AI's recursive self-improvement might not come so quickly after all AI agents are not yet creative enough to carry out genuinely innovative open-ended AI research, it seems. The AI industry's boldest promise right now is that AI will soon improve itself, with almost no need for human oversight. LLMs can already write code, generate synthetic data for training, and optimize the computer chips they run on. Forecasts of explosive AI progress predict that what researchers call recursive self-improvement is on the horizon. But a new study suggests that it might take a while for us to get there. The researchers behind it found that AI agents are not yet capable of conducting open-ended AI research--free-form investigations that have no clear-cut answers and require judgment and taste, which may be integral to building self-improving AI.

Improving energy performance can effectively extend the time a robot can operate and reduce battery load, enabling lighter, more flexible, and more durable robotic systems. Nature has evolved optimal energy-saving locomotion strategies through billions of years of natural selection, providing unparalleled blueprints for robotic optimization. Among diverse modes of aquatic locomotion, intermittent swimming, also called bout-and-glide swimming, is a widespread adaptive behavior in aquatic organisms of a wide range of sizes, including larval zebrafish, red-nose tetra, koi carp, and even whales. This natural bout-and-glide gait features alternating motion phases: short periods of active body and tail undulation for propulsion, followed by passive gliding with a streamlined, straight body posture. It is widely recognized that this intermittent swimming gait is closely associated with optimizing biological energy, making it of great research value to transplant and explore such natural motion mechanisms into robotic control systems.

AI agents that can model the human process of research will accelerate discoveries in science. Every few decades, someone announces that science has reached its end. In 1903, the revered physicist Albert Michelson wrote that the "facts of physical science have all been discovered." In the 1980s, Stephen Hawking predicted that theoretical physics might be finished by the end of the century. With the explosive arrival of artificial intelligence, the feeling is in the air again--this time accompanied by a Nobel Prize. In 2024, Demis Hassabis and John Jumper of Google DeepMind were awarded part of the Nobel in chemistry for their neural network AlphaFold, which predicts the three-dimensional structures of proteins by learning from thousands of experimentally measured shapes.

Penalty Shootouts: Is the Team That Kicks First More Likely to Win? Penalty kicks are already proving critical to big wins at this year's World Cup. But the advantage in penalty kicks has more to do with psychological effects than who kicks first. A penalty kick during the Netherlands' round of 32 match against Morocco. In a World Cup, some of the most important matches are decided by a penalty shootout. When that moment comes, the captains want to win the coin toss to decide the order of the kicks.

Classical hypothesis testing frameworks break down in contemporary settings in which null hypotheses are increasingly abstract, the same data are used to both generate and test hypotheses, and minimal assumptions about the underlying data are made. In this work, we propose a new framework for conducting valid hypothesis tests in broad contexts. We propose to add and subtract external noise generated from a symmetric shift-family to our data, $X$, to partition it into two pieces, $X^{(1)}$ and $X^{(2)}$. We provide a generic strategy for orthogonalizing $X^{(2)}$ against $X^{(1)}$ under the null hypothesis $H_0$, then show that testing whether the orthogonalization was successful provides a valid test of $H_0$ under mild assumptions. Remarkably, this framework extends naturally to the post-selection inference setting: we simply select a hypothesis on $X^{(1)}$, then perform orthogonalization under the selected null. As our approach neither requires pre-specification of the selection mechanism, nor is restricted to a small class of data-generating distributions, it dramatically expands the settings for which valid post-selection inference can be conducted. We showcase the flexibility of our proposal in several case studies involving challenging pre-specified null hypotheses and post-selection inference scenarios.

