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Publications
Tight Lower Bounds and Improved Convergence in Performative Prediction
Performative prediction is a framework accounting for the shift in the data distribution induced by the prediction of a model deployed in th… (voir plus)e real world. Ensuring rapid convergence to a stable solution where the data distribution remains the same after the model deployment is crucial, especially in evolving environments. This paper extends the Repeated Risk Minimization (RRM) framework by utilizing historical datasets from previous retraining snapshots, yielding a class of algorithms that we call Affine Risk Minimizers and enabling convergence to a performatively stable point for a broader class of problems. We introduce a new upper bound for methods that use only the final iteration of the dataset and prove for the first time the tightness of both this new bound and the previous existing bounds within the same regime. We also prove that utilizing historical datasets can surpass the lower bound for last iterate RRM, and empirically observe faster convergence to the stable point on various performative prediction benchmarks. We offer at the same time the first lower bound analysis for RRM within the class of Affine Risk Minimizers, quantifying the potential improvements in convergence speed that could be achieved with other variants in our framework.
In many domains, such as healthcare, time-series data is irregularly sampled with varying intervals between observations. This creates chall… (voir plus)enges for classical time-series models that require equally spaced data. To address this, we propose a novel time-series Transformer called **Trajectory Generative Pre-trained Transformer (TrajGPT)**. It introduces a data-dependent decay mechanism that adaptively forgets irrelevant information based on clinical context. By interpreting TrajGPT as ordinary differential equations (ODEs), our approach captures continuous dynamics from sparse and irregular time-series data. Experimental results show that TrajGPT, with its time-specific inference approach, accurately predicts trajectories without requiring task-specific fine-tuning.
In many domains, such as healthcare, time-series data is irregularly sampled with varying intervals between observations. This creates chall… (voir plus)enges for classical time-series models that require equally spaced data. To address this, we propose a novel time-series Transformer called **Trajectory Generative Pre-trained Transformer (TrajGPT)**. It introduces a data-dependent decay mechanism that adaptively forgets irrelevant information based on clinical context. By interpreting TrajGPT as ordinary differential equations (ODEs), our approach captures continuous dynamics from sparse and irregular time-series data. Experimental results show that TrajGPT, with its time-specific inference approach, accurately predicts trajectories without requiring task-specific fine-tuning.
Despite its widespread adoption, Adam's advantage over Stochastic Gradient Descent (SGD) lacks a comprehensive theoretical explanation. This… (voir plus) paper investigates Adam's sensitivity to rotations of the parameter space. We demonstrate that Adam's performance in training transformers degrades under random rotations of the parameter space, indicating a crucial sensitivity to the choice of basis. This reveals that conventional rotation-invariant assumptions are insufficient to capture Adam's advantages theoretically. To better understand the rotation-dependent properties that benefit Adam, we also identify structured rotations that preserve or even enhance its empirical performance. We then examine the rotation-dependent assumptions in the literature, evaluating their adequacy in explaining Adam's behavior across various rotation types. This work highlights the need for new, rotation-dependent theoretical frameworks to fully understand Adam's empirical success in modern machine learning tasks.
Linear mode connectivity (LMC) has become a topic of great interest in recent years. It has been empirically demonstrated that popular deep … (voir plus)learning models trained from different initializations exhibit linear model connectivity up to permutation. Based on this, several approaches for finding a permutation of the model's features or weights have been proposed leading to several popular methods for model merging. These methods enable the simple averaging of two models to create a new high-performance model. However, besides accuracy, the properties of these models and their relationships to the representations of the models they derive from are poorly understood.
In this work, we study the inner mechanisms behind LMC in model merging through the lens of classic feature visualization methods. Focusing on convolutional neural networks (CNNs) we make several observations that shed light on the underlying mechanisms of model merging by permute and average.
Linear mode connectivity (LMC) has become a topic of great interest in recent years. It has been empirically demonstrated that popular deep … (voir plus)learning models trained from different initializations exhibit linear model connectivity up to permutation. Based on this, several approaches for finding a permutation of the model's features or weights have been proposed leading to several popular methods for model merging. These methods enable the simple averaging of two models to create a new high-performance model. However, besides accuracy, the properties of these models and their relationships to the representations of the models they derive from are poorly understood.
