Leiden researchers Professor Daniela Kraft and Mengshi Wei have created microscopic robots that move without sensors, software, or external control. Instead, their behaviour emerges entirely from their shape and the way they interact with their environment. This class of robots opens up entirely new possibilities for biomedical applications. Inspiration to build these robots came from nature. Kraft: "Animals like worms and snakes constantly adapt their shape as they move, which helps them to navigate their environments. Macroscopic robots similarly use flexibility for their function. However, until now, microrobots were either small and rigid, or large and flexible. We wondered if we could realize small and flexible microrobots in our lab."

Chris Mason: Why a coffee is overshadowing the King's Speech It is quite something when two blokes having a cup of coffee can generate more headlines and conversation than the King coming to parliament for the main ceremonial event of the parliamentary calendar. Both these things are happening this morning. The prime minister has met the Health Secretary Wes Streeting in private - a meeting offered by Sir Keir Starmer to cabinet ministers after Tuesday's cabinet meeting and an offer Streeting took up. It was a very short meeting - under 20 minutes - and we may not know what happened in Number 10 immediately. And then, not long afterwards, the King will arrive in Westminster for the State Opening of Parliament, in which the sovereign reads out the government's planned new laws for the year and a bit ahead. This ceremonial occasion was scheduled for this week precisely because government figures anticipated a rough set of election results and a splash of political tumult afterwards.

Smart glasses are'an invasion of privacy' - Meta's are selling better than ever Issues with a new wave of smart glasses seem to be piling up. Yet some of the biggest technology companies in the world are poised to sell many millions of pairs in the coming years. Women leaving the beach, going into a shop, or simply standing outside are now being approached by men usually wearing Meta's Ray-Bans, the company's smart or AI glasses, often in order to film the women's responses to casual questions or pick-up lines without their knowledge or consent. The women only find out about the videos of them after they gain traction, and often abuse, online. They have little legal recourse as photography in public is broadly considered legal.

Matt Keightley in his 2015 Chelsea garden, designed for Prince Harry. This year he is launching an AI app that has'designed' three full-size gardens for the show. Matt Keightley in his 2015 Chelsea garden, designed for Prince Harry. This year he is launching an AI app that has'designed' three full-size gardens for the show. Wed 13 May 2026 01.00 EDTLast modified on Wed 13 May 2026 01.01 EDT With glasses of champagne sipped among the peonies, Chelsea flower show is generally a friendly and genteel occasion.

Is Big Brother watching you shop? - podcast From supermarkets to corner shops, live facial recognition could be coming to retailers near you. Live facial recognition is being hailed as a powerful new frontier in the fight against crime, not only by police but by private companies too. Retailers from supermarkets to corner shops hope it will help them fight back against shoplifting. And the technology doesn't always get it right. With more police forces wanting to take up the technology, what could the consequences be?

We present a machine learning framework for testing general relativity (GR) with gravitational wave signals from binary black hole mergers. Using the source parameters of 173 BBH events from the GWTC catalog as a realistic astrophysical population, we generate simulated GR waveforms and construct beyond GR (BGR) waveforms by applying controlled phase deformations. We introduce a response function formalism that provides a systematic framework for quantifying how any observable responds to modifications of GR. We train convolutional neural networks (CNNs) on two input representations: whitened waveforms and a response function type observable derived from the waveform mismatch, which isolates the effect of phase deviations from the bulk signal. Using response functions as the CNN input improves the classification sensitivity by a factor of approximately 33 compared to whitened waveforms, demonstrating that the choice of observable representation is as important as the classifier architecture. We study the fundamental limits of this classification through Bayes optimal error analysis, averaging methods that reveal coherent patterns hidden in noise, and a comparison between CNN accuracy and a single feature classifier as a proxy for human performance. At all deformation scales, the CNN outperforms the best single feature approach. We extend the framework to physically motivated theories using the parameterized post Einsteinian (ppE) formalism and apply it to massive gravity, where the classifier detects deviations for graviton masses of order $m_g \sim 10^{-23}\;\mathrm{eV}/c^2$ with aLIGO design sensitivity.

