Aligning large language models (LLMs) with human preferences has gained significant attention, with Proximal Policy Optimization (PPO) as a standard yet computationally expensive method and Direct Preference Optimization (DPO) as a more efficient alternative. While DPO offers simplicity, it remains underutilized in state-of-the-art LLMs, suggesting potential limitations. In this work, we revisit DPO, analyzing its theoretical foundations and empirical performance to bridge this gap. We identify three key properties—termed \textbf{3D}-properties—that emerge from DPO’s learning process: \textbf{D}rastic drop in rejected response likelihood, \textbf{D}egradation into response suppression, and \textbf{D}ispersion effect on unseen responses. We show that these issues arise from DPO’s optimization dynamics, where the interaction between chosen and rejected response gradients leads to instability. Our findings are supported by experiments on both a controlled toy model and real-world LLM tasks, including mathematical problem-solving and instruction following. To address these challenges, we propose simple regularization techniques that improve training stability and performance. Additionally, we examine how preference data distribution impacts DPO’s effectiveness, offering insights into how alignment models handle out-of-domain (OOD) data. Our work connects these observations to broader research and provides a theoretical explanation for DPO’s limitations. We hope these insights will guide future advancements in reward-model-free preference learning, bringing it closer to reward-model-based approaches.
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Theory · Domain Adaptation and Transfer Learning
We study continual learning on multiple linear classification tasks by sequentially running gradient descent (GD) for a fixed budget of iterations per each given task. When all tasks are jointly linearly separable and are presented in a cyclic/random order, we show the directional convergence of the trained linear classifier to the joint (offline) max-margin solution. This is surprising because GD training on a single task is implicitly biased towards the individual max-margin solution for the task, and the direction of the joint max-margin solution can be largely different from these individual solutions. Additionally, when tasks are given in a cyclic order, we present a non-asymptotic analysis on cycle-averaged forgetting, revealing that (1) alignment between tasks is indeed closely tied to catastrophic forgetting and backward knowledge transfer and (2) the amount of forgetting vanishes to zero as the cycle repeats. Lastly, we analyze the case where the tasks are no longer jointly separable and show that the model trained in a cyclic order converges to the unique minimum of the joint loss function.
Social Aspects · Accountability, Transparency and Interpretability
Extracting a small subset of crucial rationales from the full input is a key problem in explainability research. The most widely used fundamental criterion for rationale extraction is the maximum mutual information (MMI) criterion. In this paper, we first demonstrate that MMI suffers from diminishing marginal returns. Once part of the rationale has been identified, finding the remaining portions contributes only marginally to increasing the mutual information, making it difficult to use MMI to locate the rest. In contrast to MMI that aims to reproduce the prediction, we seek to identify the parts of the input that the network can actually utilize. This is achieved by comparing how different rationale candidates match the capability space of the weight matrix. The weight matrix of a neural network is typically low-rank, meaning that the linear combinations of its column vectors can only cover part of the directions in a high-dimensional space (high-dimension: the dimensions of an input vector). If an input is fully utilized by the network, it generally matches these directions (e.g., a portion of a hypersphere), resulting in a representation with a high norm. Conversely, if an input primarily falls outside (orthogonal to) these directions, its representation norm will approach zero, behaving like noise that the network cannot effectively utilize. Building on this, we propose using the norms of rationale candidates as an alternative objective to MMI. Through experiments on four text classification datasets and one graph classification dataset using three network architectures (GRUs, BERT, and GCN), we show that our method outperforms MMI and its improved variants in identifying better rationales. We also compare our method with a representative LLM (llama-3.1-8b-instruct) and find that our simple method gets comparable results to it and can sometimes even outperform it.
Deep Learning · Algorithms
Transformers often struggle with *length generalization*, meaning they fail to generalize to sequences longer than those encountered during training. While arithmetic tasks are commonly used to study length generalization, certain tasks are considered notoriously difficult, e.g., multi-operand addition (requiring generalization over both the number of operands and their lengths) and multiplication (requiring generalization over both operand lengths). In this work, we achieve approximately 2–3× length generalization on both tasks, which is the first such achievement in arithmetic Transformers. We design task-specific scratchpads enabling the model to focus on a fixed number of tokens per each next-token prediction step, and apply multi-level versions of *Position Coupling* (Cho et al., 2024; McLeish et al., 2024) to let Transformers know the right position to attend to. On the theory side, we prove that a 1-layer Transformer using our method can solve multi-operand addition, up to operand length and operand count that are exponential in embedding dimension.
