We explore if RL can be useful for symbolic mathematics. Previous work showed contrastive learning can solve linear equations in one variable. We show model-free PPO \cite{schulman2017proximal} augmented with curiosity-based exploration and graph-based actions can solve nonlinear equations such as those involving radicals, exponentials, and trig functions. Our work suggests curiosity-based exploration may be useful for general symbolic reasoning tasks.

Large Language Models (LLMs) rely on the Key-Value (KV) Cache to store token history, enabling efficient decoding of tokens. As the KV-Cache grows, it becomes a major memory and computation bottleneck, however, there is an opportunity to alleviate this bottleneck, especially because prior research has shown that only a small subset of tokens contribute meaningfully to each decoding step. A key challenge in finding these critical tokens is that they are dynamic, and heavily input query-dependent. Existing methods either risk quality by evicting tokens permanently, or retain the full KV-Cache but rely on retrieving chunks (pages) of tokens at generation, failing at dense, context-rich tasks. Additionally, many existing KV-Cache sparsity methods rely on inaccurate proxies for token importance. To address these limitations, we introduce TokenButler, a high-granularity, query-aware predictor that learns to identify these critical tokens. By training a light-weight predictor with less than 1.2% parameter overhead, TokenButler prioritizes tokens based on their contextual, predicted importance. This improves perplexity & downstream accuracy by over 8% relative to SoTA methods for estimating token importance. We evaluate TokenButler on a novel synthetic small-context co-referential retrieval task, demonstrating near-oracle accuracy. Code, models and benchmarks: https://github.com/abdelfattah-lab/TokenButler

Recently machine unlearning (MU) is proposed to remove the imprints of revoked samples from the already trained model parameters, to solve users' privacy concern. Different from the runtime expensive retraining from scratch, there exist two research lines, exact MU and approximate MU with different favorites in terms of accuracy and efficiency. In this paper, we present a novel hybrid strategy on top of them to achieve an overall success. It implements the unlearning operation with an acceptable computation cost, while simultaneously improving the accuracy as much as possible. Specifically, it runs reasonable unlearning techniques by estimating the retraining workloads caused by revocations. If the workload is lightweight, it performs retraining to derive the model parameters consistent with the accurate ones retrained from scratch. Otherwise, it outputs the unlearned model by directly modifying the current parameters, for better efficiency. In particular, to improve the accuracy in the latter case, we propose an optimized version to amend the output model with lightweight runtime penalty. We particularly study the boundary of two approaches in our frameworks to adaptively make the smart selection. Extensive experiments on real datasets validate that our proposals can improve the unlearning efficiency by 1.5$\times$ to 8$\times$ while achieving comparable accuracy.

Chain-of-Thought (CoT) prompting reveals that large language models are capable of performing complex reasoning via intermediate steps. CoT prompting is primarily categorized into three approaches. The first approach utilizes straightforward prompts like ``Let's think step by step'' to generate a sequential thought process before yielding an answer. The second approach makes use of human-crafted, step-by-step demonstrations to guide the model's reasoning process. The third automates the generation of reasoned demonstrations with the 'Let's think step by step'.This approach sometimes leads to reasoning errors, highlighting the need to diversify demonstrations to mitigate its misleading effects. However, diverse demonstrations pose challenges for effective representations. In this work, we propose ECHO, a self-harmonized chain-of-thought prompting method. It consolidates diverse solution paths into a uniform and effective solution pattern.ECHO demonstrates the best overall performance across three reasoning domains.

Large language models (LLMs) demonstrate substantial capabilities in solving math problems. However, they tend to produce hallucinations when given questions containing unreasonable errors. In this paper, we study the behavior of LLMs when faced with unreasonable math problems and further explore their potential to address these problems. We construct the Unreasonable Math Problem (UMP) benchmark to examine the error detection ability of LLMs. Experiments show that LLMs are able to detect unreasonable errors, but still fail in generating non-hallucinatory content. In order to improve their ability of error detection and correction, we further design a strategic prompt template called Critical Calculation and Conclusion(CCC). With CCC, LLMs can better self-evaluate and detect unreasonable errors in math questions, making them more reliable and safe in practical application scenarios.

Recent advancements in Large Multimodal Models (LMMs) have shown promising results in mathematical reasoning within visual contexts, with models approaching human-level performance on existing benchmarks such as MathVista. However, we observe significant limitations in the diversity of questions and breadth of subjects covered by these benchmarks. To address this issue, we present the MATH-Vision (MATH-V) dataset, a meticulously curated collection of 3,040 high-quality mathematical problems with visual contexts sourced from real math competitions. Spanning 16 distinct mathematical disciplines and graded across 5 levels of difficulty, our dataset provides a comprehensive and diverse set of challenges for evaluating the mathematical reasoning abilities of LMMs. Through extensive experimentation, we unveil a notable performance gap between current LMMs and human performance on MATH-V, underscoring the imperative for further advancements in LMMs. Moreover, our detailed categorization allows for a thorough error analysis of LMMs, offering valuable insights to guide future research and development. The project is available at https://mathvision-cuhk.github.io

We introduce a large language model (LLM) based approach to answer complex questions requiring multi-hop numerical reasoning over financial reports. While LLMs have exhibited remarkable performance on various natural language and reasoning tasks, complex reasoning problems often rely on few-shot prompts that require carefully crafted examples. In contrast, our approach uses novel zero-shot prompts that guide the LLM to encode the required reasoning into a Python program or a domain specific language. The generated program is then executed by a program interpreter, thus mitigating the limitations of LLM in performing accurate arithmetic calculations. We evaluate the proposed approach on three financial datasets using some of the recently developed generative pretrained transformer (GPT) models and perform comparisons with various zero-shot baselines. The experimental results demonstrate that our approach significantly improves the accuracy for all the LLMs over their respective baselines. We provide a detailed analysis of the results, generating insights to support our findings. The success of our approach demonstrates the enormous potential to extract complex domain specific numerical reasoning by designing zero-shot prompts to effectively exploit the knowledge embedded in LLMs.

Imagine you had a model that could give you the probability of an input image being a handwritten digit. You could use this model to generate handwritten digits by altering the input. You can make each pixel slightly lighter or slightly darker and see how that affects the output probability. So all you need is a model that tells you how to alter the input to generate a good output. However, how do you train a model like this?