Sometimes I am a Tree: Data Drives Unstable Hierarchical Generalization

Neural networks often favor shortcut heuristics based on surface-level patterns. As one example, language models (LMs) behave like n-gram models early in training. However, to correctly apply grammatical rules, LMs must rely on hierarchical syntactic representations instead of n-grams. In this work, we use cases studies of English grammar to explore how latent structure in training data drives models toward improved out-of-distribution (OOD) generalization.We then investigate how data composition can lead to inconsistent OOD behavior across random seeds and to unstable training dynamics. Our results show that models stabilize in their OOD behavior only when they fully commit to either a surface-level linear rule or a hierarchical rule. The hierarchical rule, furthermore, is induced by grammatically complex sequences with deep embedding structures, whereas the linear rule is induced by simpler sequences. When the data contains a mix of simple and complex examples, potential rules compete; each independent training run either stabilizes by committing to a single rule or remains unstable in its OOD behavior. These conditions lead `stable seeds' to cluster around simple rules, forming bimodal performance distributions across seeds. We also identify an exception to the relationship between stability and generalization: models which memorize patterns from low-diversity training data can overfit stably, with different rules for memorized and unmemorized patterns. Our findings emphasize the critical role of training data in shaping generalization patterns and how competition between data subsets contributes to inconsistent generalization outcomes across random seeds. Code is available at https://github.com/sunnytqin/concept_comp.git.

Adapting Language Models via Token Translation

Modern large language models use a fixed tokenizer to effectively compress text drawn from a source domain. However, applying the same tokenizer to a new target domain often leads to inferior compression, more costly inference, and reduced semantic alignment. To address this deficiency, we introduce Sparse Sinkhorn Token Translation (S2T2). S2T2 trains a tailored tokenizer for the target domain and learns to translate between target and source tokens, enabling more effective reuse of the pre-trained next-source-token predictor. In our experiments with finetuned English language models, S2T2 improves both the perplexity and the compression of out-of-domain protein sequences, outperforming direct finetuning with either the source or target tokenizer. In addition, we find that token translations learned for smaller, less expensive models can be directly transferred to larger, more powerful models to reap the benefits of S2T2 at lower cost.

Mixture of Parrots: Experts improve memorization more than reasoning

The Mixture-of-Experts (MoE) architecture enables a significant increase in the total number of model parameters with minimal computational overhead. However, it is not clear what performance tradeoffs, if any, exist between MoEs and standard dense transformers. In this paper, we show that as we increase the number of experts (while fixing the number of active parameters), the memorization performance consistently increases while the reasoning capabilities saturate. We begin by analyzing the theoretical limitations of MoEs at reasoning. We prove that there exist graph problems that cannot be solved by any number of experts of a certain width; however, the same task can be easily solved by a dense model with a slightly larger width. On the other hand, we find that on memory-intensive tasks, MoEs can effectively leverage a small number of active parameters with a large number of experts to memorize the data. We empirically validate these findings on synthetic graph problems and memory-intensive closed book retrieval tasks. Lastly, we pre-train a series of MoEs and dense transformers and evaluate them on commonly used benchmarks in math and natural language. We find that increasing the number of experts helps solve knowledge-intensive tasks, but fails to yield the same benefits for reasoning tasks.

What is the Right Notion of Distance between Predict-then-Optimize Tasks?

Comparing datasets is a fundamental task in machine learning, essential for various learning paradigms; from evaluating train and test datasets for model generalization to using dataset similarity for detecting data drift. While traditional notions of dataset distances offer principled measures of similarity, their utility has largely been assessed through prediction error minimization. However, in Predict-then-Optimize (PtO) frameworks, where predictions serve as inputs for downstream optimization tasks, model performance is measured through decision regret minimization rather than prediction error minimization. In this work, we (i) show that traditional dataset distances, which rely solely on feature and label dimensions, lack informativeness in the PtO context, and (ii) propose a new dataset distance that incorporates the impacts of downstream decisions. Our results show that this decision-aware dataset distance effectively captures adaptation success in PtO contexts, providing a PtO adaptation bound in terms of dataset distance. Empirically, we show that our proposed distance measure accurately predicts transferability across three different PtO tasks from the literature.

Understanding the Role of Functional Diversity in Weight-Ensembling with Ingredient Selection and Multidimensional Scaling

Weight-ensembles are formed when the parameters of multiple neural networks are directly averaged into a single model. They have demonstrated generalization capability in-distribution (ID) and out-of-distribution (OOD) which is not completely understood, though they are thought to successfully exploit functional diversity allotted by each distinct model. Given a collection of models, it is also unclear which combination leads to the optimal weight-ensemble; the SOTA is a linear-time ``greedy" method. We introduce two novel weight-ensembling approaches to study the link between performance dynamics and the nature of how each method decides to use apply the functionally diverse components, akin to diversity-encouragement in the prediction-ensemble literature. We develop a visualization tool to explain how each algorithm explores various domains defined via pairwise-distances to further investigate selection and algorithms' convergence. Empirical analyses shed perspectives which reinforce how high-diversity enhances weight-ensembling while qualifying the extent to which diversity alone improves accuracy. We also demonstrate that sampling positionally distinct models can contribute just as meaningfully to improvements in a weight-ensemble.

