We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem setups that assume the matrix von Mises-Fisher distribution (a.k.a., matrix Langevin distribution or chordal distance)for isotropic rotational uncertainty. However, another common way to represent uncertainty for rotations and poses is to define anisotropic noise in the associated Lie algebra. Starting from a noise model based on the Cayley map, we define our estimation problems, convert them to Quadratically Constrained Quadratic Programs (QCQPs), then relax them to Semidefinite Programs (SDPs), which can be solved using standard interior-point optimization methods; global optimality follows from Lagrangian strong duality. We first show how to carry out basic rotation and pose averaging. We then turn to the more complex problem of trajectory estimation, which involves many pose variables with both individual and inter-pose measurements (or motion priors). Our contribution is to formulate SDP relaxations for all these problems based on the Cayley map (including the identification of redundant constraints) and to show them working in practical settings. We hope our results can add to the catalogue of useful estimation problems whose solutions can be a posteriori guaranteed to be globally optimal.
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In the past few years, large-scale pre-trained vision-language models like CLIP have achieved tremendous success in various fields. Naturally, how to transfer the rich knowledge in such huge pre-trained models to downstream tasks and datasets becomes a hot topic. During downstream adaptation, the most challenging problems are overfitting and catastrophic forgetting, which can cause the model to overly focus on the current data and lose more crucial domain-general knowledge. Existing works use classic regularization techniques to solve the problems. As solutions become increasingly complex, the ever-growing storage and inference costs are also a significant problem that urgently needs to be addressed. While in this paper, we start from an observation that proper random noise can suppress overfitting and catastrophic forgetting. Then we regard quantization error as a kind of noise, and explore quantization for regularizing vision-language model, which is quite efficiency and effective. Furthermore, to improve the model's generalization capability while maintaining its specialization capacity at minimal cost, we deeply analyze the characteristics of the weight distribution in prompts, conclude several principles for quantization module design and follow such principles to create several competitive baselines. The proposed method is significantly efficient due to its inherent lightweight nature, making it possible to adapt on extremely resource-limited devices. Our method can be fruitfully integrated into many existing approaches like MaPLe, enhancing accuracy while reducing storage overhead, making it more powerful yet versatile. Extensive experiments on 11 datasets shows great superiority of our method sufficiently. Code is available at //github.com/beyondhtx/QPrompt.
Most real-world systems exhibit a multiscale behaviour that needs to be taken into consideration when fitting the effective dynamics to data sampled at a given scale. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the Maximum Likelihood Estimators of the parameters of the limiting dynamics to be consistent, data needs to be subsampled at an appropriate rate. Recent advances in extracting effective dynamics for fractional multiscale systems make the same question relevant in the fractional diffusion setting. We study the problem of parameter estimation of the diffusion coefficient in this context. In particular, we consider the multiscale fractional Ornstein-Uhlenbeck system (fractional kinetic Brownian motion) and we provide convergence results for the Maximum Likelihood Estimator of the diffusion coefficient of the limiting dynamics, using multiscale data. To do so, we derive asymptotic bounds for the spectral norm of the inverse covariance matrix of fractional Gaussian noise.
Proteins are fundamental components of biological systems and can be represented through various modalities, including sequences, structures, and textual descriptions. Despite the advances in deep learning and scientific large language models (LLMs) for protein research, current methodologies predominantly focus on limited specialized tasks -- often predicting one protein modality from another. These approaches restrict the understanding and generation of multimodal protein data. In contrast, large multimodal models have demonstrated potential capabilities in generating any-to-any content like text, images, and videos, thus enriching user interactions across various domains. Integrating these multimodal model technologies into protein research offers significant promise by potentially transforming how proteins are studied. To this end, we introduce HelixProtX, a system built upon the large multimodal model, aiming to offer a comprehensive solution to protein research by supporting any-to-any protein modality generation. Unlike existing methods, it allows for the transformation of any input protein modality into any desired protein modality. The experimental results affirm the advanced capabilities of HelixProtX, not only in generating functional descriptions from amino acid sequences but also in executing critical tasks such as designing protein sequences and structures from textual descriptions. Preliminary findings indicate that HelixProtX consistently achieves superior accuracy across a range of protein-related tasks, outperforming existing state-of-the-art models. By integrating multimodal large models into protein research, HelixProtX opens new avenues for understanding protein biology, thereby promising to accelerate scientific discovery.
