ICML 2024 Papers

Self-attention and masked self-attention are at the heart of Transformers' outstanding success. Still, our mathematical understanding of attention, in particular of its Lipschitz properties — which are key when it comes to analyzing robustness and expressive power — is incomplete. We provide a detailed study of the Lipschitz constant of self-attention in several practical scenarios, discussing the impact of the sequence length $n$ and layer normalization on the local Lipschitz constant of both unmasked and masked self-attention. In particular, we show that for inputs of length $n$ in any compact set, the Lipschitz constant of self-attention is bounded by $\sqrt{n}$ up to a constant factor and that this bound is tight for reasonable sequence lengths. When the sequence length $n$ is too large for the previous bound to be tight, which we refer to as the mean-field regime, we provide an upper bound and a matching lower bound which are independent of $n$. Our mean-field framework for masked self-attention is novel and of independent interest. Our experiments on pretrained and randomly initialized BERT and GPT-2 support our theoretical findings.

RNA properties, such as function and stability, are intricately tied to their two-dimensional conformations. This has spurred the development of computational models for predicting the RNA secondary structures, leveraging dynamic programming or machine learning (ML) techniques. These structures are governed by specific rules; for example, only Watson-Crick and Wobble pairs are allowed, and sequences must not form sharp bends. Recent efforts introduced a systematic approach to post-process the predictions made by ML algorithms, aiming to modify them to respect the constraints. However, we still observe instances violating the requirements, significantly reducing biological relevance. To address this challenge, we present a novel post-processing framework for ML-based predictions on RNA secondary structures, inspired by the assignment problem in integer linear programming. Our algorithm offers a theoretical guarantee, ensuring that the resulting predictions adhere to the fundamental constraints of RNAs. Empirical evidence supports the efficacy of our approach, demonstrating improved predictive performance with no constraint violation, while requiring less running time.

This work tackles the problem of geo-localization with a new paradigm using a large vision-language model (LVLM) augmented with human inference knowledge. A primary challenge here is the scarcity of data for training the LVLM - existing street-view datasets often contain numerous low-quality images lacking visual clues, and lack any reasoning inference. To address the data-quality issue, we devise a CLIP-based network to quantify the degree of street-view images being locatable, leading to the creation of a new dataset comprising highly locatable street views. To enhance reasoning inference, we integrate external knowledge obtained from real geo-localization games, tapping into valuable human inference capabilities. The data are utilized to train GeoReasoner, which undergoes fine-tuning through dedicated reasoning and location-tuning stages. Qualitative and quantitative evaluations illustrate that GeoReasoner outperforms counterpart LVLMs by more than 25% at country-level and 38% at city-level geo-localization tasks, and surpasses StreetCLIP performance while requiring fewer training resources. The data and code are available at https://github.com/lingli1996/GeoReasoner.

Sequential decision-making algorithms such as reinforcement learning (RL) in real-world scenarios inevitably face environments with partial observability. This paper scrutinizes the effectiveness of a popular architecture, namely Transformers, in Partially Observable Markov Decision Processes (POMDPs) and reveals its theoretical limitations. We establish that regular languages, which Transformers struggle to model, are reducible to POMDPs. This poses a significant challenge for Transformers in learning POMDP-specific inductive biases, due to their lack of inherent recurrence found in other models like RNNs. This paper casts doubt on the prevalent belief in Transformers as sequence models for RL and proposes to introduce a point-wise recurrent structure. The Deep Linear Recurrent Unit (LRU) emerges as a well-suited alternative for Partially Observable RL, with empirical results highlighting the sub-optimal performance of the Transformer and considerable strength of LRU.

