 2D input, together with their corresponding plausibility. Unlike previous multi-hypothesis approaches, our solution is completely supervised and does not rely on complex generative models, thus greatly facilitating its training and usage. Furthermore, by constraining our model to lie within the human pose manifold, we can guarantee the consistency of all hypothetical poses predicted with our approach, which was not possible in previous works. We illustrate the usefulness of ManiPose in a synthetic 1D-to-2D lifting setting and demonstrate on real-world datasets that it outperforms state-of-the-art models in pose consistency by a large margin, while still reaching competitive MPJPE performance.

We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function $V$ depending on the space variable in front of the power nonlinearity and an inhomogeneous term $W$ depending on both time and space variables. Namely, we establish sufficient conditions for the nonexistence of weak solutions in both cases: $W\equiv 0$ and $W\not\equiv 0$. The obtained conditions depend on the parameters of the problem as well as the geometry of the manifold. Some special cases of manifolds, and of $V$ and $W$ are discussed in detail., Comment: 21 pages