In the domain of differential equation-based generative modeling, conventional approaches often rely on single-dimensional scalar values as interpolation coefficients during both training and inference phases. In this work, we introduce, for the first time, a multidimensional interpolant that extends these coefficients into multiple dimensions, leveraging the stochastic interpolant framework. Additionally, we propose a novel path optimization problem tailored to adaptively determine multidimensional inference trajectories, with a predetermined differential equation solver and a fixed number of function evaluations. Our solution involves simulation dynamics coupled with adversarial training to optimize the inference path. Notably, employing a multidimensional interpolant during training improves the model's inference performance, even in the absence of path optimization. When the adaptive, multidimensional path derived from our optimization process is employed, it yields further performance gains, even with fixed solver configurations. The introduction of multidimensional interpolants not only enhances the efficacy of models but also opens up a new domain for exploration in training and inference methodologies, emphasizing the potential of multidimensional paths as an untapped frontier.
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Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with insights from optimal transport to obtain novel particle-based algorithms for fitting latent variable models to data. Drawing inspiration from prior works which interpret `momentum-enriched' optimization algorithms as discretizations of ordinary differential equations, we propose an analogous dynamical-systems-inspired approach to minimizing the free energy functional. The result is a dynamical system that blends elements of Nesterov's Accelerated Gradient method, the underdamped Langevin diffusion, and particle methods. Under suitable assumptions, we prove that the continuous-time system minimizes the functional. By discretizing the system, we obtain a practical algorithm for MLE in latent variable models. The algorithm outperforms existing particle methods in numerical experiments and compares favourably with other MLE algorithms.
Data distillation and coresets have emerged as popular approaches to generate a smaller representative set of samples for downstream learning tasks to handle large-scale datasets. At the same time, machine learning is being increasingly applied to decision-making processes at a societal level, making it imperative for modelers to address inherent biases towards subgroups present in the data. While current approaches focus on creating fair synthetic representative samples by optimizing local properties relative to the original samples, their impact on downstream learning processes has yet to be explored. In this work, we present fair Wasserstein coresets (FWC), a novel coreset approach which generates fair synthetic representative samples along with sample-level weights to be used in downstream learning tasks. FWC uses an efficient majority minimization algorithm to minimize the Wasserstein distance between the original dataset and the weighted synthetic samples while enforcing demographic parity. We show that an unconstrained version of FWC is equivalent to Lloyd's algorithm for k-medians and k-means clustering. Experiments conducted on both synthetic and real datasets show that FWC: (i) achieves a competitive fairness-utility tradeoff in downstream models compared to existing approaches, (ii) improves downstream fairness when added to the existing training data and (iii) can be used to reduce biases in predictions from large language models (GPT-3.5 and GPT-4).
Quantum squaring operation is a useful building block in implementing quantum algorithms such as linear regression, regularized least squares algorithm, order-finding algorithm, quantum search algorithm, Newton Raphson division, Euclidean distance calculation, cryptography, and in finding roots and reciprocals. Quantum circuits could be made fault-tolerant by using error correcting codes and fault-tolerant quantum gates (such as the Clifford + T-gates). However, the T-gate is very costly to implement. Two qubit gates (such as the CNOT-gate) are more prone to noise errors than single qubit gates. Consequently, in order to realize reliable quantum algorithms, the quantum circuits should have a low T-count and CNOT-count. In this paper, we present a novel quantum integer squaring architecture optimized for T-count, CNOT-count, T-depth, CNOT-depth, and $KQ_T$ that produces no garbage outputs. To reduce costs, we use a novel approach for arranging the generated partial products that allows us to reduce the number of adders by 50%. We also use the resource efficient logical-AND gate and uncomputation gate shown in [1] to further save resources. The proposed quantum squaring circuit sees an asymptotic reduction of 66.67% in T-count, 50% in T-depth, 29.41% in CNOT-count, 42.86% in CNOT-depth, and 25% in KQ T with respect to Thapliyal et al. [2]. With respect to Nagamani et al. [3] the design sees an asymptotic reduction of 77.27% in T-count, 68.75% in T-depth, 50% in CNOT-count, 61.90% in CNOT-depth, and 6.25% in the $KQ_T$.
