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This note introduces the $\texttt{LikelihoodGeometry}$ package for the computer algebra system $\textit{Macaulay2}$. This package gives tools to construct the likelihood correspondence of a discrete algebraic statistical model, a variety that that ties together data and their maximum likelihood estimators. This includes methods for constructing and combining popular statistical models and calculating their ML-degree., Comment: 6 pagess. arXiv admin note: text overlap with arXiv:2312.08501

Osteoporosis is a common condition that increases fracture risk, especially in older adults. Early diagnosis is vital for preventing fractures, reducing treatment costs, and preserving mobility. However, healthcare providers face challenges like limited labeled data and difficulties in processing medical images. This study presents a novel multi-modal learning framework that integrates clinical and imaging data to improve diagnostic accuracy and model interpretability. The model utilizes three pre-trained networks-VGG19, InceptionV3, and ResNet50-to extract deep features from X-ray images. These features are transformed using PCA to reduce dimensionality and focus on the most relevant components. A clustering-based selection process identifies the most representative components, which are then combined with preprocessed clinical data and processed through a fully connected network (FCN) for final classification. A feature importance plot highlights key variables, showing that Medical History, BMI, and Height were the main contributors, emphasizing the significance of patient-specific data. While imaging features were valuable, they had lower importance, indicating that clinical data are crucial for accurate predictions. This framework promotes precise and interpretable predictions, enhancing transparency and building trust in AI-driven diagnoses for clinical integration.

The ``AI Olympics with RealAIGym'' competition challenges participants to stabilize chaotic underactuated dynamical systems with advanced control algorithms. In this paper, we present a novel solution submitted to IROS'24 competition, which builds upon Soft Actor-Critic (SAC), a popular model-free entropy-regularized Reinforcement Learning (RL) algorithm. We add a `context' vector to the state, which encodes the immediate history via a Convolutional Neural Network (CNN) to counteract the unmodeled effects on the real system. Our method achieves high performance scores and competitive robustness scores on both tracks of the competition: Pendubot and Acrobot., Comment: 5 Pages, 3 Figures, 3 Tables

Efficient video tokenization remains a key bottleneck in learning general purpose vision models that are capable of processing long video sequences. Prevailing approaches are restricted to encoding videos to a fixed number of tokens, where too few tokens will result in overly lossy encodings, and too many tokens will result in prohibitively long sequence lengths. In this work, we introduce ElasticTok, a method that conditions on prior frames to adaptively encode a frame into a variable number of tokens. To enable this in a computationally scalable way, we propose a masking technique that drops a random number of tokens at the end of each frames's token encoding. During inference, ElasticTok can dynamically allocate tokens when needed -- more complex data can leverage more tokens, while simpler data only needs a few tokens. Our empirical evaluations on images and video demonstrate the effectiveness of our approach in efficient token usage, paving the way for future development of more powerful multimodal models, world models, and agents.

Self-correction is a highly desirable capability of large language models (LLMs), yet it has consistently been found to be largely ineffective in modern LLMs. Current methods for training self-correction typically depend on either multiple models, a more advanced model, or additional forms of supervision. To address these shortcomings, we develop a multi-turn online reinforcement learning (RL) approach, SCoRe, that significantly improves an LLM's self-correction ability using entirely self-generated data. To build SCoRe, we first show that variants of supervised fine-tuning (SFT) on offline model-generated correction traces are often insufficient for instilling self-correction behavior. In particular, we observe that training via SFT falls prey to either a distribution mismatch between mistakes made by the data-collection policy and the model's own responses, or to behavior collapse, where learning implicitly prefers only a certain mode of correction behavior that is often not effective at self-correction on test problems. SCoRe addresses these challenges by training under the model's own distribution of self-generated correction traces and using appropriate regularization to steer the learning process into learning a self-correction behavior that is effective at test time as opposed to fitting high-reward responses for a given prompt. This regularization process includes an initial phase of multi-turn RL on a base model to generate a policy initialization that is less susceptible to collapse, followed by using a reward bonus to amplify self-correction. With Gemini 1.0 Pro and 1.5 Flash models, we find that SCoRe achieves state-of-the-art self-correction performance, improving the base models' self-correction by 15.6% and 9.1% respectively on MATH and HumanEval.

