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Most mathematical distortions used in ML are fundamentally integral in nature: $f$-divergences, Bregman divergences, (regularized) optimal transport distances, integral probability metrics, geodesic distances, etc. In this paper, we unveil a grounded theory and tools which can help improve these distortions to better cope with ML requirements. We start with a generalization of Riemann integration that also encapsulates functions that are not strictly additive but are, more generally, $t$-additive, as in nonextensive statistical mechanics. Notably, this recovers Volterra's product integral as a special case. We then generalize the Fundamental Theorem of calculus using an extension of the (Euclidean) derivative. This, along with a series of more specific Theorems, serves as a basis for results showing how one can specifically design, alter, or change fundamental properties of distortion measures in a simple way, with a special emphasis on geometric- and ML-related properties that are the metricity, hyperbolicity, and encoding. We show how to apply it to a problem that has recently gained traction in ML: hyperbolic embeddings with a "cheap" and accurate encoding along the hyperbolic vs Euclidean scale. We unveil a new application for which the Poincar\'e disk model has very appealing features, and our theory comes in handy: \textit{model} embeddings for boosted combinations of decision trees, trained using the log-loss (trees) and logistic loss (combinations).

Model-based reinforcement learning (MBRL) holds the promise of sample-efficient learning by utilizing a world model, which models how the environment works and typically encompasses components for two tasks: observation modeling and reward modeling. In this paper, through a dedicated empirical investigation, we gain a deeper understanding of the role each task plays in world models and uncover the overlooked potential of sample-efficient MBRL by mitigating the domination of either observation or reward modeling. Our key insight is that while prevalent approaches of explicit MBRL attempt to restore abundant details of the environment via observation models, it is difficult due to the environment's complexity and limited model capacity. On the other hand, reward models, while dominating implicit MBRL and adept at learning compact task-centric dynamics, are inadequate for sample-efficient learning without richer learning signals. Motivated by these insights and discoveries, we propose a simple yet effective approach, HarmonyDream, which automatically adjusts loss coefficients to maintain task harmonization, i.e. a dynamic equilibrium between the two tasks in world model learning. Our experiments show that the base MBRL method equipped with HarmonyDream gains 10%-69% absolute performance boosts on visual robotic tasks and sets a new state-of-the-art result on the Atari 100K benchmark.

The \emph{Fast Gaussian Transform} (FGT) enables subquadratic-time multiplication of an $n\times n$ Gaussian kernel matrix $\mathsf{K}_{i,j}= \exp ( - \| x_i - x_j \|_2^2 ) $ with an arbitrary vector $h \in \mathbb{R}^n$, where $x_1,\dots, x_n \in \mathbb{R}^d$ are a set of \emph{fixed} source points. This kernel plays a central role in machine learning and random feature maps. Nevertheless, in most modern data analysis applications, datasets are dynamically changing (yet often have low rank), and recomputing the FGT from scratch in (kernel-based) algorithms incurs a major computational overhead ($\gtrsim n$ time for a single source update $\in \mathbb{R}^d$). These applications motivate a \emph{dynamic FGT} algorithm, which maintains a dynamic set of sources under \emph{kernel-density estimation} (KDE) queries in \emph{sublinear time} while retaining Mat-Vec multiplication accuracy and speed. Assuming the dynamic data-points $x_i$ lie in a (possibly changing) $k$-dimensional subspace ($k\leq d$), our main result is an efficient dynamic FGT algorithm, supporting the following operations in $\log^{O(k)}(n/\varepsilon)$ time: (1) Adding or deleting a source point, and (2) Estimating the ``kernel-density'' of a query point with respect to sources with $\varepsilon$ additive accuracy. The core of the algorithm is a dynamic data structure for maintaining the \emph{projected} ``interaction rank'' between source and target boxes, decoupled into finite truncation of Taylor and Hermite expansions.

Supervised fairness-aware machine learning under distribution shifts is an emerging field that addresses the challenge of maintaining equitable and unbiased predictions when faced with changes in data distributions from source to target domains. In real-world applications, machine learning models are often trained on a specific dataset but deployed in environments where the data distribution may shift over time due to various factors. This shift can lead to unfair predictions, disproportionately affecting certain groups characterized by sensitive attributes, such as race and gender. In this survey, we provide a summary of various types of distribution shifts and comprehensively investigate existing methods based on these shifts, highlighting six commonly used approaches in the literature. Additionally, this survey lists publicly available datasets and evaluation metrics for empirical studies. We further explore the interconnection with related research fields, discuss the significant challenges, and identify potential directions for future studies.

