An algorithm is a set of instructions for accomplishing a task. Every piece of code could be called an algorithm, but this book covers the more interesting bits. I chose the algorithms in this book for inclusion because they’re fast, or they solve interesting problems, or both. Here are some highlights:
Posted in information science, mathematics, robotics/AI | Leave a Comment on The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity
Recent generations of frontier language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their fundamental capabilities, scal-ing properties, and limitations remain insufficiently understood. Current evaluations primarily fo-cus on established mathematical and coding benchmarks, emphasizing final answer accuracy. How-ever, this evaluation paradigm often suffers from data contamination and does not provide insights into the reasoning traces’ structure and quality. In this work, we systematically investigate these gaps with the help of controllable puzzle environments that allow precise manipulation of composi-tional complexity while maintaining consistent logical structures. This setup enables the analysis of not only final answers but also the internal reasoning traces, offering insights into how LRMs “think”. Through extensive experimentation across diverse puzzles, we show that frontier LRMs face a complete accuracy collapse beyond certain complexities. Moreover, they exhibit a counter-intuitive scaling limit: their reasoning effort increases with problem complexity up to a point, then declines despite having an adequate token budget. By comparing LRMs with their standard LLM counterparts under equivalent inference compute, we identify three performance regimes: low-complexity tasks where standard models surprisingly outperform LRMs, medium-complexity tasks where additional thinking in LRMs demonstrates advantage, and high-complexity tasks where both models experience complete collapse. We found that LRMs have limitations in exact computation: they fail to use explicit algorithms and reason inconsistently across puzzles. We also investigate the reasoning traces in more depth, studying the patterns of explored solutions and analyzing the models’ computational behavior, shedding light on their strengths, limitations, and ultimately raising crucial questions about their true reasoning capabilities.
*Equal contribution. †Work done during an internship at Apple.
For decades, we’ve thought the control center of life lies in DNA. But a new scientific framework is emerging that challenges that idea, and suggests that vast portions of the genome are immaterial and lie outside the physical world. Today, physicist Dr. Brian Miller shares his perspective on the cutting-edge, potentially revolutionary research of mathematical biologist Dr. Richard Sternberg on the immaterial aspects of the genome. In this exchange, Dr. Miller shares several examples of the immaterial nature of life. These ideas point towards the earliest stages of the next great scientific revolution and have significant implications for the intelligent design debate.
Machine learning models have seeped into the fabric of our lives, from curating playlists to explaining hard concepts in a few seconds. Beyond convenience, state-of-the-art algorithms are finding their way into modern-day medicine as a powerful potential tool. In one such advance, published in Cell Systems, Stanford researchers are using machine learning to improve the efficacy and safety of targeted cell and gene therapies by potentially using our own proteins.
Most human diseases occur due to the malfunctioning of proteins in our bodies, either systematically or locally. Naturally, introducing a new therapeutic protein to cure the one that is malfunctioning would be ideal.
Although nearly all therapeutic protein antibodies are either fully human or engineered to look human, a similar approach has yet to make its way to other therapeutic proteins, especially those that operate in cells, such as those involved in CAR-T and CRISPR-based therapies. The latter still runs the risk of triggering immune responses. To solve this problem, researchers at the Gao Lab have now turned to machine learning models.
No image is infinitely sharp. For 150 years, it has been known that no matter how ingeniously you build a microscope or a camera, there are always fundamental resolution limits that cannot be exceeded in principle. The position of a particle can never be measured with infinite precision; a certain amount of blurring is unavoidable. This limit does not result from technical weaknesses, but from the physical properties of light and the transmission of information itself.
TU Wien (Vienna), the University of Glasgow and the University of Grenoble therefore posed the question: Where is the absolute limit of precision that is possible with optical methods? And how can this limit be approached as closely as possible?
And indeed, the international team succeeded in specifying a lowest limit for the theoretically achievable precision and in developing AI algorithms for neural networks that come very close to this limit after appropriate training. This strategy is now set to be employed in imaging procedures, such as those used in medicine. The study is published in the journal Nature Photonics.