Dynamic topic modeling is useful at discovering the development and change in latent topics over time. However, present methodology relies on algorithms that separate document and word representations. This prevents the creation of a meaningful embedding space where changes in word usage and documents can be directly analyzed in a temporal context. This paper proposes an expansion of the compass-aligned temporal Word2Vec methodology into dynamic topic modeling. Such a method allows for the direct comparison of word and document embeddings across time in dynamic topics. This enables the creation of visualizations that incorporate temporal word embeddings within the context of documents into topic visualizations. In experiments against the current state-of-the-art, our proposed method demonstrates overall competitive performance in topic relevancy and diversity across temporal datasets of varying size. Simultaneously, it provides insightful visualizations focused on temporal word embeddings while maintaining the insights provided by global topic evolution, advancing our understanding of how topics evolve over time., Comment: 11 pages, 9 figures, conference paper

Many algorithms for aligning LLMs with human preferences assume that human preferences are binary and deterministic. However, human preferences can vary across individuals, and therefore should be represented distributionally. In this work, we introduce the distributional soft preference labels and improve Direct Preference Optimization (DPO) with a weighted geometric average of the LLM output likelihood in the loss function. This approach adjusts the scale of learning loss based on the soft labels such that the loss would approach zero when the responses are closer to equally preferred. This simple modification can be easily applied to any DPO-based methods and mitigate over-optimization and objective mismatch, which prior works suffer from. Our experiments simulate the soft preference labels with AI feedback from LLMs and demonstrate that geometric averaging consistently improves performance on standard benchmarks for alignment research. In particular, we observe more preferable responses than binary labels and significant improvements where modestly-confident labels are in the majority., Comment: Accepted at NeurIPS 2024

Dimension reduction (DR) can transform high-dimensional text embeddings into a 2D visual projection facilitating the exploration of document similarities. However, the projection often lacks connection to the text semantics, due to the opaque nature of text embeddings and non-linear dimension reductions. To address these problems, we propose a gradient-based method for visualizing the spatial semantics of dimensionally reduced text embeddings. This method employs gradients to assess the sensitivity of the projected documents with respect to the underlying words. The method can be applied to existing DR algorithms and text embedding models. Using these gradients, we designed a visualization system that incorporates spatial word clouds into the document projection space to illustrate the impactful text features. We further present three usage scenarios that demonstrate the practical applications of our system to facilitate the discovery and interpretation of underlying semantics in text projections.

The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a parameterised quasi-static solid-mechanical problem. The local basis method by Amsallem et al. [1] addresses this deficiency by introducing a locally, rather than globally, linear approximation of the solution manifold. However, this generally successful approach comes with some limitations, especially in the data-poor setting. In this proof-of-concept investigation, we instead propose a graph-based manifold learning approach to nonlinear projection-based MOR which uses a global, continuously nonlinear approximation of the solution manifold. Approximations of local tangents to the solution manifold, which are necessary for a Galerkin scheme, are computed in the online phase. As an example application for the resulting nonlinear MOR algorithms, we consider simple representative volume element computations. On this example, the manifold learning approach Pareto-dominates the POD and local basis method in terms of the error and runtime achieved using a range of model dimensionalities., Comment: Submitted to Computer Methods in Applied Mechanics and Engineering. 51 pages, 36 figures

Semantic interaction (SI) in Dimension Reduction (DR) of images allows users to incorporate feedback through direct manipulation of the 2D positions of images. Through interaction, users specify a set of pairwise relationships that the DR should aim to capture. Existing methods for images incorporate feedback into the DR through feature weights on abstract embedding features. However, if the original embedding features do not suitably capture the users' task then the DR cannot either. We propose ImageSI, an SI method for image DR that incorporates user feedback directly into the image model to update the underlying embeddings, rather than weighting them. In doing so, ImageSI ensures that the embeddings suitably capture the features necessary for the task so that the DR can subsequently organize images using those features. We present two variations of ImageSI using different loss functions - ImageSI_MDS_Inverse, which prioritizes the explicit pairwise relationships from the interaction and ImageSI_Triplet, which prioritizes clustering, using the interaction to define groups of images. Finally, we present a usage scenario and a simulation based evaluation to demonstrate the utility of ImageSI and compare it to current methods.