We consider a variant of matrix completion where entries are revealed in a biased manner, adopting a model akin to that introduced by Ma and Chen. Instead of treating this observation bias as a disadvantage, as is typically the case, the goal is to exploit the shared information between the bias and the outcome of interest to improve predictions. Towards this, we consider a natural model where the observation pattern and outcome of interest are driven by the same set of underlying latent or unobserved factors. This leads to a two stage matrix completion algorithm: first, recover (distances between) the latent factors by utilizing matrix completion for the fully observed noisy binary matrix corresponding to the observation pattern; second, utilize the recovered latent factors as features and sparsely observed noisy outcomes as labels to perform non-parametric supervised learning. The finite-sample error rates analysis suggests that, ignoring logarithmic factors, this approach is competitive with the corresponding supervised learning parametric rates. This implies the two-stage method has performance that is comparable to having access to the unobserved latent factors through exploiting the shared information between the bias and outcomes. Through empirical evaluation using a real-world dataset, we find that with this two-stage algorithm, the estimates have 30x smaller mean squared error compared to traditional matrix completion methods, suggesting the utility of the model and the method proposed in this work.

Kahneman & Tversky's $\textit{prospect theory}$ tells us that humans perceive random variables in a biased but well-defined manner; for example, humans are famously loss-averse. We show that objectives for aligning LLMs with human feedback implicitly incorporate many of these biases -- the success of these objectives (e.g., DPO) over cross-entropy minimization can partly be ascribed to them being $\textit{human-aware loss functions}$ (HALOs). However, the utility functions these methods attribute to humans still differ from those in the prospect theory literature. Using a Kahneman-Tversky model of human utility, we propose a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, as current methods do. We call this approach Kahneman-Tversky Optimization (KTO), and it matches or exceeds the performance of preference-based methods at scales from 1B to 30B. Crucially, KTO does not need preferences -- only a binary signal of whether an output is desirable or undesirable for a given input. This makes it far easier to use in the real world, where preference data is scarce and expensive.

Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant when guidance scale is large. To address this issue, we propose characteristic guidance, a guidance method that provides first-principle non-linear correction for classifier-free guidance. Such correction forces the guided DDPMs to respect the Fokker-Planck (FP) equation of diffusion process, in a way that is training-free and compatible with existing sampling methods. Experiments show that characteristic guidance enhances semantic characteristics of prompts and mitigate irregularities in image generation, proving effective in diverse applications ranging from simulating magnet phase transitions to latent space sampling.

We introduce SMUTF, a unique approach for large-scale tabular data schema matching (SM), which assumes that supervised learning does not affect performance in open-domain tasks, thereby enabling effective cross-domain matching. This system uniquely combines rule-based feature engineering, pre-trained language models, and generative large language models. In an innovative adaptation inspired by the Humanitarian Exchange Language, we deploy 'generative tags' for each data column, enhancing the effectiveness of SM. SMUTF exhibits extensive versatility, working seamlessly with any pre-existing pre-trained embeddings, classification methods, and generative models. Recognizing the lack of extensive, publicly available datasets for SM, we have created and open-sourced the HDXSM dataset from the public humanitarian data. We believe this to be the most exhaustive SM dataset currently available. In evaluations across various public datasets and the novel HDXSM dataset, SMUTF demonstrated exceptional performance, surpassing existing state-of-the-art models in terms of accuracy and efficiency, and} improving the F1 score by 11.84% and the AUC of ROC by 5.08%.

Joint image-text embedding is the bedrock for most Vision-and-Language (V+L) tasks, where multimodality inputs are jointly processed for visual and textual understanding. In this paper, we introduce UNITER, a UNiversal Image-TExt Representation, learned through large-scale pre-training over four image-text datasets (COCO, Visual Genome, Conceptual Captions, and SBU Captions), which can power heterogeneous downstream V+L tasks with joint multimodal embeddings. We design three pre-training tasks: Masked Language Modeling (MLM), Image-Text Matching (ITM), and Masked Region Modeling (MRM, with three variants). Different from concurrent work on multimodal pre-training that apply joint random masking to both modalities, we use conditioned masking on pre-training tasks (i.e., masked language/region modeling is conditioned on full observation of image/text). Comprehensive analysis shows that conditioned masking yields better performance than unconditioned masking. We also conduct a thorough ablation study to find an optimal setting for the combination of pre-training tasks. Extensive experiments show that UNITER achieves new state of the art across six V+L tasks (over nine datasets), including Visual Question Answering, Image-Text Retrieval, Referring Expression Comprehension, Visual Commonsense Reasoning, Visual Entailment, and NLVR2.

With the capability of modeling bidirectional contexts, denoising autoencoding based pretraining like BERT achieves better performance than pretraining approaches based on autoregressive language modeling. However, relying on corrupting the input with masks, BERT neglects dependency between the masked positions and suffers from a pretrain-finetune discrepancy. In light of these pros and cons, we propose XLNet, a generalized autoregressive pretraining method that (1) enables learning bidirectional contexts by maximizing the expected likelihood over all permutations of the factorization order and (2) overcomes the limitations of BERT thanks to its autoregressive formulation. Furthermore, XLNet integrates ideas from Transformer-XL, the state-of-the-art autoregressive model, into pretraining. Empirically, XLNet outperforms BERT on 20 tasks, often by a large margin, and achieves state-of-the-art results on 18 tasks including question answering, natural language inference, sentiment analysis, and document ranking.