LG AI Research 在 ICML 2026 提出 GEAR 与 Sim-GEAR：用黎曼几何解决科学数据稀缺

ICML 2026 and AI for Science, Held in South Korea

ICML 2026, one of the world’s leading AI conferences, was held in South Korea this year. Researchers from around the world participated, and the event drew such high interest that registration closed early. At the conference, it was evident that global interest is growing not only in Korean culture but also in AI research and industry.

Large-scale AI conferences have a slightly different character than typical science and engineering conferences. Unlike traditional conferences, which are organized around specific technologies or academic fields, AI conferences cover research across a wide range of fields, including language, imagery, robotics, healthcare, manufacturing, and science. At this year’s ICML 2026, “Agents” emerged as a major keyword, and active research and discussion also took place in the field of AI for Science. Companies and researchers from diverse fields including materials development, computational fluid dynamics, and new drug development participated in the event, and the LG AI Research booth attracted many researchers interested in materials development research and related career opportunities.

AI for Science is rapidly evolving from an experimental field limited to a select few researchers into a core research area that bridges scientific discovery and industrial innovation.

1. Real-World Challenges and Research Inspiration
Data is missing where it is needed most

AI for Science deals not with everyday data such as language or images, but with subjects that require specialized scientific knowledge, such as molecules, crystal structures, and chemical reactions. Because of these characteristics, researchers from a wide range of disciplines including computer science, physics, chemistry, life sciences, mathematics, and materials engineering are collaborating on such research.

Recently, there has been a rapid increase in the number of startups and research organizations promoting AI for Science. However, using AI to propose new molecules or materials is a very different matter from turning them into actual products. Synthesizing candidate substances, measuring their physical properties, and then proceeding to product design and mass production requires a large-scale research, development, and production infrastructure.

LG already has this infrastructure in place across various manufacturing sectors, including chemicals, energy, electronics, displays, and consumer goods. Building on this foundation, LG’s ability to integrate the entire process from AI-driven candidate screening to experimentation, validation, product development, and mass production into a single pipeline is a key competitive advantage in the field of AI for Science.

However, there are fundamental challenges related to data in the actual materials development process. This is because the amount of data that can be obtained varies significantly depending on the physical property. While some physical properties yield over hundreds of millions of data points, others may yield as few as several dozen.

In particular, the more time- and cost-intensive it is to measure a physical property, the more likely it is that data on that property is scarce. These physical properties often serve as important goals in the development of new materials. In other words, the problems that most require AI are precisely those for which the data needed to train AI is lacking.

GEAR and Sim-GEAR, presented at ICML 2026, are research projects launched to address this issue of scientific data imbalance.

2. The Research of LG AI Research
How to convey knowledge of physical properties supported by data

One of the most common methods for addressing the issue of data scarcity is transfer learning. This approach involves first training a model on a source task with sufficient data, then transferring the knowledge gained from that task to a target task with insufficient data.

In existing approaches, it was common to copy some of the source model’s parameters to the target model or to train the models so that their latent vectors would directly resemble one another. However, if the two models learn different physical properties, their internal latent spaces may also take on different forms.

For example, let’s assume that one model predicts the boiling point of a molecule, while another predicts its melting point. Although both models take the same molecular structure as input, they are trained to achieve different goals. Therefore, even if the latent vectors of the two models contain the same information about the substance, they may be represented by different coordinates and forms.

Research by LG AI Research interprets these differences not as simple vector values, but as geometric differences in space.

The curved space created by deep learning models

Deep learning models repeatedly transform input data through multiple linear transformations and nonlinear activations. The latent vectors within the model are not simply arrays of numbers; rather, they can be viewed as coordinates represented in a way that is suitable for predicting the input data.

In existing transfer learning, it was often assumed that these latent vectors reside in a flat Euclidean space, and the distances between two vectors were directly compared. However, it is difficult to view the latent space, which is generated through complex nonlinear transformations, as entirely flat.

Just as it is difficult to describe the distance between two points on the surface of a sphere using only the straight-line distance on a plane, the latent spaces of different models can only be accurately compared by taking into account the curvature of the space.

The branch of mathematics that deals with such curved surfaces is Riemannian geometry. LG AI Research has developed a new transfer learning method that uses Riemannian geometry to connect the latent spaces of different physical property prediction models.

GEAR: Conveying the curvature of latent space

GEAR is a method that calculates curvature in the latent spaces of a data-rich source model and a data-poor target model, and trains the models so that the geometric structures of the two spaces become similar.

First, the latent vectors of the source and target are each transformed into a common coordinate system via a transformation model. As both models take the same molecular or solid-state structure as input, representations corresponding to the same substance can be aligned in the common coordinate system so that they are close to one another.

Differentiating the transformation model yields the Jacobian. The Jacobian describes how a small change in the latent space before transformation manifests as a specific direction and magnitude in the common coordinate system.

From this Jacobian, it is possible to calculate a metric that defines distance and angle in the latent space. In matrix form, it is expressed as g = J?J, and this is called the induced metric.

Differentiating the metric yields the connection, which describes the change in vectors on a curved surface, and by combining these, we can calculate the curvature of the space. In GEAR, we used the Ricci scalar, which condenses complex curvature information into a single value.

By training the model so that the Ricci scalars of the source and target latent spaces become similar, the target model does not simply copy the coordinate values from the source model, but instead inherits the geometric structure of the space learned by the data-rich source task.

This approach can be applied even when different model structures or embeddings are used. This is because while the actual coordinates of latent vectors may vary depending on the model, curvature is a geometric property that is not affected by simple coordinate transformations.

