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Researchers Unveil Breakthrough in Efficient Machine Learning with Symmetric Data

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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.

The Sciences

Researchers crack greener way to mine lithium, cobalt and nickel from dead batteries

A breakthrough recycling method developed at Monash University in Australia can recover over 95% of critical metals from spent lithium-ion batteries—without extreme heat or toxic chemicals—offering a major boost to clean energy and circular economy goals.

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Parisa Biniaz (left), PhD student and co-author, with Dr Parama Banerjee (right), principal supervisor and project lead.
Parisa Biniaz (left), PhD student and co-author, with Dr Parama Banerjee (right), principal supervisor and project lead.

Researchers at Monash University, based in Melbourne, Australia, have developed a breakthrough, environmentally friendly method to recover high-purity nickel, cobalt, manganese and lithium from spent lithium-ion batteries, offering a safer alternative to conventional recycling processes.

The new approach uses a mild and sustainable solvent, avoiding the high temperatures and hazardous chemicals typically associated with battery recycling. The innovation comes at a critical time, as an estimated 500,000 tonnes of spent lithium-ion batteries have already accumulated globally. Despite their growing volume, recycling rates remain low, with only around 10 per cent of spent batteries fully recycled in countries such as Australia.

Most discarded batteries end up in landfills, where toxic substances can seep into soil and groundwater, gradually entering the food chain and posing long-term health and environmental risks. This is particularly concerning given that spent lithium-ion batteries are rich secondary resources, containing strategic metals including lithium, cobalt, nickel, manganese, copper, aluminium and graphite.

Existing recovery methods often extract only a limited range of elements and rely on energy-intensive or chemically aggressive processes. The Monash team’s solution addresses these limitations by combining a novel deep eutectic solvent (DES) with an integrated chemical and electrochemical leaching process.

Dr Parama Banerjee, principal supervisor and project lead from the Department of Chemical and Biological Engineering, said the new method achieves more than 95 per cent recovery of nickel, cobalt, manganese and lithium, even from industrial-grade “black mass” that contains mixed battery chemistries and common impurities.

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Dr Parama Banerjee

“This is the first report of selective recovery of high-purity Ni, Co, Mn, and Li from spent battery waste using a mild solvent,” Dr Banerjee said.

“Our process not only provides a safer, greener alternative for recycling lithium-ion batteries but also opens pathways to recover valuable metals from other electronic wastes and mine tailings.”

Parisa Biniaz, PhD student and co-author of the study, said the breakthrough represents a significant step towards a circular economy for critical metals while reducing the environmental footprint of battery disposal.

“Our integrated process allows high selectivity and recovery even from complex, mixed battery black mass. The research demonstrates a promising approach for industrial-scale recycling, recovering critical metals efficiently while minimising environmental harm,” Biniaz said.

The researchers say the method could play a key role in supporting sustainable energy transitions by securing critical mineral supplies while cutting down on environmental damage from waste batteries.

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Sustainable Energy

Can ammonia power a low-carbon future? New MIT study maps global costs and emissions

Under what conditions can ammonia truly become a low-carbon energy solution? MIT researchers attempt to resolve this

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Ammonia is being studied as a future low-carbon fuel for hard-to-abate sectors such as aviation. Image credit: RonaK Pitamber Choudhary/Pexels

Ammonia, long known as the backbone of global fertiliser production, is increasingly being examined as a potential pillar of the clean energy transition. Energy-dense, carbon-free at the point of use, and already traded globally at scale, ammonia is emerging as a candidate fuel and a carrier of hydrogen. But its climate promise comes with a contradiction: today’s dominant method of producing ammonia carries a heavy carbon footprint.

A new study by researchers from the MIT Energy Initiative (MITEI) attempts to resolve this tension by answering a foundational question for policymakers and industry alike: under what conditions can ammonia truly become a low-carbon energy solution?

A global view of ammonia’s future

In a paper published in Energy and Environmental Science, the researchers present the largest harmonised dataset to date on the economic and environmental impacts of global ammonia supply chains. The analysis spans 63 countries and evaluates multiple production pathways, trade routes, and energy inputs, offering a comprehensive view of how ammonia could be produced, shipped, and used in a decarbonising world.

“This is the most comprehensive work on the global ammonia landscape,” says senior author Guiyan Zang, a research scientist at MITEI. “We developed many of these frameworks at MIT to be able to make better cost-benefit analyses. Hydrogen and ammonia are the only two types of fuel with no carbon at scale. If we want to use fuel to generate power and heat, but not release carbon, hydrogen and ammonia are the only options, and ammonia is easier to transport and lower-cost.”

Why data matters

Until now, assessments of ammonia’s climate potential have been fragmented. Individual studies often focused on single regions, isolated technologies, or only cost or emissions, making global comparisons difficult.

“Before this, there were no harmonized datasets quantifying the impacts of this transition,” says lead author Woojae Shin, a postdoctoral researcher at MITEI. “Everyone is talking about ammonia as a super important hydrogen carrier in the future, and also ammonia can be directly used in power generation or fertilizer and other industrial uses. But we needed this dataset. It’s filling a major knowledge gap.”

