Math

Researchers Unveil Breakthrough in Efficient Machine Learning with Symmetric Data

Published

11 hours ago

July 31, 2025

Illustrated image

MIT researchers have developed the first mathematically proven method for training machine learning models that can efficiently interpret symmetric data—an advance that could significantly enhance the accuracy and speed of AI systems in fields ranging from drug discovery to climate analysis.

In traditional drug discovery, for example, a human looking at a rotated image of a molecule can easily recognize it as the same compound. However, standard machine learning models may misclassify the rotated image as a completely new molecule, highlighting a blind spot in current AI approaches. This shortcoming stems from the concept of symmetry, where an object’s fundamental properties remain unchanged even when it undergoes transformations like rotation.

“If a drug discovery model doesn’t understand symmetry, it could make inaccurate predictions about molecular properties,” the researchers explained. While some empirical techniques have shown promise, there was previously no provably efficient way to train models that rigorously account for symmetry—until now.

“These symmetries are important because they are some sort of information that nature is telling us about the data, and we should take it into account in our machine-learning models. We’ve now shown that it is possible to do machine-learning with symmetric data in an efficient way,” said Behrooz Tahmasebi, MIT graduate student and co-lead author of the new study, in a media statement.

The research, recently presented at the International Conference on Machine Learning, is co-authored by fellow MIT graduate student Ashkan Soleymani (co-lead author), Stefanie Jegelka (associate professor of EECS, IDSS member, and CSAIL member), and Patrick Jaillet (Dugald C. Jackson Professor of Electrical Engineering and Computer Science and principal investigator at LIDS).

Rethinking how AI sees the world

Symmetric data appears across numerous scientific disciplines. For instance, a model capable of recognizing an object irrespective of its position in an image demonstrates such symmetry. Without built-in mechanisms to process these patterns, machine learning models can make more mistakes and require massive datasets for training. Conversely, models that leverage symmetry can work faster and with fewer data points.

“Graph neural networks are fast and efficient, and they take care of symmetry quite well, but nobody really knows what these models are learning or why they work. Understanding GNNs is a main motivation of our work, so we started with a theoretical evaluation of what happens when data are symmetric,” Tahmasebi noted.

The MIT researchers explored the trade-off between how much data a model needs and the computational effort required. Their resulting algorithm brings symmetry to the fore, allowing models to learn from fewer examples without spending excessive computing resources.

Blending algebra and geometry

The team combined strategies from both algebra and geometry, reformulating the problem so the machine learning model could efficiently process the inherent symmetries in the data. This innovative blend results in an optimization problem that is computationally tractable and requires fewer training samples.

“Most of the theory and applications were focusing on either algebra or geometry. Here we just combined them,” explained Tahmasebi.

By demonstrating that symmetry-aware training can be both accurate and efficient, the breakthrough paves the way for the next generation of neural network architectures, which promise to be more precise and less resource-intensive than conventional models.

“Once we know that better, we can design more interpretable, more robust, and more efficient neural network architectures,” added Soleymani.

This foundational advance is expected to influence future research in diverse applications, including materials science, astronomy, and climate modeling, wherever symmetry in data is a key feature.

Learning & Teaching

What India’s Foundational Learning Crisis Is Really Telling Us About Math

“They Can Count in the Market, But Not in the Classroom”: What India’s Foundational Learning Crisis Is Really Telling Us

Published

3 weeks ago

July 12, 2025

Dipin Damodharan

Image credit: Dorothe from Pixabay

Earlier this year, EdPublica reported on an unsettling truth emerging from a collaborative study by MIT and Indian education researchers: Indian children demonstrate impressive mathematical ability when navigating real-life situations—like calculating change in a vegetable market—but often fail when asked to solve similar problems in the classroom. The findings struck a chord, revealing a deep fracture between what children learn and how they learn it.

Now, new data from the government-backed PARAKH Rashtriya Sarvekshan 2024 confirms the broader scale of that crisis. Together, the two reports offer a sobering diagnosis of foundational learning in India—and an urgent call to rethink how education is delivered.

The transfer gap: Street-smart, classroom-stranded

In the February study we reported on, researchers observed that children who work in markets—some out of necessity—could perform complex mental arithmetic swiftly and accurately. But the same children struggled with formal school problems like structured division or textbook subtraction. Meanwhile, their peers in schools did well on written math tests but faltered when asked to apply the same concepts in spontaneous, real-life situations.

This disconnect isn’t just about math—it’s about transferability. What good is education if it doesn’t translate beyond the exam sheet?

PARAKH’s alarming snapshot

The Performance Assessment, Review, and Analysis of Knowledge for Holistic Development (PARAKH) is India’s new national assessment platform launched under the National Education Policy 2020. Managed by the NCERT in collaboration with CBSE and overseen by the Ministry of Education, PARAKH represents a shift away from traditional rote exams to competency-based evaluation.

Its first large-scale survey, conducted in December 2024 across 23 lakh students from Classes 3, 6, and 9, paints a picture that is both revealing and troubling.

In Class 3, only 55% of students could correctly sequence numbers up to 99 or perform simple addition and subtraction. By Class 6, just 53% had mastered multiplication tables up to 10. Math proficiency hovered at 46% overall. The pattern held across language and environmental studies as well.

Perhaps most alarming is the steady decline in foundational ability as students progress. What begins as a fragile grasp in Class 3 becomes a gaping void by Class 9.

Where you study matters

The data also revealed a curious twist: in Class 3, rural students marginally outperformed their urban peers in both math and language. But by Class 6 and 9, the urban students pulled ahead decisively. It suggests that whatever edge rural systems may offer in the early years is quickly lost due to resource constraints, poor infrastructure, or lack of academic support.

Meanwhile, central government-run schools—such as Kendriya Vidyalayas—consistently outperformed state-run and aided schools, particularly in mathematics. The gaps are not just between regions, but embedded within the structure of the system itself.

A system teaching at children, not with them

What both the MIT study and the PARAKH survey show is this: India’s education system, despite enormous progress in enrolment and infrastructure, still hasn’t solved the puzzle of meaningful learning. It teaches children how to arrive at the “right” answer on paper, but not how to reason, estimate, or solve problems in the real world.

This isn’t simply a curriculum issue—it’s pedagogical. Teachers often default to formulas and procedures, driven by syllabus completion and exam pressures. Conceptual understanding, critical thinking, and the space to make mistakes are rare in crowded classrooms with little support for differentiated learning.

Moving from numbers to nuance

To its credit, the Ministry of Education has recognized this crisis. The PARAKH framework is designed not just to assess but to inform change. Its next phase will involve teacher workshops, state- and district-level consultations, and detailed “health reports” of learning outcomes.

A country with one of the youngest populations in the world cannot afford a foundational crisis

But meaningful change will require more than data. It demands political will, sustained investment in teacher training, reduced pupil–teacher ratios, and a shift in classroom culture. Most of all, it requires a rethinking of what education is meant to do—not just pass students from one grade to the next, but prepare them for life.

The stakes couldn’t be higher

A country with one of the youngest populations in the world cannot afford a foundational crisis. Poor learning in early years compounds over time, leading to disengagement, dropout, and economic vulnerability. The students struggling to divide 96 by 8 today are tomorrow’s workforce—and the gaps in their learning will define the future of the nation.

If India wants to reap its much-discussed demographic dividend, it must invest in the one thing that can turn numbers into citizens, and citizens into leaders: deep, transferable learning.