Stochastic natural gradient variational inference (NGVI) is a popular posterior inference method with applications in various probabilistic models. Despite its wide usage, little is known about the non-asymptotic convergence rate in the \emph{stochastic} setting. We aim to lessen this gap and provide a better understanding. For conjugate likelihoods, we prove the first $\mathcal{O}(\frac{1}{T})$ non-asymptotic convergence rate of stochastic NGVI. The complexity is no worse than stochastic gradient descent (\aka black-box variational inference) and the rate likely has better constant dependency that leads to faster convergence in practice. For non-conjugate likelihoods, we show that stochastic NGVI with the canonical parameterization implicitly optimizes a non-convex objective. Thus, a global convergence rate of $\mathcal{O}(\frac{1}{T})$ is unlikely without some significant new understanding of optimizing the ELBO using natural gradients.
We demonstrate a compactness result holding broadly across supervised learning with a general class of loss functions: Any hypothesis class $H$ is learnable with transductive sample complexity $m$ precisely when all of its finite projections are learnable with sample complexity $m$. We prove that this exact form of compactness holds for realizable and agnostic learning with respect to any proper metric loss function (e.g., any norm on $\mathbb{R}^d$) and any continuous loss on a compact space (e.g., cross-entropy, squared loss). For realizable learning with improper metric losses, we show that exact compactness of sample complexity can fail, and provide matching upper and lower bounds of a factor of 2 on the extent to which such sample complexities can differ. We conjecture that larger gaps are possible for the agnostic case. Furthermore, invoking the equivalence between sample complexities in the PAC and transductive models (up to lower order factors, in the realizable case) permits us to directly port our results to the PAC model, revealing an almost-exact form of compactness holding broadly in PAC learning.
Despite the potential of differentially private data visualization to harmonize data analysis and privacy, research in this area remains relatively underdeveloped. Boxplots are a widely popular visualization used for summarizing a dataset and for comparison of multiple datasets. Consequentially, we introduce a differentially private boxplot. We evaluate its effectiveness for displaying location, scale, skewness and tails of a given empirical distribution. In our theoretical exposition, we show that the location and scale of the boxplot are estimated with optimal sample complexity, and the skewness and tails are estimated consistently. In simulations, we show that this boxplot performs similarly to a non-private boxplot, and it outperforms a boxplot naively constructed from existing differentially private quantile algorithms. Additionally, we conduct a real data analysis of Airbnb listings, which shows that comparable analysis can be achieved through differentially private boxplot visualization.
Software engineering is a domain characterized by intricate decision-making processes, often relying on nuanced intuition and consultation. Recent advancements in deep learning have started to revolutionize software engineering practices through elaborate designs implemented at various stages of software development. In this paper, we present an innovative paradigm that leverages large language models (LLMs) throughout the entire software development process, streamlining and unifying key processes through natural language communication, thereby eliminating the need for specialized models at each phase. At the core of this paradigm lies ChatDev, a virtual chat-powered software development company that mirrors the established waterfall model, meticulously dividing the development process into four distinct chronological stages: designing, coding, testing, and documenting. Each stage engages a team of agents, such as programmers, code reviewers, and test engineers, fostering collaborative dialogue and facilitating a seamless workflow. The chat chain acts as a facilitator, breaking down each stage into atomic subtasks. This enables dual roles, allowing for proposing and validating solutions through context-aware communication, leading to efficient resolution of specific subtasks. The instrumental analysis of ChatDev highlights its remarkable efficacy in software generation, enabling the completion of the entire software development process in under seven minutes at a cost of less than one dollar. It not only identifies and alleviates potential vulnerabilities but also rectifies potential hallucinations while maintaining commendable efficiency and cost-effectiveness. The potential of ChatDev unveils fresh possibilities for integrating LLMs into the realm of software development.
Disentangled Representation Learning (DRL) aims to learn a model capable of identifying and disentangling the underlying factors hidden in the observable data in representation form. The process of separating underlying factors of variation into variables with semantic meaning benefits in learning explainable representations of data, which imitates the meaningful understanding process of humans when observing an object or relation. As a general learning strategy, DRL has demonstrated its power in improving the model explainability, controlability, robustness, as well as generalization capacity in a wide range of scenarios such as computer vision, natural language processing, data mining etc. In this article, we comprehensively review DRL from various aspects including motivations, definitions, methodologies, evaluations, applications and model designs. We discuss works on DRL based on two well-recognized definitions, i.e., Intuitive Definition and Group Theory Definition. We further categorize the methodologies for DRL into four groups, i.e., Traditional Statistical Approaches, Variational Auto-encoder Based Approaches, Generative Adversarial Networks Based Approaches, Hierarchical Approaches and Other Approaches. We also analyze principles to design different DRL models that may benefit different tasks in practical applications. Finally, we point out challenges in DRL as well as potential research directions deserving future investigations. We believe this work may provide insights for promoting the DRL research in the community.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.
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