Large language models (LLMs) excel at few-shot in-context learning (ICL) -- learning from a few examples provided in context at inference, without any weight updates. Newly expanded context windows allow us to investigate ICL with hundreds or thousands of examples -- the many-shot regime. Going from few-shot to many-shot, we observe significant performance gains across a wide variety of generative and discriminative tasks. While promising, many-shot ICL can be bottlenecked by the available amount of human-generated examples. To mitigate this limitation, we explore two new settings: Reinforced and Unsupervised ICL. Reinforced ICL uses model-generated chain-of-thought rationales in place of human examples. Unsupervised ICL removes rationales from the prompt altogether, and prompts the model only with domain-specific questions. We find that both Reinforced and Unsupervised ICL can be quite effective in the many-shot regime, particularly on complex reasoning tasks. Finally, we demonstrate that, unlike few-shot learning, many-shot learning is effective at overriding pretraining biases, can learn high-dimensional functions with numerical inputs, and performs comparably to fine-tuning. We also find that inference cost increases linearly in the many-shot regime, and frontier LLMs benefit from many-shot ICL to varying degrees. Our analysis also reveals the limitations of next-token prediction loss as an indicator of downstream ICL performance., Comment: NeurIPS (Spotlight)

Polymer particle size constitutes a crucial characteristic of product quality in polymerization. Raman spectroscopy is an established and reliable process analytical technology for in-line concentration monitoring. Recent approaches and some theoretical considerations show a correlation between Raman signals and particle sizes but do not determine polymer size from Raman spectroscopic measurements accurately and reliably. With this in mind, we propose three alternative machine learning workflows to perform this task, all involving diffusion maps, a nonlinear manifold learning technique for dimensionality reduction: (i) directly from diffusion maps, (ii) alternating diffusion maps, and (iii) conformal autoencoder neural networks. We apply the workflows to a data set of Raman spectra with associated size measured via dynamic light scattering of 47 microgel (cross-linked polymer) samples in a diameter range of 208nm to 483 nm. The conformal autoencoders substantially outperform state-of-the-art methods and results for the first time in a promising prediction of polymer size from Raman spectra., Comment: 51 pages, 12 figures, 4 tables

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

Value functions are a central component of deep reinforcement learning (RL). These functions, parameterized by neural networks, are trained using a mean squared error regression objective to match bootstrapped target values. However, scaling value-based RL methods that use regression to large networks, such as high-capacity Transformers, has proven challenging. This difficulty is in stark contrast to supervised learning: by leveraging a cross-entropy classification loss, supervised methods have scaled reliably to massive networks. Observing this discrepancy, in this paper, we investigate whether the scalability of deep RL can also be improved simply by using classification in place of regression for training value functions. We demonstrate that value functions trained with categorical cross-entropy significantly improves performance and scalability in a variety of domains. These include: single-task RL on Atari 2600 games with SoftMoEs, multi-task RL on Atari with large-scale ResNets, robotic manipulation with Q-transformers, playing Chess without search, and a language-agent Wordle task with high-capacity Transformers, achieving state-of-the-art results on these domains. Through careful analysis, we show that the benefits of categorical cross-entropy primarily stem from its ability to mitigate issues inherent to value-based RL, such as noisy targets and non-stationarity. Overall, we argue that a simple shift to training value functions with categorical cross-entropy can yield substantial improvements in the scalability of deep RL at little-to-no cost.

An increasing number of studies have utilized interactive deep learning as the analytic model of visual analytics systems for complex sensemaking tasks. In these systems, traditional interactive dimensionality reduction (DR) models are commonly utilized to build a bi-directional bridge between high-dimensional deep learning representations and low-dimensional visualizations. While these systems better capture analysts' intents in the context of human-in-the-loop interactive deep learning, traditional DR cannot support several desired properties for visual analytics, including out-of-sample extensions, stability, and real-time inference. To avoid this issue, we propose the neural design framework of semantic interaction for interactive deep learning. In our framework, we replace the traditional DR with a neural projection network and append it to the deep learning model as the task-specific output layer. Therefore, the analytic model (deep learning) and visualization method (interactive DR) form one integrated end-to-end trainable deep neural network. In order to understand the performance of the neural design in comparison to the state-of-the-art, we systematically performed two complementary studies, a human-centered qualitative case study and an algorithm-centered simulation-based quantitative experiment. The results of these studies indicate that the neural design can give semantic interaction systems substantial advantages while still keeping comparable inference ability compared to the state-of-the-art model., Comment: 19 pages, 9 figures

How to automatically design better machine learning programs is an open problem within AutoML. While evolution has been a popular tool to search for better ML programs, using learning itself to guide the search has been less successful and less understood on harder problems but has the promise to dramatically increase the speed and final performance of the optimization process. We propose guiding evolution with a binary discriminator, trained online to distinguish which program is better given a pair of programs. The discriminator selects better programs without having to perform a costly evaluation and thus speed up the convergence of evolution. Our method can encode a wide variety of ML components including symbolic optimizers, neural architectures, RL loss functions, and symbolic regression equations with the same directed acyclic graph representation. By combining this representation with modern GNNs and an adaptive mutation strategy, we demonstrate our method can speed up evolution across a set of diverse problems including a 3.7x speedup on the symbolic search for ML optimizers and a 4x speedup for RL loss functions.

Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety that ties together data and their maximum likelihood estimators. We construct this ideal for the large class of toric models and find a Gr\"{o}bner basis in the case of complete and joint independence models arising from multi-way contingency tables. All of our constructions are implemented in $\textit{Macaulay2}$ in a package $\texttt{LikelihoodGeometry}$ along with other tools of use in algebraic statistics. We end with an experimental section using these implementations on several interesting examples., Comment: 15 pages

Language model agents (LMA) recently emerged as a promising paradigm on muti-step decision making tasks, often outperforming humans and other reinforcement learning agents. Despite the promise, their performance on real-world applications that often involve combinations of tasks is still underexplored. In this work, we introduce a new benchmark, called CompWoB -- 50 new compositional web automation tasks reflecting more realistic assumptions. We show that while existing prompted LMAs (gpt-3.5-turbo or gpt-4) achieve 94.0% average success rate on base tasks, their performance degrades to 24.9% success rate on compositional tasks. On the other hand, transferred LMAs (finetuned only on base tasks) show less generalization gap, dropping from 85.4% to 54.8%. By balancing data distribution across tasks, we train a new model, HTML-T5++, that surpasses human-level performance (95.2%) on MiniWoB, and achieves the best zero-shot performance on CompWoB (61.5%). While these highlight the promise of small-scale finetuned and transferred models for task compositionality, their performance further degrades under different instruction compositions changing combinational order. In contrast to the recent remarkable success of LMA, our benchmark and detailed analysis emphasize the necessity of building LMAs that are robust and generalizable to task compositionality for real-world deployment., Comment: Code: https://github.com/google-research/google-research/tree/master/compositional_rl/compwob

We propose a framework for classifying the capabilities and behavior of Artificial General Intelligence (AGI) models and their precursors. This framework introduces levels of AGI performance, generality, and autonomy, providing a common language to compare models, assess risks, and measure progress along the path to AGI. To develop our framework, we analyze existing definitions of AGI, and distill six principles that a useful ontology for AGI should satisfy. With these principles in mind, we propose "Levels of AGI" based on depth (performance) and breadth (generality) of capabilities, and reflect on how current systems fit into this ontology. We discuss the challenging requirements for future benchmarks that quantify the behavior and capabilities of AGI models against these levels. Finally, we discuss how these levels of AGI interact with deployment considerations such as autonomy and risk, and emphasize the importance of carefully selecting Human-AI Interaction paradigms for responsible and safe deployment of highly capable AI systems., Comment: version 4 - Position Paper accepted to ICML 2024. Note that due to ICML position paper titling format requirements, the title has changed slightly from that of the original arXiv pre-print. The original pre-print title was "Levels of AGI: Operationalizing Progress on the Path to AGI" but the official published title for ICML 2024 is "Levels of AGI for Operationalizing Progress on the Path to AGI"

Simulation is an essential tool to develop and benchmark autonomous vehicle planning software in a safe and cost-effective manner. However, realistic simulation requires accurate modeling of nuanced and complex multi-agent interactive behaviors. To address these challenges, we introduce Waymax, a new data-driven simulator for autonomous driving in multi-agent scenes, designed for large-scale simulation and testing. Waymax uses publicly-released, real-world driving data (e.g., the Waymo Open Motion Dataset) to initialize or play back a diverse set of multi-agent simulated scenarios. It runs entirely on hardware accelerators such as TPUs/GPUs and supports in-graph simulation for training, making it suitable for modern large-scale, distributed machine learning workflows. To support online training and evaluation, Waymax includes several learned and hard-coded behavior models that allow for realistic interaction within simulation. To supplement Waymax, we benchmark a suite of popular imitation and reinforcement learning algorithms with ablation studies on different design decisions, where we highlight the effectiveness of routes as guidance for planning agents and the ability of RL to overfit against simulated agents.