Deep Learning · Large Language Models
While a lot of recent research focuses on enhancing the textual reasoning capabilities of Large Language Models (LLMs) by optimizing the multi-agent framework or reasoning chains, several benchmark tasks can be solved with 100\% success through direct coding, which is more scalable and avoids the computational overhead associated with textual iterating and searching. Textual reasoning has inherent limitations in solving tasks with challenges in math, logics, optimization, and searching, which is unlikely to be solved by simply scaling up the model and data size. The recently released OpenAI GPT Code Interpreter and multi-agent frameworks such as AutoGen have demonstrated remarkable proficiency of integrating code generation and execution to solve complex tasks using LLMs. However, based on our experiments on 7 existing popular methods for steering code/text generation in both single- and multi-turn settings with 14 tasks and 6 types of LLMs (including the new O1-preview), currently there is no optimal method to correctly steer LLMs to write code when needed. We discover some interesting patterns on when models use code vs. textual reasoning with the evolution to task complexity and model sizes, which even result in an astonishingly inverse scaling behavior. We also discover that results from LLM written code are not always better than using textual reasoning, even if the task could be solved through code. To mitigate the above issues, we propose three methods to better steer LLM code/text generation and achieve a notable improvement. The costs of token lengths and runtime are thoroughly discussed for all the methods. We believe the problem of steering LLM code/text generation is critical for future research and has much space for further improvement. Project Page, Datasets, and Codes are available at https://yongchao98.github.io/CodeSteer/.
Reinforcement Learning · Deep RL
Linear temporal logic (LTL) has recently been adopted as a powerful formalism for specifying complex, temporally extended tasks in multi-task reinforcement learning (RL). However, learning policies that efficiently satisfy arbitrary specifications not observed during training remains a challenging problem. Existing approaches suffer from several shortcomings: they are often only applicable to finite-horizon fragments of LTL, are restricted to suboptimal solutions, and do not adequately handle safety constraints. In this work, we propose a novel learning approach to address these concerns. Our method leverages the structure of Büchi automata, which explicitly represent the semantics of LTL specifications, to learn policies conditioned on sequences of truth assignments that lead to satisfying the desired formulae. Experiments in a variety of discrete and continuous domains demonstrate that our approach is able to zero-shot satisfy a wide range of finite- and infinite-horizon specifications, and outperforms existing methods in terms of both satisfaction probability and efficiency. Code available at: https://deep-ltl.github.io/
Advances in reinforcement learning (RL) have led to its successful application in complex tasks with continuous state and action spaces. Despite these advances in practice, most theoretical work pertains to finite state and action spaces. We propose building a theoretical understanding of continuous state and action spaces by employing a geometric lens to understand the locally attained set of states. The set of all parametrised policies learnt through a semi-gradient based approach induce a set of attainable states in RL. We show that training dynamics of a two layer neural policy induce a low dimensional manifold of attainable states embedded in the high-dimensional nominal state space trained using an actor-critic algorithm. We prove that, under certain conditions, the dimensionality of this manifold is of the order of the dimensionality of the action space. This is the first result of its kind, linking the geometry of the state space to the dimensionality of the action space. We empirically corroborate this upper bound for four MuJoCo environments and also demonstrate the results in a toy environment with varying dimensionality. We also show the applicability of this theoretical result by introducing a local manifold learning layer to the policy and value function networks to improve the performance in control environments with very high degrees of freedom by changing one layer of the neural network to learn sparse representations.
