GeoCoder: Solving Geometry Problems by Generating Modular Code through Vision-Language Models

Geometry problem-solving demands advanced reasoning abilities to process multimodal inputs and employ mathematical knowledge effectively. Vision-language models (VLMs) have made significant progress in various multimodal tasks. Yet, they still struggle with geometry problems and are significantly limited by their inability to perform mathematical operations not seen during pre-training, such as calculating the cosine of an arbitrary angle, and by difficulties in correctly applying relevant geometry formulas. To overcome these challenges, we present GeoCoder, which leverages modular code-finetuning to generate and execute code using a predefined geometry function library. By executing the code, we achieve accurate and deterministic calculations, contrasting the stochastic nature of autoregressive token prediction, while the function library minimizes errors in formula usage. We also propose a multimodal retrieval-augmented variant of GeoCoder, named RAG-GeoCoder, which incorporates a non-parametric memory module for retrieving functions from the geometry library, thereby reducing reliance on parametric memory. Our modular code-finetuning approach enhances the geometric reasoning capabilities of VLMs, yielding an average improvement of over 16% across various question complexities on the GeomVerse dataset compared to other finetuning methods.

Smaller, Weaker, Yet Better: Training LLM Reasoners via Compute-Optimal Sampling

Training on high-quality synthetic data from strong language models (LMs) is a common strategy to improve the reasoning performance of LMs. In this work, we revisit whether this strategy is compute-optimal under a fixed inference budget (e.g., FLOPs). To do so, we investigate the trade-offs between generating synthetic data using a stronger but more expensive (SE) model versus a weaker but cheaper (WC) model. We evaluate the generated data across three key metrics: coverage, diversity, and false positive rate, and show that the data from WC models may have higher coverage and diversity, but also exhibit higher false positive rates. We then finetune LMs on data from SE and WC models in different settings: knowledge distillation, self-improvement, and a novel weak-to-strong improvement setup where a weaker LM teaches reasoning to a stronger LM. Our findings reveal that models finetuned on WC-generated data consistently outperform those trained on SE-generated data across multiple benchmarks and multiple choices of WC and SE models. These results challenge the prevailing practice of relying on SE models for synthetic data generation, suggesting that WC may be the compute-optimal approach for training advanced LM reasoners.

Generative Verifiers: Reward Modeling as Next-Token Prediction

Verifiers or reward models are often used to enhance the reasoning performance of large language models (LLMs). A common approach is the Best-of-N method, where N candidate solutions generated by the LLM are ranked by a verifier, and the best one is selected. While LLM-based verifiers are typically trained as discriminative classifiers to score solutions, they do not utilize the text generation capabilities of pretrained LLMs. To overcome this limitation, we instead propose training verifiers using the ubiquitous next-token prediction objective, jointly on verification and solution generation. Compared to standard verifiers, such generative verifiers (GenRM) can benefit from several advantages of LLMs: they integrate seamlessly with instruction tuning, enable chain-of-thought reasoning, and can utilize additional inference-time compute via majority voting for better verification. We demonstrate that when using Gemma-based verifiers on algorithmic and grade-school math reasoning tasks, GenRM outperforms discriminative verifiers and LLM-as-a-Judge, showing a 16-64% improvement in the percentage of problems solved with Best-of-N. Furthermore, we show that GenRM scales favorably across dataset size, model capacity, and inference-time compute.

Gemma 2: Improving Open Language Models at a Practical Size

In this work, we introduce Gemma 2, a new addition to the Gemma family of lightweight, state-of-the-art open models, ranging in scale from 2 billion to 27 billion parameters. In this new version, we apply several known technical modifications to the Transformer architecture, such as interleaving local-global attentions (Beltagy et al., 2020a) and group-query attention (Ainslie et al., 2023). We also train the 2B and 9B models with knowledge distillation (Hinton et al., 2015) instead of next token prediction. The resulting models deliver the best performance for their size, and even offer competitive alternatives to models that are 2-3 times bigger. We release all our models to the community.

SocialQuotes: Learning Contextual Roles of Social Media Quotes on the Web

Web authors frequently embed social media to support and enrich their content, creating the potential to derive web-based, cross-platform social media representations that can enable more effective social media retrieval systems and richer scientific analyses. As step toward such capabilities, we introduce a novel language modeling framework that enables automatic annotation of roles that social media entities play in their embedded web context. Using related communication theory, we liken social media embeddings to quotes, formalize the page context as structured natural language signals, and identify a taxonomy of roles for quotes within the page context. We release SocialQuotes, a new data set built from the Common Crawl of over 32 million social quotes, 8.3k of them with crowdsourced quote annotations. Using SocialQuotes and the accompanying annotations, we provide a role classification case study, showing reasonable performance with modern-day LLMs, and exposing explainable aspects of our framework via page content ablations. We also classify a large batch of un-annotated quotes, revealing interesting cross-domain, cross-platform role distributions on the web.

