ICLR 2025 Papers

Time-series modeling is broadly adopted to capture underlying patterns present in historical data, allowing prediction of future values. However, one crucial aspect of such modeling is often overlooked: in highly dynamic environments, data distributions can shift drastically within a second or less. Under these circumstances, traditional predictive models, and even online learning methods, struggle to adapt to the ultra-fast and complex distribution shifts present in highly dynamic scenarios. To address this, we propose InstaTrain, a novel learning approach that enables ultra-fast model updates for real-world prediction tasks, thereby keeping pace with rapidly evolving data distributions. In this work, (1) we transform the slow and expensive training process into an ultra-fast natural annealing process within a dynamical system. (2) Leveraging a recently proposed electronic dynamical system, we augment the system with parameter update modules, extending its capabilities to encompass both rapid training and inference. Experimental results on highly dynamic datasets demonstrate that our method achieves orders-of-magnitude improvements in training speed and energy efficiency while delivering superior accuracy compared to baselines running on GPUs.

Efficient inference in high-dimensional models is a central challenge in machine learning. We introduce the Gaussian Ensemble Belief Propagation (GEnBP) algorithm, which combines the strengths of the Ensemble Kalman Filter (EnKF) and Gaussian Belief Propagation (GaBP) to address this challenge. GEnBP updates ensembles of prior samples into posterior samples by passing low-rank local messages over the edges of a graphical model, enabling efficient handling of high-dimensional states, parameters, and complex, noisy, black-box generative processes. By utilizing local message passing within a graphical model structure, GEnBP effectively manages complex dependency structures and remains computationally efficient even when the ensemble size is much smaller than the inference dimension --- a common scenario in spatiotemporal modeling, image processing, and physical model inversion. We demonstrate that GEnBP can be applied to various problem structures, including data assimilation, system identification, and hierarchical models, and show through experiments that it outperforms existing belief propagation methods in terms of accuracy and computational efficiency. Supporting code is available at https://github.com/danmackinlay/GEnBP}{github.com/danmackinlay/GEnBP

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN.

The training of large language models (LLMs) faces significant computational cost challenges, limiting their scalability toward artificial general intelligence (AGI) and broader adoption. With model sizes doubling approximately every 3.4 months and training costs escalating from 64 million USD for GPT-4 in 2020 to 191 million USD for Gemini Ultra in 2023, the economic burden has become unsustainable. While techniques such as quantization offer incremental improvements, they fail to address the fundamental computational bottleneck. In this work, we introduce DS-LLM, a novel framework that leverages dynamical system (DS)-based machines, which exploit Natural Annealing to rapidly converge to minimal energy states, yielding substantial efficiency gains. Unlike traditional methods, DS-LLM maps LLM components to optimization problems solvable via Hamiltonian configurations and utilizes continuous electric current flow in DS-machines for hardware-native gradient descent during training. We mathematically demonstrate the equivalence between conventional LLMs and DS-LLMs and present a method for transforming a trained LLM into a DS-LLM. Experimental evaluations across multiple model sizes demonstrate orders-of-magnitude improvements in speed and energy efficiency for both training and inference while maintaining consistent accuracy. Additionally, we provide an in-depth analysis of the challenges and potential solutions associated with this emerging computing paradigm, aiming to lay a solid foundation for future research.

Controlling high-dimensional nonlinear systems, such as those found in biological and robotic applications, is challenging due to large state and action spaces. While deep reinforcement learning has achieved a number of successes in these domains, it is computationally intensive and time consuming, and therefore not suitable for solving large collections of tasks that require significant manual tuning. In this work, we introduce Model Predictive Control with Morphology-aware Proportional Control (MPC$^2$), a hierarchical model-based learning algorithm for zero-shot and near-real-time control of high-dimensional complex dynamical systems. MPC$^2$ uses a sampling-based model predictive controller for target posture planning, and enables robust control for high-dimensional tasks by incorporating a morphology-aware proportional controller for actuator coordination. The algorithm enables motion control of a high-dimensional human musculoskeletal model in a variety of motion tasks, such as standing, walking on different terrains, and imitating sports activities. The reward function of MPC$^2$ can be tuned via black-box optimization, drastically reducing the need for human-intensive reward engineering.

Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative dynamics of the system. As a result, new causal relationships may emerge, while existing ones change or disappear, resulting in an altered causal graph. To analyze these qualitative changes on the causal graph, we propose the concept of meta-causal states, which groups classical causal models into clusters based on equivalent qualitative behavior and consolidates specific mechanism parameterizations. We demonstrate how meta-causal states can be inferred from observed agent behavior, and discuss potential methods for disentangling these states from unlabeled data. Finally, we direct our analysis towards the application of a dynamical system, showing that meta-causal states can also emerge from inherent system dynamics, and thus constitute more than a context-dependent framework in which mechanisms emerge only as a result of external factors.

We explore the emergence of intelligent behavior in artificial systems by investigating how the complexity of rule-based systems influences the capabilities of models trained to predict these rules. Our study focuses on elementary cellular automata (ECA), simple yet powerful one-dimensional systems that generate behaviors ranging from trivial to highly complex. By training distinct Large Language Models (LLMs) on different ECAs, we evaluated the relationship between the complexity of the rules' behavior and the intelligence exhibited by the LLMs, as reflected in their performance on downstream tasks. Our findings reveal that rules with higher complexity lead to models exhibiting greater intelligence, as demonstrated by their performance on reasoning and chess move prediction tasks. Both uniform and periodic systems, and often also highly chaotic systems, resulted in poorer downstream performance, highlighting a sweet spot of complexity conducive to intelligence. We conjecture that intelligence arises from the ability to predict complexity and that creating intelligence may require only exposure to complexity.