Deep Learning · Graph Neural Networks
Graph Transformers (GTs), adept at capturing the locality and globality of graphs, have shown promising potential in node classification tasks. Most state-of-the-art GTs succeed through integrating local Graph Neural Networks (GNNs) with their global Self-Attention (SA) modules to enhance structural awareness. Nonetheless, this architecture faces limitations arising from scalability challenges and the trade-off between capturing local and global information. On the one hand, the quadratic complexity associated with the SA modules poses a significant challenge for many GTs, particularly when scaling them to large-scale graphs. Numerous GTs necessitated a compromise, relinquishing certain aspects of their expressivity to garner computational efficiency. On the other hand, GTs face challenges in maintaining detailed local structural information while capturing long-range dependencies. As a result, they typically require significant computational costs to balance the local and global expressivity. To address these limitations, this paper introduces a novel GT architecture, dubbed DUALFormer, featuring a dual-dimensional design of its GNN and SA modules. Leveraging approximation theory from Linearized Transformers and treating the query as the surrogate representation of node features, DUALFormer \emph{efficiently} performs the computationally intensive global SA module on feature dimensions. Furthermore, by such a separation of local and global modules into dual dimensions, DUALFormer achieves a natural balance between local and global expressivity. In theory, DUALFormer can reduce intra-class variance, thereby enhancing the discriminability of node representations. Extensive experiments on eleven real-world datasets demonstrate its effectiveness and efficiency over existing state-of-the-art GTs.
Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits
*Continual learning (CL)* enables deep neural networks to adapt to ever-changing data distributions. In practice, there may be scenarios where annotation is costly, leading to *active continual learning (ACL)*, which performs *active learning (AL)* for the CL scenarios when reducing the labeling cost by selecting the most informative subset is preferable. However, conventional AL strategies are not suitable for ACL, as they focus solely on learning the new knowledge, leading to *catastrophic forgetting* of previously learned tasks. Therefore, ACL requires a new AL strategy that can balance the prevention of catastrophic forgetting and the ability to quickly learn new tasks. In this paper, we propose **AccuACL**, **Accu**mulated informativeness-based **A**ctive **C**ontinual **L**earning, by the novel use of the Fisher information matrix as a criterion for sample selection, derived from a theoretical analysis of the Fisher-optimality preservation properties within the framework of ACL, while also addressing the scalability issue of Fisher information-based AL. Extensive experiments demonstrate that AccuACL significantly outperforms AL baselines across various CL algorithms, increasing the average accuracy and forgetting by 23.8% and 17.0%, respectively, on average.
Deep Learning · Large Language Models
Aligning large language models (LLMs) with human preferences becomes a key component to obtaining state-of-the-art performance, but it yields a huge cost to construct a large human-annotated preference dataset. To tackle this problem, we propose a new framework, Spread Preference Annotation with direct preference judgment (SPA), that boosts the alignment of LLMs using only a very small amount of human-annotated preference data.Our key idea is leveraging the human prior knowledge within the small (seed) data and progressively improving the alignment of LLM, by iteratively generating the responses and learning from them with the self-annotated preference data.To be specific, we propose to derive the preference label from the logits of LLM to explicitly extract the model's inherent preference. Compared to the previous approaches using external reward models or implicit in-context learning, we observe that the proposed approach is significantly more effective.In addition, we introduce a noise-aware preference learning algorithm to mitigate the risk of low quality within generated preference data.Our experimental results demonstrate that the proposed framework significantly boosts the alignment of LLMs.For example, we achieve superior alignment performance on AlpacaEval 2.0 with only 3.3% of the ground-truth preference labels in the Ultrafeedback data compared to the cases using the entire data or state-of-the-art baselines.
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 insufficient for instilling self-correction behavior. In particular, we observe that training via SFT either suffers from a distribution mismatch between the training data and the model's own responses or implicitly prefers only a certain mode of correction behavior that is often not effective at test time. 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 strategy that is effective at test time as opposed to simply fitting high-reward responses for a given prompt. This regularization prescribes running a first phase of RL on a base model to generate a policy initialization that is less susceptible to collapse and then using a reward bonus to amplify self-correction during training. When applied to 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 the MATH and HumanEval benchmarks.
