We propose geodesic-based optimization methods on dually flat spaces, where the geometric structure of the parameter manifold is closely related to the form of the objective function. A primary application is maximum likelihood estimation in statistical models, especially exponential families, whose model manifolds are dually flat. We show that an m-geodesic update, which directly optimizes the log-likelihood, can theoretically reach the maximum likelihood estimator in a single step. In contrast, an e-geodesic update has a practical advantage in cases where the parameter space is geodesically complete, allowing optimization without explicitly handling parameter constraints. We establish the theoretical properties of the proposed methods and validate their effectiveness through numerical experiments.

Given a query and dataset, the optimal way of answering the query is to make use all the information available. Modern LLMs exhibit impressive ability to memorize training data, but data not deemed important during training is forgotten, and information outside that training set cannot be made use of. Processing an entire dataset at inference time is infeasible due to the bounded nature of model resources (e.g. context size in transformers or states in state space models), meaning we must resort to external memory. This constraint naturally leads to the following problem: How can we decide based on the present query and model, what among a virtually unbounded set of known data matters for inference? To minimize model uncertainty for a particular query at test-time, we introduce Retrieval In-Context Optimization (RICO), a retrieval method that uses gradients from the LLM itself to learn the optimal mixture of documents for answer generation. Unlike traditional retrieval-augmented generation (RAG), which relies on external heuristics for document retrieval, our approach leverages direct feedback from the model. Theoretically, we show that standard top-$k$ retrieval with model gradients can approximate our optimization procedure, and provide connections to the leave-one-out loss. We demonstrate empirically that by minimizing an unsupervised loss objective in the form of question perplexity, we can achieve comparable retriever metric performance to BM25 with \emph{no finetuning}. Furthermore, when evaluated on quality of the final prediction, our method often outperforms fine-tuned dense retrievers such as E5.

Much machine learning research progress is based on developing models and evaluating them on a benchmark dataset (e.g., ImageNet for images). However, applying such benchmark-successful methods to real-world data often does not work as expected. This is particularly the case for biological data where we expect variability at multiple time and spatial scales. In this work, we are using grain data and the goal is to detect diseases and damages. Pink fusarium, skinned grains, and other diseases and damages are key factors in setting the price of grains or excluding dangerous grains from food production. Apart from challenges stemming from differences of the data from the standard toy datasets, we also present challenges that need to be overcome when explaining deep learning models. For example, explainability methods have many hyperparameters that can give different results, and the ones published in the papers do not work on dissimilar images. Other challenges are more general: problems with visualization of the explanations and their comparison since the magnitudes of their values differ from method to method. An open fundamental question also is: How to evaluate explanations? It is a non-trivial task because the "ground truth" is usually missing or ill-defined. Also, human annotators may create what they think is an explanation of the task at hand, yet the machine learning model might solve it in a different and perhaps counter-intuitive way. We discuss several of these challenges and evaluate various post-hoc explainability methods on grain data. We focus on robustness, quality of explanations, and similarity to particular "ground truth" annotations made by experts. The goal is to find the methods that overall perform well and could be used in this challenging task. We hope the proposed pipeline will be used as a framework for evaluating explainability methods in specific use cases.

Feature attribution methods (FAs), such as gradients and attention, are widely employed approaches to derive the importance of all input features to the model predictions. Existing work in natural language processing has mostly focused on developing and testing FAs for encoder-only language models (LMs) in classification tasks. However, it is unknown if it is faithful to use these FAs for decoder-only models on text generation, due to the inherent differences between model architectures and task settings respectively. Moreover, previous work has demonstrated that there is no `one-wins-all' FA across models and tasks. This makes the selection of a FA computationally expensive for large LMs since input importance derivation often requires multiple forward and backward passes including gradient computations that might be prohibitive even with access to large compute. To address these issues, we present a model-agnostic FA for generative LMs called Recursive Attribution Generator (ReAGent). Our method updates the token importance distribution in a recursive manner. For each update, we compute the difference in the probability distribution over the vocabulary for predicting the next token between using the original input and using a modified version where a part of the input is replaced with RoBERTa predictions. Our intuition is that replacing an important token in the context should have resulted in a larger change in the model's confidence in predicting the token than replacing an unimportant token. Our method can be universally applied to any generative LM without accessing internal model weights or additional training and fine-tuning, as most other FAs require. We extensively compare the faithfulness of ReAGent with seven popular FAs across six decoder-only LMs of various sizes. The results show that our method consistently provides more faithful token importance distributions.

Data augmentation has emerged as a powerful technique in machine learning, strengthening model robustness while mitigating overfitting and under-fitting issues by generating diverse synthetic data. Nevertheless, despite its success in other domains, data augmentation's potential remains largely untapped in mobility data analysis, primarily due to the intricate nature and unique format of trajectory data. Additionally, there is a lack of frameworks capable of point-wise data augmentation, which can reliably generate synthetic trajectories while preserving the inherent characteristics of the original data. To address these challenges, this research introduces AugmenTRAJ, an open-source Python3 framework designed explicitly for trajectory data augmentation. AugmenTRAJ offers a reliable and well-controlled approach for generating synthetic trajectories, thereby enabling the harnessing of data augmentation benefits in mobility analysis. This thesis presents a comprehensive overview of the methodologies employed in developing AugmenTRAJ and showcases the various data augmentation techniques available within the framework. AugmenTRAJ opens new possibilities for enhancing mobility data analysis models' performance and generalization capabilities by providing researchers with a practical and versatile tool for augmenting trajectory data, Its user-friendly implementation in Python3 facilitates easy integration into existing workflows, offering the community an accessible resource to leverage the full potential of data augmentation in trajectory-based applications.

The TanH activation function is a commonly used activation function in neural networks. Similar to the Sigmoid function, the TanH function is particularly useful for binary classification tasks. In this post, we'll be exploring the power and limitations of using the TanH activation function in neural networks. We'll look at its unique properties, advantages, and disadvantages, and discuss some use cases where the TanH function is particularly effective. One of the main advantages of using the TanH function is that it's a zero-centered function.

Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in physics-based machine learning of dynamical (or Hamiltonian) systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture. But these types of architectures have not been applied to solve Bayesian inference problems efficiently. We propose the use of HNNs for performing Bayesian inference efficiently without requiring numerous posterior gradients. We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity and reduced integration errors. We integrate L-HNNs in NUTS and further propose an online error monitoring scheme to prevent sampling degeneracy in regions where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with online error monitoring considering several complex high-dimensional posterior densities and compare its performance to NUTS.