ReMI: A Dataset for Reasoning with Multiple Images

With the continuous advancement of large language models (LLMs), it is essential to create new benchmarks to effectively evaluate their expanding capabilities and identify areas for improvement. This work focuses on multi-image reasoning, an emerging capability in state-of-the-art LLMs. We introduce ReMI, a dataset designed to assess LLMs' ability to Reason with Multiple Images. This dataset encompasses a diverse range of tasks, spanning various reasoning domains such as math, physics, logic, code, table/chart understanding, and spatial and temporal reasoning. It also covers a broad spectrum of characteristics found in multi-image reasoning scenarios. We have benchmarked several cutting-edge LLMs using ReMI and found a substantial gap between their performance and human-level proficiency. This highlights the challenges in multi-image reasoning and the need for further research. Our analysis also reveals the strengths and weaknesses of different models, shedding light on the types of reasoning that are currently attainable and areas where future models require improvement. To foster further research in this area, we are releasing ReMI publicly: https://huggingface.co/datasets/mehrankazemi/ReMI.

Test of Time: A Benchmark for Evaluating LLMs on Temporal Reasoning

Large language models (LLMs) have showcased remarkable reasoning capabilities, yet they remain susceptible to errors, particularly in temporal reasoning tasks involving complex temporal logic. Existing research has explored LLM performance on temporal reasoning using diverse datasets and benchmarks. However, these studies often rely on real-world data that LLMs may have encountered during pre-training or employ anonymization techniques that can inadvertently introduce factual inconsistencies. In this work, we address these limitations by introducing novel synthetic datasets specifically designed to assess LLM temporal reasoning abilities in various scenarios. The diversity of question types across these datasets enables systematic investigation into the impact of the problem structure, size, question type, fact order, and other factors on LLM performance. Our findings provide valuable insights into the strengths and weaknesses of current LLMs in temporal reasoning tasks. To foster further research in this area, we are open-sourcing the datasets and evaluation framework used in our experiments: https://huggingface.co/datasets/baharef/ToT.

Understanding Transformer Reasoning Capabilities via Graph Algorithms

Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding of their algorithmic reasoning capabilities in realistic parameter regimes is lacking. We investigate this question in terms of the network's depth, width, and number of extra tokens for algorithm execution. Our novel representational hierarchy separates 9 algorithmic reasoning problems into classes solvable by transformers in different realistic parameter scaling regimes. We prove that logarithmic depth is necessary and sufficient for tasks like graph connectivity, while single-layer transformers with small embedding dimensions can solve contextual retrieval tasks. We also support our theoretical analysis with ample empirical evidence using the GraphQA benchmark. These results show that transformers excel at many graph reasoning tasks, even outperforming specialized graph neural networks.

Using Domain Knowledge to Guide Dialog Structure Induction via Neural Probabilistic Soft Logic

Dialog Structure Induction (DSI) is the task of inferring the latent dialog structure (i.e., a set of dialog states and their temporal transitions) of a given goal-oriented dialog. It is a critical component for modern dialog system design and discourse analysis. Existing DSI approaches are often purely data-driven, deploy models that infer latent states without access to domain knowledge, underperform when the training corpus is limited/noisy, or have difficulty when test dialogs exhibit distributional shifts from the training domain. This work explores a neural-symbolic approach as a potential solution to these problems. We introduce Neural Probabilistic Soft Logic Dialogue Structure Induction (NEUPSL DSI), a principled approach that injects symbolic knowledge into the latent space of a generative neural model. We conduct a thorough empirical investigation on the effect of NEUPSL DSI learning on hidden representation quality, few-shot learning, and out-of-domain generalization performance. Over three dialog structure induction datasets and across unsupervised and semi-supervised settings for standard and cross-domain generalization, the injection of symbolic knowledge using NEUPSL DSI provides a consistent boost in performance over the canonical baselines.

Let Your Graph Do the Talking: Encoding Structured Data for LLMs

How can we best encode structured data into sequential form for use in large language models (LLMs)? In this work, we introduce a parameter-efficient method to explicitly represent structured data for LLMs. Our method, GraphToken, learns an encoding function to extend prompts with explicit structured information. Unlike other work which focuses on limited domains (e.g. knowledge graph representation), our work is the first effort focused on the general encoding of structured data to be used for various reasoning tasks. We show that explicitly representing the graph structure allows significant improvements to graph reasoning tasks. Specifically, we see across the board improvements - up to 73% points - on node, edge and, graph-level tasks from the GraphQA benchmark.