Strongly Isomorphic Neural Optimal Transport Across Incomparable Spaces

Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming the same space for both distributions. However, the setting across ``incomparable spaces'' (e.g., of different dimensionality), corresponding to the Gromov- Wasserstein distance, remains underexplored, with existing methods often imposing restrictive assumptions on the cost function. In this paper, we present a novel neural formulation of the Gromov-Monge (GM) problem rooted in one of its fundamental properties: invariance to strong isomorphisms. We operationalize this property by decomposing the learnable OT map into two components: (i) an approximate strong isomorphism between the source distribution and an intermediate reference distribution, and (ii) a GM-optimal map between this reference and the target distribution. Our formulation leverages and extends the Monge gap regularizer of Uscidda & Cuturi (2023) to eliminate the need for complex architectural requirements of other neural OT methods, yielding a simple but practical method that enjoys favorable theoretical guarantees. Our preliminary empirical results show that our framework provides a promising approach to learn OT maps across diverse spaces.

A Label is Worth a Thousand Images in Dataset Distillation

Data $\textit{quality}$ is a crucial factor in the performance of machine learning models, a principle that dataset distillation methods exploit by compressing training datasets into much smaller counterparts that maintain similar downstream performance. Understanding how and why data distillation methods work is vital not only for improving these methods but also for revealing fundamental characteristics of "good" training data. However, a major challenge in achieving this goal is the observation that distillation approaches, which rely on sophisticated but mostly disparate methods to generate synthetic data, have little in common with each other. In this work, we highlight a largely overlooked aspect common to most of these methods: the use of soft (probabilistic) labels. Through a series of ablation experiments, we study the role of soft labels in depth. Our results reveal that the main factor explaining the performance of state-of-the-art distillation methods is not the specific techniques used to generate synthetic data but rather the use of soft labels. Furthermore, we demonstrate that not all soft labels are created equal; they must contain $\textit{structured information}$ to be beneficial. We also provide empirical scaling laws that characterize the effectiveness of soft labels as a function of images-per-class in the distilled dataset and establish an empirical Pareto frontier for data-efficient learning. Combined, our findings challenge conventional wisdom in dataset distillation, underscore the importance of soft labels in learning, and suggest new directions for improving distillation methods. Code for all experiments is available at https://github.com/sunnytqin/no-distillation.

Continuous Language Model Interpolation for Dynamic and Controllable Text Generation

As large language models (LLMs) have gained popularity for a variety of use cases, making them adaptable and controllable has become increasingly important, especially for user-facing applications. While the existing literature on LLM adaptation primarily focuses on finding a model (or models) that optimizes a single predefined objective, here we focus on the challenging case where the model must dynamically adapt to diverse -- and often changing -- user preferences. For this, we leverage adaptation methods based on linear weight interpolation, casting them as continuous multi-domain interpolators that produce models with specific prescribed generation characteristics on-the-fly. Specifically, we use low-rank updates to fine-tune a base model to various different domains, yielding a set of anchor models with distinct generation profiles. Then, we use the weight updates of these anchor models to parametrize the entire (infinite) class of models contained within their convex hull. We empirically show that varying the interpolation weights yields predictable and consistent change in the model outputs with respect to all of the controlled attributes. We find that there is little entanglement between most attributes and identify and discuss the pairs of attributes for which this is not the case. Our results suggest that linearly interpolating between the weights of fine-tuned models facilitates predictable, fine-grained control of model outputs with respect to multiple stylistic characteristics simultaneously.

Distributional Dataset Distillation with Subtask Decomposition

What does a neural network learn when training from a task-specific dataset? Synthesizing this knowledge is the central idea behind Dataset Distillation, which recent work has shown can be used to compress large datasets into a small set of input-label pairs ($\textit{prototypes}$) that capture essential aspects of the original dataset. In this paper, we make the key observation that existing methods distilling into explicit prototypes are very often suboptimal, incurring in unexpected storage cost from distilled labels. In response, we propose $\textit{Distributional Dataset Distillation}$ (D3), which encodes the data using minimal sufficient per-class statistics and paired with a decoder, we distill dataset into a compact distributional representation that is more memory-efficient compared to prototype-based methods. To scale up the process of learning these representations, we propose $\textit{Federated distillation}$, which decomposes the dataset into subsets, distills them in parallel using sub-task experts and then re-aggregates them. We thoroughly evaluate our algorithm on a three-dimensional metric and show that our method achieves state-of-the-art results on TinyImageNet and ImageNet-1K. Specifically, we outperform the prior art by $6.9\%$ on ImageNet-1K under the storage budget of 2 images per class.

Tag-LLM: Repurposing General-Purpose LLMs for Specialized Domains

Large Language Models (LLMs) have demonstrated remarkable proficiency in understanding and generating natural language. However, their capabilities wane in highly specialized domains underrepresented in the pretraining corpus, such as physical and biomedical sciences. This work explores how to repurpose general LLMs into effective task solvers for specialized domains. We introduce a novel, model-agnostic framework for learning custom input tags, which are parameterized as continuous vectors appended to the LLM's embedding layer, to condition the LLM. We design two types of input tags: domain tags are used to delimit specialized representations (e.g., chemical formulas) and provide domain-relevant context; function tags are used to represent specific functions (e.g., predicting molecular properties) and compress function-solving instructions. We develop a three-stage protocol to learn these tags using auxiliary data and domain knowledge. By explicitly disentangling task domains from task functions, our method enables zero-shot generalization to unseen problems through diverse combinations of the input tags. It also boosts LLM's performance in various specialized domains, such as predicting protein or chemical properties and modeling drug-target interactions, outperforming expert models tailored to these tasks.