Very soon after the Big Bang, the universe enjoyed a brief phase where quarks and gluons roamed freely, not yet joined up into hadrons such as protons, neutrons and mesons. This state, called a quark-gluon plasma, existed for a brief time until the temperature dropped to about 20 trillion Kelvin, after which this “hadronization” took place.
Now a research group from Italy has presented new calculations of the plasma’s equation of state that show how important the strong force was before the hadrons formed. Their work is published in Physical Review Letters.
The equation of state of quantum chromodynamics (QCD) represents the collective behavior of particles that experience the strong force—a gas of strongly interacting particles at equilibrium, with its numbers and net energy unchanging. It’s analogous to the well-known, simple equation of state of atoms in a gas, PV=nRT, but can’t be so simply summarized.
As artificial intelligence takes off, how do we efficiently integrate it into our lives and our work? Bridging the gap between promise and practice, Jann Spiess, an associate professor of operations, information, and technology at Stanford Graduate School of Business, is exploring how algorithms can be designed to most effectively support—rather than replace—human decision-makers.
This research, published on the arXiv preprint server, is particularly pertinent as prediction machines are integrated into real-world applications. Mounting empirical evidence suggests that high-stakes decisions made with AI assistance are often no better than those made without it.
From credit reports, where an overreliance on AI may lead to misinterpretation of risk scores, to social media, where models may depend on certain words to flag toxicity, leading to misclassifications—successful implementation lags behind the technology’s remarkable capabilities.
Long-read sequencing technologies analyze long, continuous stretches of DNA. These methods have the potential to improve researchers’ ability to detect complex genetic alterations in cancer genomes. However, the complex structure of cancer genomes means that standard analysis tools, including existing methods specifically developed to analyze long-read sequencing data, often fall short, leading to false-positive results and unreliable interpretations of the data.
These misleading results can compromise our understanding of how tumors evolve, respond to treatment, and ultimately how patients are diagnosed and treated.
To address this challenge, researchers developed SAVANA, a new algorithm which they describe in the journal Nature Methods.
The advancement of artificial intelligence (AI) and the study of neurobiological processes are deeply interlinked, as a deeper understanding of the former can yield valuable insight about the other, and vice versa. Recent neuroscience studies have found that mental state transitions, such as the transition from wakefulness to slow-wave sleep and then to rapid eye movement (REM) sleep, modulate temporary interactions in a class of neurons known as layer 5 pyramidal two-point neurons (TPNs), aligning them with a person’s mental states.
These are interactions between information originating from the external world, broadly referred to as the receptive field (RF1), and inputs emerging from internal states, referred to as the contextual field (CF2). Past findings suggest that RF1 and CF2 inputs are processed at two distinct sites within the neurons, known as the basal site and apical site, respectively.
Current AI algorithms employing attention mechanisms, such as transformers, perceiver and flamingo models, are inspired by the capabilities of the human brain. In their current form, however, they do not reliably emulate high-level perceptual processing and the imaginative states experienced by humans.
A team of researchers at AI Google Quantum AI, led by Craig Gidney, has outlined advances in quantum computer algorithms and error correction methods that could allow such computers to crack Rivest–Shamir–Adleman (RSA) encryption keys with far fewer resources than previously thought. The development, the team notes, suggests encryption experts need to begin work toward developing next-generation encryption techniques. The paper is published on the arXiv preprint server.
RSA is an encryption technique developed in the late 1970s that involves generating public and private keys; the former is used for encryption and the latter decryption. Current standards call for using a 2,048-bit encryption key. Over the past several years, research has suggested that quantum computers would one day be able to crack RSA encryption, but because quantum development has been slow, researchers believed that it would be many years before it came to pass.
Some in the field have accepted a theory that a quantum computer capable of cracking such codes in a reasonable amount of time would have to have at least 20 million qubits. In this new work, the team at Google suggests it could theoretically be done with as few as a million qubits—and it could be done in a week.