Reinforcement Learning · Everything Else
We present the first mechanistic evidence that model-free reinforcement learning agents can learn to plan. This is achieved by applying a methodology based on concept-based interpretability to a model-free agent in Sokoban -- a commonly used benchmark for studying planning. Specifically, we demonstrate that DRC, a generic model-free agent introduced by [Guez et al. (2019)](https://arxiv.org/abs/1901.03559), uses learned concept representations to internally formulate plans that both predict the long-term effects of actions on the environment and influence action selection. Our methodology involves: (1) probing for planning-relevant concepts, (2) investigating plan formation within the agent's representations, and (3) verifying that discovered plans (in the agent's representations) have a causal effect on the agent's behavior through interventions. We also show that the emergence of these plans coincides with the emergence of a planning-like property: the ability to benefit from additional test-time compute. Finally, we perform a qualitative analysis of the planning algorithm learned by the agent and discover a strong resemblance to parallelized bidirectional search. Our findings advance understanding of the internal mechanisms underlying planning behavior in agents, which is important given the recent trend of emergent planning and reasoning capabilities in LLMs through RL.
As language models grow ever larger, so do their vocabularies.This has shifted the memory footprint of LLMs during training disproportionately to one single layer: the cross-entropy in the loss computation.Cross-entropy builds up a logit matrix with entries for each pair of input tokens and vocabulary items and, for small models, consumes an order of magnitude more memory than the rest of the LLM combined.We propose Cut Cross-Entropy (CCE), a method that computes the cross-entropy loss without materializing the logits for all tokens into global memory.Rather, CCE only computes the logit for the correct token and evaluates the log-sum-exp over all logits on the fly.We implement a custom kernel that performs the matrix multiplications and the log-sum-exp reduction over the vocabulary in flash memory, making global memory consumption for the cross-entropy computation negligible. This has a dramatic effect. Taking the Gemma 2 (2B) model as an example, CCE reduces the memory footprint of the loss computation from 24 GB to 1 MB, and the total training-time memory consumption of the classifier head from 28 GB to 1 GB.To improve the throughput of CCE, we leverage the inherent sparsity of softmax and propose to skip elements of the gradient computation that have a negligible (i.e. below numerical precision) contribution to the gradient.Experiments demonstrate that the dramatic reduction in memory consumption is accomplished without sacrificing training speed or convergence.
The group of permutations $S_n$, also known as the finite symmetric groups, are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over $S_n$ poses significant challenges due to its intractable size and discrete nature. In this paper, we introduce *SymmetricDiffusers*, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over $S_n$ by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performance on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems. Our code is released at <https://github.com/DSL-Lab/SymmetricDiffusers>.
Social Aspects · Privacy-preserving Statistics and Machine Learning
How much of my data was used to train a machine learning model? This is a critical question for data owners assessing the risk of unauthorized usage of their data to train models. However, previous work mistakenly treats this as a binary problem—inferring whether all-or-none or any-or-none of the data was used—which is fragile when faced with real, non-binary data usage risks. To address this, we propose a fine-grained analysis called Dataset Usage Cardinality Inference (DUCI), which estimates the exact proportion of data used. Our algorithm, leveraging debiased membership guesses, matches the performance of the optimal MLE approach (with a maximum error <0.1) but with significantly lower (e.g., $300 \times$ less) computational cost.
Deep Learning · Algorithms
Machine learning is increasingly deployed in safety-critical domains where erroneous predictions may lead to potentially catastrophic consequences, highlighting the need for learning systems to be aware of how confident they are in their own predictions: in other words, 'to know when they do not know’. In this paper, we propose a novel Random-Set Neural Network (RS-NN) approach to classification which predicts *belief functions* (rather than classical probability vectors) over the class list using the mathematics of *random sets*, i.e., distributions over the collection of *sets* of classes. RS-NN encodes the 'epistemic' uncertainty induced by training sets that are insufficiently representative or limited in size via the size of the convex set of probability vectors associated with a predicted belief function. Our approach outperforms state-of-the-art Bayesian and Ensemble methods in terms of accuracy, uncertainty estimation and out-of-distribution (OoD) detection on multiple benchmarks (CIFAR-10 vs SVHN/Intel-Image, MNIST vs FMNIST/KMNIST, ImageNet vs ImageNet-O). RS-NN also scales up effectively to large-scale architectures (e.g. WideResNet-28-10, VGG16, Inception V3, EfficientNetB2 and ViT-Base-16),exhibits remarkable robustness to adversarial attacks and can provide statistical guarantees in a conformal learning setting.
