Electronic commerce, or e-commerce, is the buying and selling of goods and services, or the transmitting of funds or data online. E-commerce platforms come in many kinds, with global players such as Amazon, Airbnb, Alibaba, eBay and platforms targeting specific geographic regions. Information retrieval has a natural role to play in e-commerce, especially in connecting people to goods and services. Information discovery in e-commerce concerns different types of search (e.g., exploratory search vs. lookup tasks), recommender systems, and natural language processing in e-commerce portals. The rise in popularity of e-commerce sites has made research on information discovery in e-commerce an increasingly active research area. This is witnessed by an increase in publications and dedicated workshops in this space. Methods for information discovery in e-commerce largely focus on improving the effectiveness of e-commerce search and recommender systems, on enriching and using knowledge graphs to support e-commerce, and on developing innovative question answering and bot-based solutions that help to connect people to goods and services. In this survey, an overview is given of the fundamental infrastructure, algorithms, and technical solutions for information discovery in e-commerce. The topics covered include user behavior and profiling, search, recommendation, and language technology in e-commerce.

Recent large language models (LLMs) demonstrate impressive capabilities in handling long contexts, some exhibiting near-perfect recall on synthetic retrieval tasks. However, these evaluations have mainly focused on English text and involved a single target sentence within lengthy contexts. Our work investigates how LLM performance generalizes to multilingual settings with multiple hidden target sentences. We create a new dataset -- mLongRR -- to comprehensively evaluate several multilingual long-context LLMs on retrieval and reasoning tasks across five languages: English, Vietnamese, Indonesian, Swahili, and Somali. These languages share the Latin script but belong to distinct language families and resource levels. Our analysis reveals a significant performance gap between languages. The best-performing models such as Gemini-1.5 and GPT-4o, achieve around 96% accuracy in English to around 36% in Somali with a single target sentence. However, this accuracy drops to 40% in English and 0% in Somali when dealing with three target sentences. Our findings highlight the challenges long-context LLMs face when processing longer contexts, an increase in the number of target sentences, or languages of lower resource levels.

Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on dynamical systems excited by temporally uncorrelated processes. In this article, we present a novel algorithm for guaranteed topology learning of networks that are excited by temporally (colored) cyclostationary processes, which encompasses a wide range of temporal correlation including wide-sense stationarity. Furthermore, unlike prior work, the framework applies to linear dynamic system with complex valued dependencies, and leverages group lasso regularization for effective learning of the network structure. In the second part of the article, we analyze conditions for consistent topology learning for bidirected tree networks when a subset of the network is unobserved. Here, the full topology along with unobserved nodes are recovered from observed node's time-series alone. Our theoretical contributions are validated on simulated data as well as on real-world climate data.

The information exponent (Ben Arous et al. [2021]) -- which is equivalent to the lowest degree in the Hermite expansion of the link function for Gaussian single-index models -- has played an important role in predicting the sample complexity of online stochastic gradient descent (SGD) in various learning tasks. In this work, we demonstrate that, for multi-index models, focusing solely on the lowest degree can miss key structural details of the model and result in suboptimal rates. Specifically, we consider the task of learning target functions of form $f_*(\mathbf{x}) = \sum_{k=1}^{P} \phi(\mathbf{v}_k^* \cdot \mathbf{x})$, where $P \ll d$, the ground-truth directions $\{ \mathbf{v}_k^* \}_{k=1}^P$ are orthonormal, and only the second and $2L$-th Hermite coefficients of the link function $\phi$ can be nonzero. Based on the theory of information exponent, when the lowest degree is $2L$, recovering the directions requires $d^{2L-1}\mathrm{poly}(P)$ samples, and when the lowest degree is $2$, only the relevant subspace (not the exact directions) can be recovered due to the rotational invariance of the second-order terms. In contrast, we show that by considering both second- and higher-order terms, we can first learn the relevant space via the second-order terms, and then the exact directions using the higher-order terms, and the overall sample and complexity of online SGD is $d \mathrm{poly}(P)$.

Orthogonal nonnegative matrix factorization (ONMF) has become a standard approach for clustering. As far as we know, most works on ONMF rely on the Frobenius norm to assess the quality of the approximation. This paper presents a new model and algorithm for ONMF that minimizes the Kullback-Leibler (KL) divergence. As opposed to the Frobenius norm which assumes Gaussian noise, the KL divergence is the maximum likelihood estimator for Poisson-distributed data, which can model better sparse vectors of word counts in document data sets and photo counting processes in imaging. We develop an algorithm based on alternating optimization, KL-ONMF, and show that it performs favorably with the Frobenius-norm based ONMF for document classification and hyperspectral image unmixing.