To build the database, the team synthesised results from dozens of prior studies and applied common frameworks to calculate full lifecycle emissions and costs. These calculations included feedstock extraction, production, storage, shipping, and import processing, alongside country-specific factors such as electricity prices, natural gas costs, financing conditions, and energy mix.

Comparing production pathways

Today, most ammonia is produced using the Haber–Bosch process powered by fossil fuels, commonly referred to as “grey ammonia.” In 2020, this process accounted for about 1.8 percent of global greenhouse gas emissions. While economically attractive, it is also the most carbon-intensive option.

The study finds that conventional grey ammonia produced via steam methane reforming (SMR) remains the cheapest option in the U.S. context, at around 48 cents per kilogram. However, it also carries the highest emissions, at 2.46 kilograms of CO₂ equivalent per kilogram of ammonia.

Cleaner alternatives offer substantial emissions reductions at higher cost. Pairing SMR with carbon capture and storage cuts emissions by about 61 percent, with a 29 percent cost increase. A full global shift to ammonia produced with conventional methods plus carbon capture could reduce global greenhouse gas emissions by nearly 71 percent, while raising costs by 23.2 percent.

More advanced “blue ammonia” pathways, such as auto-thermal reforming (ATR) with carbon capture, deliver deeper emissions cuts at relatively modest cost increases. One ATR configuration achieved emissions of 0.75 kilograms of CO₂ equivalent per kilogram of ammonia, at roughly 10 percent higher cost than conventional SMR.

At the far end of the spectrum, “green ammonia” produced using renewable electricity can reduce emissions by as much as 99.7 percent, but at a significantly higher cost—around 46 percent more than today’s baseline. Ammonia produced using nuclear electricity showed near-zero emissions in the analysis.

Geography matters

The study also reveals that the viability of low-carbon ammonia depends heavily on geography. Countries with abundant, low-cost natural gas are better positioned to produce blue ammonia competitively, while regions with cheap renewable electricity are more favourable for green ammonia.

China emerged as a potential future supplier of green ammonia to multiple regions, while parts of the Middle East showed strong competitiveness in low-carbon ammonia production. In contrast, ammonia produced using carbon-intensive grid electricity was often both more expensive and more polluting than conventional methods.

From research to policy

Interest in low-carbon ammonia is no longer theoretical. Countries such as Japan and South Korea have incorporated ammonia into national energy strategies, including pilot projects using ammonia for power generation and financial incentives tied to verified emissions reductions.

“Ammonia researchers, producers, as well as government officials require this data to understand the impact of different technologies and global supply corridors,” Shin says.

Zang adds that the dataset is designed not just as an academic exercise, but as a decision-making tool. “We collaborate with companies, and they need to know the full costs and lifecycle emissions associated with different options. Governments can also use this to compare options and set future policies. Any country producing ammonia needs to know which countries they can deliver to economically.”

As global demand for low-carbon fuels accelerates toward mid-century, the study suggests that ammonia’s role will depend less on ambition alone, and more on informed choices—grounded in data—about how and where it is produced.

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The Sciences

Why Octopuses Have Three Hearts, And Why Their Bodies Are Stranger Than Fiction

And the reason is surprisingly practical

Rishika Nair

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Octopuses are already odd enough — eight arms, no bones, a brain that wraps around their throat — but one detail still stops people in their tracks: they have three hearts. Not two. Not one. Three.

And the reason is surprisingly practical.

Three Hearts for a Tough Life Underwater

Two of the hearts — called branchial hearts — do a very specific job: each one pushes blood through a gill, where it can pick up oxygen. The third, the systemic heart, takes that oxygen-rich blood and pumps it to the rest of the body.

In other words: two hearts to breathe, one heart to live.

Why Their Blood Is Blue

Another strange thing: their blood isn’t red at all.

It’s blue — literally blue — because it’s based on copper, not iron.

The copper-based protein, hemocyanin, works better in the cold, low-oxygen parts of the ocean where many octopuses live. It keeps them alive in places where most animals wouldn’t last a minute. But it’s not very efficient, so their bodies need extra pumping power to keep the oxygen flowing.

Evolution’s answer? Give them more hearts.

A Heart That Stops When They Swim

Here’s the part that sounds almost fictional: when an octopus swims, its main heart actually stops.

Imagine going for a swim and your heart taking a break halfway through. That’s why octopuses prefer to crawl on the seafloor. Swimming is simply too tiring — it literally costs them heartbeats.

The Ocean’s Quiet Genius

When you combine all of this — the blue blood, the three hearts, the bizarre nervous system, the ability to vanish into their surroundings — you get one of the most unusual and surprisingly intelligent creatures on the planet.

Octopuses don’t just survive in harsh oceans; they’ve evolved in ways that feel almost alien. And maybe that’s why we’re endlessly fascinated by them — they remind us how strange and creative life can be.

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