Many real-world user queries (e.g. *"How do to make egg fried rice?"*) could benefit from systems capable of generating responses with both textual steps with accompanying images, similar to a cookbook.Models designed to generate interleaved text and images face challenges in ensuring consistency within and across these modalities.To address these challenges, we present ISG, a comprehensive evaluation framework for interleaved text-and-image generation. ISG leverages a scene graph structure to capture relationships between text and image blocks, evaluating responses on four levels of granularity: holistic, structural, block-level, and image-specific. This multi-tiered evaluation allows for a nuanced assessment of consistency, coherence, and accuracy, and provides interpretable question-answer feedback.In conjunction with ISG, we introduce a benchmark, ISG-Bench, encompassing 1,150 samples across 8 categories and 21 subcategories. This benchmark dataset includes complex language-vision dependencies and golden answers to evaluate models effectively on vision-centric tasks such as style transfer, a challenging area for current models. Using ISG-Bench, we demonstrate that recent unified vision-language models perform poorly on generating interleaved content. While compositional approaches that combine separate language and image models show a 111% improvement over unified models at the holistic level, their performance remains suboptimal at both block and image levels.To facilitate future work, we develop ISG-Agent, a baseline agent employing a *"plan-execute-refine"* pipeline to invoke tools, achieving a 122% performance improvement.
Deep Learning · Generative Models and Autoencoders
While the human brain efficiently handles various computations with a limited number of neurons, traditional deep learning networks require a significant increase in parameters to improve performance. Yet, these parameters are used inefficiently as the networks employ the same amount of computation for inputs of the same size, regardless of the input's complexity. We address this inefficiency by introducing self-introspection capabilities to the network, enabling it to adjust the number of used parameters based on the internal representation of the task and adapt the computation time based on the task complexity. This enables the network to adaptively reuse parameters across tasks, dynamically adjusting the computational effort to match the complexity of the input. We demonstrate the effectiveness of this method on language modeling and computer vision tasks. Notably, our model achieves 96.62\% accuracy on ImageNet with just a three-layer network, surpassing much larger ResNet-50 and EfficientNet. When applied to a transformer architecture, the approach achieves 95.8\%/88.7\% F1 scores on the SQuAD v1.1/v2.0 datasets at negligible parameter cost. These results showcase the potential for dynamic and reflective computation, contributing to the creation of intelligent systems that efficiently manage resources based on input data complexity.
Deep Learning · Generative Models and Autoencoders
While the human brain efficiently handles various computations with a limited number of neurons, traditional deep learning networks require a significant increase in parameters to improve performance. Yet, these parameters are used inefficiently as the networks employ the same amount of computation for inputs of the same size, regardless of the input's complexity. We address this inefficiency by introducing self-introspection capabilities to the network, enabling it to adjust the number of used parameters based on the internal representation of the task and adapt the computation time based on the task complexity. This enables the network to adaptively reuse parameters across tasks, dynamically adjusting the computational effort to match the complexity of the input. We demonstrate the effectiveness of this method on language modeling and computer vision tasks. Notably, our model achieves 96.62\% accuracy on ImageNet with just a three-layer network, surpassing much larger ResNet-50 and EfficientNet. When applied to a transformer architecture, the approach achieves 95.8\%/88.7\% F1 scores on the SQuAD v1.1/v2.0 datasets at negligible parameter cost. These results showcase the potential for dynamic and reflective computation, contributing to the creation of intelligent systems that efficiently manage resources based on input data complexity.
Deep Learning · Theory
In this paper, we propose the *geometric invariance hypothesis (GIH)*, which argues that the input space curvature of a neural network remains invariant under transformation in certain architecture-dependent directions during training. We investigate a simple, non-linear binary classification problem residing on a plane in a high dimensional space and observe that—unlike MPLs—ResNets fail to generalize depending on the orientation of the plane. Motivated by this example, we define a neural network's **average geometry** and **average geometry evolution** as compact *architecture-dependent* summaries of the model's input-output geometry and its evolution during training. By investigating the average geometry evolution at initialization, we discover that the geometry of a neural network evolves according to the data covariance projected onto its average geometry. This means that the geometry only changes in a subset of the input space when the average geometry is low-rank, such as in ResNets. This causes an architecture-dependent invariance property in the input space curvature, which we dub GIH. Finally, we present extensive experimental results to observe the consequences of GIH and how it relates to generalization in neural networks.