What's that feature called on pixel phones? I forget what Android in general about Android specifics. But yes, there there was like a magic erase option there, too Yeah, I was going to say magic eraser, but that is a that's a clean thing it's something like that too, but It works really well like in terms of highlighting a specific object and removing it there are instances where it's too big and it can't like extrapolate like what should be a background so it looks really messy but sometimes like it just like smooths out a bright ugly object in the background was just like general unfocused stuff and that actually may be better.

Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of viable algorithmic options. Despite advances in the design and testing of heuristics, there are concerns about their scalability and faithfulness at a time when we lack understanding of the complexity properties of the problems they are deployed to solve. To address this, we study circuit discovery with classical and parameterized computational complexity theory: (1) we describe a conceptual scaffolding to reason about circuit finding queries in terms of affordances for description, explanation, prediction and control; (2) we formalize a comprehensive set of queries that capture mechanistic explanation, and propose a formal framework for their analysis; (3) we use it to settle the complexity of many query variants and relaxations of practical interest on multi-layer perceptrons (part of, e.g., transformers). Our findings reveal a challenging complexity landscape. Many queries are intractable (NP-hard, $\Sigma^p_2$-hard), remain fixed-parameter intractable (W[1]-hard) when constraining model/circuit features (e.g., depth), and are inapproximable under additive, multiplicative, and probabilistic approximation schemes. To navigate this landscape, we prove there exist transformations to tackle some of these hard problems (NP- vs. $\Sigma^p_2$-complete) with better-understood heuristics, and prove the tractability (PTIME) or fixed-parameter tractability (FPT) of more modest queries which retain useful affordances. This framework allows us to understand the scope and limits of interpretability queries, explore viable options, and compare their resource demands among existing and future architectures.

In August 2023, Scott Aaronson and I reported the results of testing GPT4 with the Wolfram Alpha and Code Interpreter plug-ins over a collection of 105 original high-school level and college-level science and math problems (Davis and Aaronson, 2023). In September 2024, I tested the recently released model GPT-4o1-preview on the same collection. Overall I found that performance had significantly improved, but was still considerably short of perfect. In particular, problems that involve spatial reasoning are often stumbling blocks. On September 12, OpenAI (2024) released two preliminary versions, "ChatGPT-o1-preview" and "ChatGPT-o1-mini" of a forthcoming product "ChatGPT-o1".

We introduce a novel method for movie genre classification, capitalizing on a diverse set of readily accessible pretrained models. These models extract high-level features related to visual scenery, objects, characters, text, speech, music, and audio effects. To intelligently fuse these pretrained features, we train small classifier models with low time and memory requirements. Employing the transformer model, our approach utilizes all video and audio frames of movie trailers without performing any temporal pooling, efficiently exploiting the correspondence between all elements, as opposed to the fixed and low number of frames typically used by traditional methods. Our approach fuses features originating from different tasks and modalities, with different dimensionalities, different temporal lengths, and complex dependencies as opposed to current approaches. Our method outperforms state-of-the-art movie genre classification models in terms of precision, recall, and mean average precision (mAP). To foster future research, we make the pretrained features for the entire MovieNet dataset, along with our genre classification code and the trained models, publicly available.

The flooding extent area in a river valley is related to river gauge observations. The higher the water elevation, the larger the flooding area. Due to synthetic aperture radar\textquoteright s (SAR) capabilities to penetrate through clouds, radar images have been commonly used to estimate flooding extent area with various methods, from simple thresholding to deep learning models. In this study, we propose a physics-guided neural network for flooding area detection. Our approach takes as input data the Sentinel 1 time-series images and the water elevations in the river assigned to each image. We apply the Pearson correlation coefficient between the predicted sum of water extent areas and the local water level observations of river water elevations as the loss function. The effectiveness of our method is evaluated in five different study areas by comparing the predicted water maps with reference water maps obtained from digital terrain models and optical satellite images. The highest Intersection over Union (IoU) score achieved by our models was 0.89 for the water class and 0.96 for the non-water class. Additionally, we compared the results with other unsupervised methods. The proposed neural network provided a higher IoU than the other methods, especially for SAR images registered during low water elevation in the river.