Applying higher-order derivatives to real-world learning

While the concept of GEAR is relatively intuitive, its actual implementation is highly complex. Calculating Ricci curvature requires not only first-order derivatives of the transformation model, but also repeated higher-order derivatives to obtain the metric and connection.

Performing these calculations by nesting PyTorch’s Autograd results in a very large computational graph and a sharp increase in GPU memory usage. When the latent dimension or batch size increases, it becomes difficult to train the model in a realistic environment.

To address this issue, the research team directly derived the derivative equations for the SiLU activation and each layer that make up the transformation model. They then implemented a method to combine the layer-wise derivatives according to the chain rule to compute the Jacobian and curvature of the entire model.

This approach eliminated the need for Autograd to store all intermediate calculations, enabling curvature-based transfer learning to be performed within realistic time and memory constraints.

In recognition of these research achievements, GEAR was accepted for the main conference of ICML 2026.

Sim-GEAR: Is it really necessary to calculate curvature?

While GEAR demonstrated the potential to utilize the geometry of latent space in transfer learning, it had two limitations.

The first was computational complexity. Calculating connections and curvature from a metric requires multiple steps of higher-order differentiation. Although we implemented direct differentiation formulas to improve computational efficiency, the inherent complexity of curvature calculations remained an issue.

The second was information compression. The Ricci scalar used by GEAR summarizes the curvature information of a space into a single number. While this has the advantage of making comparisons easier, it does not preserve all distance and angle information in different directions within the space. Consequently, spaces with different geometries may have similar Ricci scalars.

These limitations gave rise to a new question.

Our goal is not to calculate curvature itself, but to ensure that the source and target latent spaces have corresponding geometric structures. In that case, it may be more effective to directly compare the metrics, the step preceding the calculation of curvature.

Sim-GEAR is a method based on this idea.

From curvature matching to metric matching

Like GEAR, Sim-GEAR calculates the metric of the latent space using the Jacobian of the transformation model. However, rather than differentiating the metric again to calculate curvature, it directly aligns the metrics of the source and target spaces.

A metric defines distance and angle in a space. Therefore, when the metrics of two spaces correspond, it means that the distance structure and the direction of change around the same input are similar.

This relationship can also be understood from the perspective of a basis. At each point in a space, there are basis vectors representing various directions, and the metric expresses the inner product relationships between these basis vectors. The Jacobian of the transformation model describes how the basis of the latent space before the transformation is transformed in a common coordinate system.

Therefore, by aligning the metric and basis structures of the source and target, we can convey not only the positions of the two latent vectors but also the way in which input changes are represented in their surroundings.

For example, if a change in a specific direction in the source latent space plays a crucial role in predicting physical properties, the model is trained to form a corresponding direction in the target latent space as well.

Sim-GEAR utilizes metric information, which is more direct than curvature, while maintaining GEAR’s geometric perspective. Unlike the Ricci scalar, which compresses information from multiple directions into a single value, the metric preserves distance and angle information for each direction in matrix form.

Simpler and more efficient geometric transfer learning

Since Sim-GEAR eliminates curvature calculations, it significantly reduces complex higher-order derivatives and large computational graphs.

The computational complexity is reduced from approximately the fourth order in GEAR to the third order in Sim-GEAR. As the latent dimension increases, this difference in computational efficiency becomes even more pronounced.

In experiments, Sim-GEAR achieved a computational speedup of approximately 91.1% compared to GEAR and reduced memory usage by approximately 62.6%. This enables the use of larger latent dimensions and batch sizes on the same hardware.

Generally, simplifying computations can lead to performance losses. However, despite using a simpler structure than GEAR, Sim-GEAR demonstrated stable transfer learning performance across various molecular physical property datasets.

This can be interpreted as follows: removing the curvature calculation did not mean sacrificing geometric information, but rather resulted from utilizing the information actually required for transfer learning more directly at the metric stage.

The potential of AI for Science, as seen at ICML 2026

LG AI Research presented GEAR at the ICML 2026 main conference and introduced Sim-GEAR at the AI for Science workshop.

Both studies share the common goal of transferring knowledge learned from data-rich physical properties to data-scarce ones. While GEAR demonstrated the potential of a new form of geometric transfer learning that leverages curvature, Sim-GEAR built on this by developing it into a simpler and more efficient form.

At the conference, in addition to research presentations, there were lively discussions on how to apply AI to materials development, the imbalance in scientific data, and the process of translating AI predictions into actual experiments and production.

This shows that AI for Science is moving beyond simply improving model benchmark performance, and is now entering a phase where it is being applied to actual scientific discoveries and industrial development processes.

3. LG AI Research's future plans

Expanding to a wider range of science problems

In the future, we plan to apply GEAR and Sim-GEAR to a wider variety of molecular and solid-state physical property data and model structures to validate the versatility of our methodology.

Current research focuses on different physical property prediction tasks that use the same molecular or solid-state structure as input. Going forward, we can expand our range of work to include the transfer of geometric information between computational and experimental data, molecular and crystal structures, and different modalities and tasks.

AI that works even with limited data

In AI for Science, physical properties for which data is scarce are actually likely to be the most important ones from an industrial perspective. Therefore, technologies that can learn reliably even with limited data and transfer knowledge from existing tasks to new problems can serve as the core foundation for the development of new materials.

LG AI Research will continue to combine geometry, physics, and chemistry with deep learning to address the fundamental limitations of scientific data.

Our ultimate goal is not to create AI that performs well only on problems with abundant data. Rather, we aim to develop AI that can understand physical and chemical structures even with limited experimental data and incomplete observations, and extend previously acquired knowledge to new problems.

GEAR and Sim-GEAR are research projects that bridge deep learning and differential geometry to achieve this goal, and we plan to further develop them into AI for Science technologies that can be applied to actual material development and industrial settings in the future.