Many real-world tasks require an agent to reason jointly over text and visual objects, (e.g., navigating in public spaces), which we refer to as context-sensitive text-rich visual reasoning. Specifically, these tasks require an understanding of the context in which the text interacts with visual elements within an image. However, there is a lack of existing datasets to benchmark the state-of-the-art multimodal models' capability on context-sensitive text-rich visual reasoning. In this paper, we introduce ConTextual, a novel dataset featuring human-crafted instructions that require context-sensitive reasoning for text-rich images. We conduct experiments to assess the performance of 14 foundation models (GPT-4V, Gemini-Pro-Vision, LLaVA-Next) and establish a human performance baseline. Further, we perform human evaluations of the model responses and observe a significant performance gap of 30.8% between GPT-4V (the current best-performing Large Multimodal Model) and human performance. Our fine-grained analysis reveals that GPT-4V encounters difficulties interpreting time-related data and infographics. However, it demonstrates proficiency in comprehending abstract visual contexts such as memes and quotes. Finally, our qualitative analysis uncovers various factors contributing to poor performance including lack of precise visual perception and hallucinations. Our dataset, code, and leaderboard can be found on the project page https://con-textual.github.io/.

State-of-the-art language models can exhibit reasoning refinement capabilities on math, science or coding tasks. However, recent work demonstrates that even the best models struggle to identify *when and where to refine* without access to external feedback. In this paper, we propose Stepwise ORMs (**SORMs**) which are trained, only on synthetic data, to approximate the expected future reward of the optimal policy or $V^{\star}$ as a form of Process-based reward modeling. Our experiments show that SORMs can more accurately detect incorrect reasoning steps compared to ORMs, thus enabling them to give precise step-level feedback to refinement models. We then train *global* refinement models, which take only the question and a draft solution as input and predict a corrected solution, and *local* refinement models which also take as input a critique indicating the location of the first reasoning error. We generate training data for both models synthetically by reusing data used to train the SORM. We find combining global and local refinements, using the ORM as a reranker, significantly outperforms either one individually, as well as a best of three sample baseline. With this strategy we can improve the accuracy of a LLaMA-2 13B model (already fine-tuned with RL) on GSM8K from 53% to 65% when greedily sampled.

Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create high-quality mathematical reasoning data using frontier LLMs (e.g., GPT-3.5). Inspired by the cognitive mechanism in human mathematical learning, it first extracts topics and knowledge points from seed math questions and then build a concept graph, which is subsequently used to generate new math questions. MathScale exhibits effective scalability along the size axis of the math dataset that we generate. As a result, we create a mathematical reasoning dataset (MathScaleQA) containing two million math question-answer pairs. To evaluate mathematical reasoning abilities of LLMs comprehensively, we construct MWPBench, a benchmark of Math Word Problems, which is a collection of 9 datasets (including GSM8K and MATH) covering K-12, college, and competition level math problems. We apply MathScaleQA to fine-tune open-source LLMs (e.g., LLaMA-2 and Mistral), resulting in significantly improved capabilities in mathematical reasoning. Evaluated on MWPBench, MathScale-7B achieves state-of-the-art performance across all datasets, surpassing its best peers of equivalent size by 42.8% in micro average accuracy and 43.6% in macro average accuracy, respectively.

We propose MM-Vet, an evaluation benchmark that examines large multimodal models (LMMs) on complicated multimodal tasks. Recent LMMs have shown various intriguing abilities, such as solving math problems written on the blackboard, reasoning about events and celebrities in news images, and explaining visual jokes. Rapid model advancements pose challenges to evaluation benchmark development. Problems include: (1) How to systematically structure and evaluate the complicated multimodal tasks; (2) How to design evaluation metrics that work well across question and answer types; and (3) How to give model insights beyond a simple performance ranking. To this end, we present MM-Vet, designed based on the insight that the intriguing ability to solve complicated tasks is often achieved by a generalist model being able to integrate different core vision-language (VL) capabilities. MM-Vet defines 6 core VL capabilities and examines the 16 integrations of interest derived from the capability combination. For evaluation metrics, we propose an LLM-based evaluator for open-ended outputs. The evaluator enables the evaluation across different question types and answer styles, resulting in a unified scoring metric. We evaluate representative LMMs on MM-Vet, providing insights into the capabilities of different LMM system paradigms and models.

Deep learning solvers for partial differential equations typically have limited accuracy. We propose to overcome this problem by using them as preconditioners. More specifically, we apply discretization-invariant neural operators to learn preconditioners for the flexible conjugate gradient method (FCG). Architecture paired with novel loss function and training scheme allows for learning efficient preconditioners that can be used across different resolutions. On the theoretical side, FCG theory allows us to safely use nonlinear preconditioners that can be applied in $O(N)$ operations without constraining the form of the preconditioners matrix. To justify learning scheme components (the loss function and the way training data is collected) we perform several ablation studies. Numerical results indicate that our approach favorably compares with classical preconditioners and allows to reuse of preconditioners learned for lower resolution to the higher resolution data.

