Summary The paper proposes a link prediction model that embeds symbols in a hyperbolic space using Poincaré embeddings. In this space, tree structures can more easily be represented as the distance to points increases exponentially w.r.t. The paper is motivated and written well. Furthermore, the presented method is intriguing and I believe it will have a notable impact on link prediction research. My concerns are regarding the comparison to state-of-the-art link prediction and how the method performs if the assumption about a hierarchy in the data is dropped.

Summary: This paper proposes a new way to develop a world model for reinforcement learning. The focus is on the encoding of the visual world, coupled with a world model that learns based on the compressed representation. The world model is a recurrent version of Bishop's (1995, neural networks book, chapter 6) mixture of gaussians network. That network outputs the weights of an MOG (using softmax), the means of the gaussians (linear outputs), and the variance (modeled as e var, so it is a scale parameter). I had not seen a recurrent version of this network before.

Chain-of-thought (CoT) has proven to be a powerful technique for enhancing reasoning in large language models [29, 63]. By instructing the model to break complex problems into smaller, manageable steps, CoT facilitates more efficient reasoning and better generalization, particularly in algorithmic and logical tasks [32, 45, 60]. Building on this, performance can be further improved through multi-step prompting and multi-path sampling techniques [10, 20, 59, 74, 75]. This focus on CoT within in-context learning has since expanded to more structured learning approaches [6, 69]. By adding reasoning examples of CoT style to the instruction-tuning dataset, models enhance their problem-solving abilities more effectively than relying solely on CoT during prompting [11, 72]. As a result, CoT is now shaping a new paradigm in language model development, marking a shift from simply scaling data [22, 25] to focusing on advanced reasoning strategies [39], which leads to more effective learning outcomes. While CoT's success is well-established, understanding why it works is still a hotly debated topic [48, 51]. Recent theoretical studies suggest that CoT enhances a model's expressiveness, increasing its representational capacity when the sequence is long enough [18, 37]. However, expressivity alone does not guarantee success.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, state-of-the-art embedding methods typically do not account for latent hierarchical structures which are characteristic for many complex symbolic datasets. In this work, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space - or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We present an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings can outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

We develop a method for comparing hierarchical image representations in terms of their ability to explain perceptual sensitivity in humans. Specifically, we utilize Fisher information to establish a model-derived prediction of sensitivity to local perturbations of an image. For a given image, we compute the eigenvectors of the Fisher information matrix with largest and smallest eigenvalues, corresponding to the model-predicted most-and least-noticeable image distortions, respectively. For human subjects, we then measure the amount of each distortion that can be reliably detected when added to the image. We use this method to test the ability of a variety of representations to mimic human perceptual sensitivity.

Neural Information Processing Systems http://nips.cc/

The ability of graph neural networks (GNNs) to count homomorphisms has recently been proposed as a practical and fine-grained measure of their expressive power. Although several existing works have investigated the homomorphism counting power of certain GNN families, a simple and unified framework for analyzing the problem is absent. In this paper, we first propose \emph{generalized folklore Weisfeiler-Leman (GFWL)} algorithms as a flexible design basis for expressive GNNs, and then provide a theoretical framework to algorithmically determine the homomorphism counting power of an arbitrary class of GNN within the GFWL design space. As the considered design space is large enough to accommodate almost all known powerful GNNs, our result greatly extends all existing works, and may find its application in the automation of GNN model design.

Large Language Models have demonstrated remarkable abilities across various tasks, with Chain-of-Thought (CoT) prompting emerging as a key technique to enhance reasoning capabilities. However, existing research primarily focuses on improving performance, lacking a comprehensive framework to explain and understand the fundamental factors behind CoT's success. To bridge this gap, we introduce a novel perspective grounded in the Hopfieldian view of cognition in cognitive neuroscience. We establish a connection between CoT reasoning and key cognitive elements such as stimuli, actions, neural populations, and representation spaces. From our view, we can understand the reasoning process as the movement between these representation spaces. Building on this insight, we develop a method for localizing reasoning errors in the response of CoTs. Moreover, we propose the Representation-of-Thought (RoT) framework, which leverages the robustness of low-dimensional representation spaces to enhance the robustness of the reasoning process in CoTs. Experimental results demonstrate that RoT improves the robustness and interpretability of CoT reasoning while offering fine-grained control over the reasoning process.

While fine-tuning pretrained models has become common practice, these models often underperform outside their specific domains. Recently developed model merging techniques enable the direct integration of multiple models, each fine-tuned for distinct tasks, into a single model. This strategy promotes multitasking capabilities without requiring retraining on the original datasets. However, existing methods fall short in addressing potential conflicts and complex correlations between tasks, especially in parameter-level adjustments, posing a challenge in effectively balancing parameter competition across various tasks. This paper introduces an innovative technique named PCB-Merging (Parameter Competition Balancing), a lightweight and training-free technique that adjusts the coefficients of each parameter for effective model merging. PCB-Merging employs intra-balancing to gauge parameter significance within individual tasks and inter-balancing to assess parameter similarities across different tasks. Parameters with low importance scores are dropped, and the remaining ones are rescaled to form the final merged model. We assessed our approach in diverse merging scenarios, including cross-task, cross-domain, and cross-training configurations, as well as out-of-domain generalization. The experimental results reveal that our approach achieves substantial performance enhancements across multiple modalities, domains, model sizes, number of tasks, fine-tuning forms, and large language models, outperforming existing model merging methods. The code is publicly available at: \url{https://github.com/duguodong7/pcb-merging}.

Modeling human preferences is crucial for aligning foundation models with human values. Traditional reward modeling methods, such as the Bradley-Terry (BT) reward model, fall short in expressiveness, particularly in addressing intransitive preferences. Although supervised pair preference models (PairPM) can express general preferences, their implementation is highly ad-hoc and cannot guarantee a consistent preference probability of compared pairs. Additionally, they impose high computational costs due to their quadratic query complexity when comparing multiple responses. In this paper, we introduce preference representation learning, an approach that embeds responses into a latent space to capture intricate preference structures efficiently, achieving linear query complexity. Additionally, we propose preference score-based General Preference Optimization (GPO), which generalizes reward-based reinforcement learning from human feedback. Experimental results show that our General Preference representation model (GPM) outperforms the BT reward model on the RewardBench benchmark with a margin of up to 5.6% and effectively models cyclic preferences where any BT reward model behaves like a random guess. Furthermore, evaluations on downstream tasks such as AlpacaEval2.0 and MT-Bench, following the language model post-training with GPO and our general preference model, reveal substantial performance improvements with margins up to 9.3%. These findings indicate that our method may enhance the alignment of foundation models with nuanced human values. The code is available at https://github.com/general-preference/general-preference-model.