Recommendation systems have become an important solution to information search problems. This article proposes a neural matrix factorization recommendation system model based on the multimodal large language model called BoNMF. This model combines BoBERTa's powerful capabilities in natural language processing, ViT in computer in vision, and neural matrix decomposition technology. By capturing the potential characteristics of users and items, and after interacting with a low-dimensional matrix composed of user and item IDs, the neural network outputs the results. recommend. Cold start and ablation experimental results show that the BoNMF model exhibits excellent performance on large public data sets and significantly improves the accuracy of recommendations.
A major challenge when describing the origin of life is to explain "how instructional information control systems emerge naturally and spontaneously from mere molecular dynamics". So far, no one has clarified how information control emerged ab initio and how primitive control mechanisms in life might have evolved, becoming increasingly refined. Based on recent experimental results showing that chemical computation does not require the presence of life-related chemistry, we elucidate the origin and early evolution of information handling by chemical automata, from information processing (computation) to information storage (memory) and information transmission (communication) and later digital messengers, covering at the same time its syntactic, semantic and pragmatic flavors. In contrast to other theories that assume the existence of initial complex structures, our representation starts from trivial self-replicators whose interaction leads to the arising of more powerful molecular machines. By describing precisely the primordial transitions in chemistry-based computation, our framework is capable of explaining the above-mentioned gaps and can be translated to other models of computation, which allow us to explore biological phenomena at multiple spatial and temporal scales. Being compatible with the free energy principle, we have developed a computational enactivist theoretical framework that could be able to describe from the origin of life to high-level cognition, as if it were a purely constructivist narrative. At the end of our manuscript, we propose some ways to extend our ideas, including experimental validation of our theory (both in vitro and in silico).
We present a unified approach to obtain scaling limits of neural networks using the genus expansion technique from random matrix theory. This approach begins with a novel expansion of neural networks which is reminiscent of Butcher series for ODEs, and is obtained through a generalisation of Fa\`a di Bruno's formula to an arbitrary number of compositions. In this expansion, the role of monomials is played by random multilinear maps indexed by directed graphs whose edges correspond to random matrices, which we call operator graphs. This expansion linearises the effect of the activation functions, allowing for the direct application of Wick's principle to compute the expectation of each of its terms. We then determine the leading contribution to each term by embedding the corresponding graphs onto surfaces, and computing their Euler characteristic. Furthermore, by developing a correspondence between analytic and graphical operations, we obtain similar graph expansions for the neural tangent kernel as well as the input-output Jacobian of the original neural network, and derive their infinite-width limits with relative ease. Notably, we find explicit formulae for the moments of the limiting singular value distribution of the Jacobian. We then show that all of these results hold for networks with more general weights, such as general matrices with i.i.d. entries satisfying moment assumptions, complex matrices and sparse matrices.
Privacy is a central challenge for systems that learn from sensitive data sets, especially when a system's outputs must be continuously updated to reflect changing data. We consider the achievable error for differentially private continual release of a basic statistic - the number of distinct items - in a stream where items may be both inserted and deleted (the turnstile model). With only insertions, existing algorithms have additive error just polylogarithmic in the length of the stream $T$. We uncover a much richer landscape in the turnstile model, even without considering memory restrictions. We show that every differentially private mechanism that handles insertions and deletions has worst-case additive error at least $T^{1/4}$ even under a relatively weak, event-level privacy definition. Then, we identify a parameter of the input stream, its maximum flippancy, that is low for natural data streams and for which we give tight parameterized error guarantees. Specifically, the maximum flippancy is the largest number of times that the contribution of a single item to the distinct elements count changes over the course of the stream. We present an item-level differentially private mechanism that, for all turnstile streams with maximum flippancy $w$, continually outputs the number of distinct elements with an $O(\sqrt{w} \cdot poly\log T)$ additive error, without requiring prior knowledge of $w$. We prove that this is the best achievable error bound that depends only on $w$, for a large range of values of $w$. When $w$ is small, the error of our mechanism is similar to the polylogarithmic in $T$ error in the insertion-only setting, bypassing the hardness in the turnstile model.
Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.
We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.
Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.
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