The Fisher Information Matrix (FIM) is the canonical local measure of the curvature of a statistical model's log-likelihood surface, and its dominant eigenvalue λmax quantifies the worst-case sensitivity of the model's output distribution to infinitesimal parameter perturbation [1, 2]. The spectral properties of the FIM of neural networks have been studied directly in the random matrix theory literature. Pennington and Worah [4] derive the limiting spectral density of the FIM of a single-hidden-layer network in the high-dimensional asymptotic regime, building on the broader programme of analysing neural network Hessian and kernel spectra via random matrix methods [5, 6], with subsequent work extending these techniques to deeper architectures and non-asymptotic regimes [7, 8]. These results characterize the typical (bulk and edge) spectral behaviour of the FIM for a fixed network and a random or structured input ensemble. This paper studies a complementary question, posed as a perturbation problem rather than an asymptotic-spectrum problem: how does the dominant eigenvalue of a fixed, evaluated empirical FIM change under two specific structured perturbations of the underlying distribution? The first perturbation is a change in the conditioning input away from a reference (in-distribution) ensemble. The second is a structured additive perturbation of the model's own parameters by finite-precision quantization noise -- a perturbation of independent mathematical interest, since it falls outside the i.i.d.-input asymptotic regime treated in the random matrix literature cited above, and instead concerns a fixed network whose parameters, not its input distribution, are perturbed by a noise process with a specific, analytically tractable structure (Definition 4.1). To our knowledge, this parameterperturbation question for the FIM's dominant eigenvalue, under either source of departure, has not been previously formalized.

Binary classification from positive-only samples is a variant of PAC learning in which the learner receives i.i.d. samples from the positive region of an unknown target concept, but is evaluated under the original distribution (which places mass on both positive and negative regions). This model dates back to Natarajan [1987, STOC], and the characterization of improper learning is well-known -- it even appears in textbooks. The characterization of proper positive-only learning, however, has long remained open. In this work, we revisit and settle this question: a concept class is properly learnable from positive-only samples if and only if it has finite VC dimension and satisfies a new combinatorial condition, which we call uniform exterior separability. Together with several separation results, this characterization reveals a surprisingly rich landscape that differs sharply from standard PAC learning: proper and improper learning are separated, randomized and deterministic proper learning are separated, there are classes for which no ERM is a learner, and finite VC dimension does not suffice even for non-uniform learning. Along the way, we introduce new combinatorial dimensions that we believe can be of broader interest in learning theory.

A fine-grained account of functional selectivity in the cortex is essential for understanding how visual information is processed and represented in the brain. Classical studies using designed experiments have identified multiple category-selective regions; however, these approaches rely on preconceived hypotheses about categories. Subsequent data-driven discovery methods have sought to address this limitation but are often limited by simple, typically linear encoding models. We propose an in silico approach for data-driven discovery of novel category-selectivity hypotheses based on an encoder-decoder transformer model. The architecture incorporates a brain-region to image-feature cross-attention mechanism, enabling nonlinear mappings between high-dimensional deep network features and semantic patterns encoded in the brain activity. We further introduce a method to characterize the selectivity of individual parcels by leveraging diffusion-based image generative models and large-scale datasets to synthesize and select images that maximally activate each parcel. Our approach reveals regions with complex, compositional selectivity involving diverse semantic concepts, which we validate in silico both within and across subjects. Using a brain encoder as a "digital twin" offers a powerful, data-driven framework for generating and testing hypotheses about visual selectivity in the human brain--hypotheses that can guide future fMRI experiments.

We investigate the robustness of Large Language Models (LLMs) to structural interventions by deleting and swapping adjacent layers during inference. Surprisingly, models retain 72-95% of their original top-1 prediction accuracy without any fine-tuning. We find that performance degradation is not uniform across layers: interventions to the early and final layers cause the most degradation, while the model is remarkably robust to dropping middle layers. This pattern of localized sensitivity motivates our hypothesis of four stages of inference, observed across diverse model families and sizes: (1) detokenization, where local context is integrated to lift raw token embeddings into higher-level representations; (2) feature engineering, where task-and entity-specific features are iteratively refined; (3) prediction ensembling, where hidden states are aggregated into plausible next-token predictions; and (4) residual calibration, where irrelevant features are suppressed to finalize the top-1 output distribution. Synthesizing behavioral and mechanistic evidence, we provide a hypothesis for interpreting depth-dependent computations in LLMs.

Prompting is the primary method by which we study and control large language models. It is also one of the most powerful: nearly every major capability attributed to LLMs--few-shot learning, chain-of-thought, constitutional AI--was first unlocked through prompting. Yet prompting is rarely treated as science and is frequently frowned upon as alchemy. We argue that this is a category error. If we treat LLMs as a new kind of organism--complex, opaque, and trained rather than programmed--then prompting is not a workaround.