As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify without replication? We focus on distribution testing problems: verifying that an unknown distribution is close to having a claimed property. Our main contribution is an interactive protocol between a verifier and an untrusted prover, which can be used to verify any distribution property that can be decided in polynomial time given a full and explicit description of the distribution. If the distribution is at statistical distance $\varepsilon$ from having the property, then the verifier rejects with high probability. This soundness property holds against any polynomial-time strategy that a cheating prover might follow, assuming the existence of collision-resistant hash functions (a standard assumption in cryptography). For distributions over a domain of size $N$, the protocol consists of $4$ messages and the communication complexity and verifier runtime are roughly $\widetilde{O}\left(\sqrt{N} / \varepsilon^2 \right)$. The verifier's sample complexity is $\widetilde{O}\left(\sqrt{N} / \varepsilon^2 \right)$, and this is optimal up to $\text{polylog}(N)$ factors (for any protocol, regardless of its communication complexity). Even for simple properties, approximately deciding whether an unknown distribution has the property can require quasi-linear sample complexity and running time. For any such property, our protocol provides a quadratic speedup over replicating the analysis.

Instruction tuning is critical for adapting large language models (LLMs) to downstream tasks, and recent studies have demonstrated that small amounts of human-curated data can outperform larger datasets, challenging traditional data scaling laws. While LLM-based data quality rating systems offer a cost-effective alternative to human annotation, they often suffer from inaccuracies and biases, even in powerful models like GPT-4. In this work, we introduce $DS^2$, a **D**iversity-aware **S**core curation method for **D**ata **S**election. By systematically modeling error patterns through a score transition matrix, $DS^2$ corrects LLM-based scores and promotes diversity in the selected data samples. Our approach shows that a curated subset (just 3.3\% of the original dataset) outperforms full-scale datasets (300k samples) across various machine-alignment benchmarks, and matches or surpasses human-aligned datasets such as LIMA with the same sample size (1k samples). These findings challenge conventional data scaling assumptions, highlighting that redundant, low-quality samples can degrade performance and reaffirming that ``more can be less''.

Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This problem becomes more challenging when the changing parameters are unobserved, meaning their value or influence cannot be directly measured when collecting data. To address this issue, we introduce Neural Context Flow (NCF), a robust and interpretable Meta-Learning framework that includes uncertainty estimation. NCF uses Taylor expansion to enable contextual self-modulation, allowing context vectors to influence dynamics from other domains while also modulating themselves. After establishing theoretical guarantees, we empirically test NCF and compare it to related adaptation methods. Our results show that NCF achieves state-of-the-art Out-of-Distribution performance on 5 out of 6 linear and non-linear benchmark problems. Through extensive experiments, we explore the flexible model architecture of NCF and the encoded representations within the learned context vectors. Our findings highlight the potential implications of NCF for foundational models in the physical sciences, offering a promising approach to improving the adaptability and generalization of NODEs in various scientific applications.

Many time series classification tasks, where labels vary over time, are affected by label noise that also varies over time. Such noise can cause label quality to improve, worsen, or periodically change over time. We first propose and formalize temporal label noise, an unstudied problem for sequential classification of time series. In this setting, multiple labels are recorded over time while being corrupted by a time-dependent noise function. We first demonstrate the importance of modeling the temporal nature of the label noise function and how existing methods will consistently underperform. We then propose methods to train noise-tolerant classifiers by estimating the temporal label noise function directly from data. We show that our methods lead to state-of-the-art performance under diverse types of temporal label noise on real-world datasets.

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when faced with data that is collected randomly over time and space, as is often the case with sensor networks in real-world applications like crowdsourced earthquake detection or pollution monitoring. In response, we developed a new method that can effectively learn spatiotemporal dynamics from such point process observations. Our model integrates techniques from neural differential equations, neural point processes, implicit neural representations and amortized variational inference to model both the dynamics of the system and the probabilistic locations and timings of observations. It outperforms existing methods on challenging spatiotemporal datasets by offering substantial improvements in predictive accuracy and computational efficiency, making it a useful tool for modeling and understanding complex dynamical systems observed under realistic, unconstrained conditions.

The challenge of mapping AI architectures to GPU hardware is creating a critical bottleneck in AI progress. Despite substantial efforts, hand-written custom kernels fail to meet their theoretical performance thresholds, even on well-established operations like linear attention. The diverse capabilities of GPUs suggests we might we need a wide variety of techniques to achieve high performance. However, our work explores if a small number of key abstractions can drastically simplify the process. We present ThunderKittens (TK), a framework for writing performant AI kernels while remaining easy to use. Our abstractions map to the three levels of the GPU hierarchy: (1) at the warp-level, we provide 16x16 matrix tiles as basic data structures and PyTorch-like operations, (2) at the thread-block level, we provide templates for asynchronously overlapping operations, and (3) at the grid-level, TK helps hide block launch, tear-down, and memory costs. We show the value of TK by providing simple & diverse kernels that match or outperform prior art. We match CuBLAS and FlashAttention-3 on GEMM and attention inference performance and outperform the strongest baselines by $10-40$\% on attention backwards, $8\times$ on state space models, and $14\times$ on linear attention.