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However, these methods face difficulties in processing high-dimensional problems and learning constants due to the large search space, and they don't scale well to unseen problems. In this work, we propose DySymNet, a novel neural-guided **Dy**namic **Sym**bolic **Net**work for SR. Instead of searching for expressions within a large search space, we explore symbolic networks with various structures, guided by reinforcement learning, and optimize them to identify expressions that better-fitting the data. Based on extensive numerical experiments on low-dimensional public standard benchmarks and the well-known SRBench with more variables, DySymNet shows clear superiority over several representative baseline models. Open source code is available at https://github.com/AILWQ/DySymNet.

We present Code Reasoning, Understanding, and eXecution Evaluation, a benchmark consisting of 800 Python functions (3-13 lines). Each function comes with an input-output pair, leading to two natural tasks: input prediction and output prediction. First, we propose a general recipe for generating our execution benchmark by sampling from a model, which can be used for more challenging versions of the benchmark if needed. Second, we evaluate twenty code models on our benchmark and discover that many recent high-scoring models on HumanEval show no improvements on our benchmark. Third, we show that simple CoT and fine-tuning schemes can improve performance on our benchmark but remain far from solving it. The best setup, GPT-4 with chain of thought (CoT), achieves a pass@1 of 75% and 81% on input and output prediction, respectively. In contrast, Code Llama 34B achieves a pass@1 of 50% and 46% on input and output prediction. When it comes to reasoning about code, GPT-4 has a huge edge over other models but still fails consistently on some surprisingly simple Python programs.

Language models (LMs) can solve tasks such as answering questions about tables or images by writing programs. However, using primitive functions often leads to verbose and error-prone programs, and higher-level functions require expert design. To enable better solutions without human labor, we ask code LMs to curate reusable high-level functions, and use them to write solutions. We present TROVE, a training-free method of inducing a verifiable and efficient toolbox of functions, by generating via using, growing, and periodically trimming the toolbox. On 11 datasets from math, table question answering, and image reasoning tasks, TROVE consistently yields simpler solutions with higher accuracy than baselines using CodeLLaMa and previous methods using GPT, while using 79-98% smaller toolboxes. TROVE further enables 31% faster and 13% more accurate human verification than baselines. With the same pipeline, it creates diverse functions for varied tasks and datasets, providing insights into their individual characteristics.

We introduce iterative reasoning through energy diffusion (IRED), a novel framework for learning to reason for a variety of tasks by formulating reasoning and decision-making problems with energy-based optimization. IRED learns energy functions to represent the constraints between input conditions and desired outputs. After training, IRED adapts the number of optimization steps during inference based on problem difficulty, enabling it to solve problems outside its training distribution --- such as more complex Sudoku puzzles, matrix completion with large value magnitudes, and path finding in larger graphs. Key to our method’s success is two novel techniques: learning a sequence of annealed energy landscapes for easier inference and a combination of score function and energy landscape supervision for faster and more stable training. Our experiments show that IRED outperforms existing methods in continuous-space reasoning, discrete-space reasoning, and planning tasks, particularly in more challenging scenarios.

Abductive learning models (ABL) and neural-symbolic predictive models (NeSy) have been recently shown effective, as they allow us to infer labels that are consistent with some prior knowledge by reasoning over high-level concepts extracted from sub-symbolic inputs. However, their generalization ability is affected by reasoning shortcuts: high accuracy on given targets but leveraging intermediate concepts with unintended semantics. Although there have been techniques to alleviate reasoning shortcuts, theoretical efforts on this issue remain to be limited. This paper proposes a simple and effective analysis to quantify harm caused by it and how can mitigate it. We quantify three main factors in how NeSy algorithms are affected by reasoning shortcuts: the complexity of the knowledge base, the sample size, and the hypothesis space. In addition, we demonstrate that ABL can reduce shortcut risk by selecting specific distance functions in consistency optimization, thereby demonstrating its potential and approach to solving shortcut problems. Empirical studies demonstrate the rationality of the analysis. Moreover, the proposal is suitable for many ABL and NeSy algorithms and can be easily extended to handle other cases of reasoning shortcuts.

