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This paper presents a computational framework for the concise encoding of an ensemble of persistence diagrams, in the form of weighted Wasserstein barycenters [100], [102] of a dictionary of atom diagrams. We introduce a multi-scale gradient descent approach for the efficient resolution of the corresponding minimization problem, which interleaves the optimization of the barycenter weights with the optimization of the atom diagrams. Our approach leverages the analytic expressions for the gradient of both sub-problems to ensure fast iterations and it additionally exploits shared-memory parallelism. Extensive experiments on public ensembles demonstrate the efficiency of our approach, with Wasserstein dictionary computations in the orders of minutes for the largest examples. We show the utility of our contributions in two applications. First, we apply Wassserstein dictionaries to data reduction and reliably compress persistence diagrams by concisely representing them with their weights in the dictionary. Second, we present a dimensionality reduction framework based on a Wasserstein dictionary defined with a small number of atoms (typically three) and encode the dictionary as a low dimensional simplex embedded in a visual space (typically in 2D). In both applications, quantitative experiments assess the relevance of our framework. Finally, we provide a C++ implementation that can be used to reproduce our results.

Invariance describes transformations that do not alter data's underlying semantics. Neural networks that preserve natural invariance capture good inductive biases and achieve superior performance. Hence, modern networks are handcrafted to handle well-known invariances (ex. translations). We propose a framework to learn novel network architectures that capture data-dependent invariances via pruning. Our learned architectures consistently outperform dense neural networks on both vision and tabular datasets in both efficiency and effectiveness. We demonstrate our framework on multiple deep learning models across 3 vision and 40 tabular datasets.

We study the algebraic complexity of annihilators of polynomials maps. In particular, when a polynomial map is `encoded by' a small algebraic circuit, we show that the coefficients of an annihilator of the map can be computed in PSPACE. Even when the underlying field is that of reals or complex numbers, an analogous statement is true. We achieve this by using the class VPSPACE that coincides with computability of coefficients in PSPACE, over integers. As a consequence, we derive the following two conditional results. First, we show that a VP-explicit hitting set generator for all of VP would separate either VP from VNP, or non-uniform P from PSPACE. Second, in relation to algebraic natural proofs, we show that proving an algebraic natural proofs barrier would imply either VP $\neq$ VNP or DSPACE($\log^{\log^{\ast}n} n$) $\not\subset$ P.

The analysis of structured complex data, such as clustered graph based datasets, usually applies a variety of visual representation techniques and formats. The majority of currently available tools and approaches to exploratory visualization are built on integrated schemes for simultaneous displaying of multiple aspects of studying objects and processes. Usually, such schemes partition screen space that is composed of multiple views and adopt interaction patterns to focus on data-driven items. Widely known concepts as overview plus-detail and focus-plus-context are ambiguous in interpretation by means of technical terms. Therefore, their implementation by UI design practitioners need reviews and a classification of the basic approaches to visual composition of graphical representation modules. We propose a description of basic components of the view and focus and an overview of their multiple combinations.

This paper presents a novel sampling scheme for masked non-autoregressive generative modeling. We identify the limitations of TimeVQVAE, MaskGIT, and Token-Critic in their sampling processes, and propose Enhanced Sampling Scheme (ESS) to overcome these limitations. ESS explicitly ensures both sample diversity and fidelity, and consists of three stages: Naive Iterative Decoding, Critical Reverse Sampling, and Critical Resampling. ESS starts by sampling a token set using the naive iterative decoding as proposed in MaskGIT, ensuring sample diversity. Then, the token set undergoes the critical reverse sampling, masking tokens leading to unrealistic samples. After that, critical resampling reconstructs masked tokens until the final sampling step is reached to ensure high fidelity. Critical resampling uses confidence scores obtained from a self-Token-Critic to better measure the realism of sampled tokens, while critical reverse sampling uses the structure of the quantized latent vector space to discover unrealistic sample paths. We demonstrate significant performance gains of ESS in both unconditional sampling and class-conditional sampling using all the 128 datasets in the UCR Time Series archive.

Neural implicit modeling permits to achieve impressive 3D reconstruction results on small objects, while it exhibits significant limitations in large indoor scenes. In this work, we propose a novel neural implicit modeling method that leverages multiple regularization strategies to achieve better reconstructions of large indoor environments, while relying only on images. A sparse but accurate depth prior is used to anchor the scene to the initial model. A dense but less accurate depth prior is also introduced, flexible enough to still let the model diverge from it to improve the estimated geometry. Then, a novel self-supervised strategy to regularize the estimated surface normals is presented. Finally, a learnable exposure compensation scheme permits to cope with challenging lighting conditions. Experimental results show that our approach produces state-of-the-art 3D reconstructions in challenging indoor scenarios.

We introduce differentiable indirection -- a novel learned primitive that employs differentiable multi-scale lookup tables as an effective substitute for traditional compute and data operations across the graphics pipeline. We demonstrate its flexibility on a number of graphics tasks, i.e., geometric and image representation, texture mapping, shading, and radiance field representation. In all cases, differentiable indirection seamlessly integrates into existing architectures, trains rapidly, and yields both versatile and efficient results.

We explore the novel application of Large Language Models to code optimization. We present a 7B-parameter transformer model trained from scratch to optimize LLVM assembly for code size. The model takes as input unoptimized assembly and outputs a list of compiler options to best optimize the program. Crucially, during training, we ask the model to predict the instruction counts before and after optimization, and the optimized code itself. These auxiliary learning tasks significantly improve the optimization performance of the model and improve the model's depth of understanding. We evaluate on a large suite of test programs. Our approach achieves a 3.0% improvement in reducing instruction counts over the compiler, outperforming two state-of-the-art baselines that require thousands of compilations. Furthermore, the model shows surprisingly strong code reasoning abilities, generating compilable code 91% of the time and perfectly emulating the output of the compiler 70% of the time.

This paper presents a novel unifying framework of bilinear LSTMs that can represent and utilize the nonlinear interaction of the input features present in sequence datasets for achieving superior performance over a linear LSTM and yet not incur more parameters to be learned. To realize this, our unifying framework allows the expressivity of the linear vs. bilinear terms to be balanced by correspondingly trading off between the hidden state vector size vs. approximation quality of the weight matrix in the bilinear term so as to optimize the performance of our bilinear LSTM, while not incurring more parameters to be learned. We empirically evaluate the performance of our bilinear LSTM in several language-based sequence learning tasks to demonstrate its general applicability.

Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.