In this work, we study the inner mechanisms behind LMC in model merging through the lens of classic feature visualization methods. Focusing on convolutional neural networks (CNNs) we make several observations that shed light on the underlying mechanisms of model merging by permute and average.
The performance of deep neural networks is enhanced by ensemble methods, which average the output of several models. However, this comes at … (voir plus)an increased cost at inference. Weight averaging methods aim at balancing the generalization of ensembling and the inference speed of a single model by averaging the parameters of an ensemble of models. Yet, naive averaging results in poor performance as models converge to different loss basins, and aligning the models to improve the performance of the average is challenging. Alternatively, inspired by distributed training, methods like DART and PAPA have been proposed to train several models in parallel such that they will end up in the same basin, resulting in good averaging accuracy. However, these methods either compromise ensembling accuracy or demand significant communication between models during training. In this paper, we introduce WASH, a novel distributed method for training model ensembles for weight averaging that achieves state-of-the-art image classification accuracy. WASH maintains models within the same basin by randomly shuffling a small percentage of weights during training, resulting in diverse models and lower communication costs compared to standard parameter averaging methods.
Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet dem… (voir plus)and for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core"skills"from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an"out of distribution"task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH
Sparse autoencoders (SAEs) have been central to the effort of finding interpretable and disentangled directions of representation spaces in … (voir plus)neural networks, in both image and text domains. While the efficacy and pitfalls of this method in the vision domain are well-studied, there is a lack of corresponding results, both qualitative and quantitative, for the text domain. We define and train language models on a set of formal grammars, and train SAEs on the latent representations of these models under a wide variety of hyperparameter settings. We identify several interpretable latents in the SAEs, and formulate a scaling law defining the relationship between the reconstruction loss of SAEs and their hidden size. We show empirically that the presence of latents correlating to certain features of the input does not imply a causal function in the computation and that the performance of SAEs is highly sensitive to inductive biases.
Scientific research often seeks to understand the causal structure underlying high-level variables in a system. For example, climate scienti… (voir plus)sts study how phenomena, such as El Ni\~no, affect other climate processes at remote locations across the globe. However, scientists typically collect low-level measurements, such as geographically distributed temperature readings. From these, one needs to learn both a mapping to causally-relevant latent variables, such as a high-level representation of the El Ni\~no phenomenon and other processes, as well as the causal model over them. The challenge is that this task, called causal representation learning, is highly underdetermined from observational data alone, requiring other constraints during learning to resolve the indeterminacies. In this work, we consider a temporal model with a sparsity assumption, namely single-parent decoding: each observed low-level variable is only affected by a single latent variable. Such an assumption is reasonable in many scientific applications that require finding groups of low-level variables, such as extracting regions from geographically gridded measurement data in climate research or capturing brain regions from neural activity data. We demonstrate the identifiability of the resulting model and propose a differentiable method, Causal Discovery with Single-parent Decoding (CDSD), that simultaneously learns the underlying latents and a causal graph over them. We assess the validity of our theoretical results using simulated data and showcase the practical validity of our method in an application to real-world data from the climate science field.
A key objective of interpretability research on large language models (LLMs) is to develop methods for robustly steering models toward desir… (voir plus)ed behaviors. To this end, two distinct approaches to interpretability -- ``bottom-up"and ``top-down"-- have been presented, but there has been little quantitative comparison between them. We present a case study comparing the effectiveness of representative vector steering methods from each branch: function vectors (FV; arXiv:2310.15213), as a bottom-up method, and in-context vectors (ICV; arXiv:2311.06668) as a top-down method. While both aim to capture compact representations of broad in-context learning tasks, we find they are effective only on specific types of tasks: ICVs outperform FVs in behavioral shifting, whereas FVs excel in tasks requiring more precision. We discuss the implications for future evaluations of steering methods and for further research into top-down and bottom-up steering given these findings.