In proof assistants, the physical proximity between two formal mathematical concepts is a strong predictor of their mutual relevance. Furthermore, lemmas with close proximity regularly exhibit similar proof structures. We show that this _locality_ property can be exploited through online learning techniques to obtain solving agents that far surpass offline learners when asked to prove theorems in an unseen mathematical setting. We extensively benchmark two such online solvers implemented in the Tactician platform for the Coq proof assistant: First, Tactician's online $k$-nearest neighbor solver, which can learn from recent proofs, shows a $1.72\times$ improvement in theorems proved over an offline equivalent. Second, we introduce a graph neural network, Graph2Tac, with a novel approach to build hierarchical representations for new definitions. Graph2Tac's online definition task realizes a $1.5\times$ improvement in theorems solved over an offline baseline. The $k$-NN and Graph2Tac solvers rely on orthogonal online data, making them highly complementary. Their combination improves $1.27\times$ over their individual performances. Both solvers outperform all other general purpose provers for Coq, including CoqHammer, Proverbot9001, and a transformer baseline by at least $1.48\times$ and are available for practical use by end-users.

Large language models (LLMs) have accomplished remarkable reasoning performance in various domains. However, in the domain of reasoning tasks, we discover a frailty: LLMs are surprisingly brittle to the ordering of the premises, despite the fact that such ordering does not alter the underlying task. In particular, we observe that LLMs achieve the best performance when the premise order aligns with the context required in intermediate reasoning steps. For example, in deductive reasoning tasks, presenting the premises in the same order as the ground truth proof in the prompt (as opposed to random ordering) drastically increases the model's accuracy. We first examine the effect of premise ordering on deductive reasoning on a variety of LLMs, and our evaluation shows that even if the model performance is decent on the optimal order, permuting the premise order can cause a performance drop of over 30%. In addition, we release the benchmark R-GSM, based on GSM8K, to examine the ordering effect for mathematical problem-solving, and we again observe a significant drop in accuracy, relative to the original GSM8K benchmark.

Despite the impressive performance in a variety of complex tasks, modern large language models (LLMs) still have trouble dealing with some math problems that are simple and intuitive for humans, such as addition. While we can easily learn basic *rules* of addition and apply them to new problems of any length, LLMs struggle to do the same. Instead, they may rely on similar *cases* seen in the training corpus for help. We define these two different reasoning mechanisms as "*rule-based reasoning*" and "*case-based reasoning*". Since rule-based reasoning is essential for acquiring systematic generalization ability, we aim to explore exactly whether transformers use rule-based or case-based reasoning for math problems. Through carefully designed intervention experiments on five math tasks, we confirm that transformers are performing case-based reasoning, no matter whether scratchpad is used, which aligns with the previous observations that transformers use subgraph matching/shortcut learning to reason. To mitigate such problems, we propose a Rule-Following Fine-Tuning (RFFT) technique to teach transformers to perform rule-based reasoning. Specifically, we provide explicit rules in the input and then instruct transformers to recite and follow the rules step by step. Through RFFT, we successfully enable LLMs fine-tuned on 1-5 digit addition to generalize to up to 12-digit addition with over 95% accuracy, which is over 40% higher than scratchpad. The significant improvement demonstrates that teaching LLMs to use rules explicitly helps them learn rule-based reasoning and generalize better in length. Code is available at https://github.com/GraphPKU/Case_or_Rule.

Recently, deep reinforcement learning has shown promising results for learning fast heuristics to solve routing problems. Meanwhile, most of the solvers suffer from generalizing to an unseen distribution or distributions with different scales. To address this issue, we propose a novel architecture, called Invariant Nested View Transformer (INViT), which is designed to enforce a nested design together with invariant views inside the encoders to promote the generalizability of the learned solver. It applies a modified policy gradient algorithm enhanced with data augmentations. We demonstrate that the proposed INViT achieves a dominant generalization performance on both TSP and CVRP problems with various distributions and different problem scales. Our source code and datasets are available in supplementary materials.