Batch normalization (BN) is central to modern deep networks, but its effect on the realized function during training remains less understood than its optimization benefits. We study training-time BN in continuous piecewise-affine (CPA) networks through the geometry of switching hyperplanes and the induced affine-region partition. Conditioned on a mini-batch, we show that BN defines for each neuron a reference hyperplane through the batch centroid, and that breakpoint-switching hyperplanes are parallel translates whose offsets are expressed in batch-standardized coordinates and are independent of the raw bias. This yields an exact criterion for when a switching hyperplane intersects a local $\ell_\infty$ window and motivates a local region-density functional based on exact affine-region counts. Under explicit sufficient conditions, we show that BN increases expected local partition refinement in ReLU and more general piecewise-affine networks, and that this mechanism transfers locally through depth inside parent affine regions where the upstream representation map is an affine embedding. These results provide a function-level geometric account of training-time BN as a batch-conditional recentering mechanism near the data.

We study the information-theoretic limits of learning a one-hidden-layer teacher network with hierarchical features from noisy queries, in the context of knowledge transfer to a smaller student model. We work in the high-dimensional regime where the teacher width $k$ scales linearly with the input dimension $d$ -- a setting that captures large-but-finite-width networks and has only recently become analytically tractable. Using a heuristic leave-one-out decoupling argument, validated numerically throughout, we derive asymptotically sharp characterizations of the Bayes-optimal generalization error and individual feature overlaps via a system of closed fixed-point equations. These equations reveal that feature learnability is governed by a sequence of sharp phase transitions: as data grows, teacher features become recoverable sequentially, each through a discontinuous jump in overlap. This sequential acquisition underlies a precise notion of \textit{effective width} $k_c$ -- the number of learnable features at a given data budget $n$ -- which unifies two distinct scaling regimes: a feature-learning regime in which the Bayes-optimal generalization error $\varepsilon^{\rm BO}$ scales as $ n^{1/(2β)-1}$, and a refinement regime in which it scales as $n^{-1}$, where $β>1/2$ is the exponent of the power-law feature hierarchy. Both laws collapse to the single relation $\varepsilon^{\rm BO}=Θ(k_c d/n)$. We further show empirically that a student trained with \textsc{Adam} near the effective width $k_c$ achieves these optimal scaling laws (up to a small algorithmic gap), and provide an information-theoretic account of the associated scaling in model size.

We study the large-depth limit of transformers trained with AdamW, by modelling the hidden-state dynamics as an interacting particle system (IPS) coupled through the attention mechanism. Under appropriate scaling of the attention heads, we prove that the joint dynamics of the hidden states and backpropagated variables converge in $L^2$, uniformly over the initial condition, to the solution of a forward--backward system of ODEs at rate $\mathcal O(L^{-1}+L^{-1/3}H^{-1/2})$. Here, $L$ and $H$ denote the depth and number of heads of the transformer, respectively. The limiting system of ODEs can be identified with a McKean--Vlasov ODE (MVODE) when the attention heads do not incorporate causal masking. By using the flow maps associated with this MVODE and applying concentration of measure techniques, we obtain bounds on the difference between the discrete and continuous models that are uniform over compact sets of initial conditions. As this is achieved without resorting to a covering argument, the constants in our bounds are independent of the number of tokens. Furthermore, under a suitable adaptation to AdamW, the bounds become independent of the token embedding dimension.

Learning generative models in settings where the source and target distributions are only specified through unpaired samples is gaining in importance. Here, one frequently-used model are Schrödinger bridges (SB), which represent the most likely evolution between both endpoint distributions. To accelerate training, simulation-free SBs avoid the path simulation of the original SB models. However, learning simulation-free SBs requires paired data; a coupling of the source and target samples is obtained as the solution of the entropic optimal transport (OT) problem. As obtaining the optimal global coupling is infeasible in many practical cases, the entropic OT problem is iteratively solved on minibatches instead. Still, the repeated cost remains substantial and the locality can distort the global transport geometry. We propose quantized diffusion Schrödinger bridges (QDSB), which compute the endpoint coupling on anchor-quantized endpoint distributions and lift the resulting plan back to original data points through cell-wise sampling. We show that the regularized optimal coupling is stable w.r.t. anchor quantization, with an error controlled by the quality of the anchor approximation. In real-world experiments, QDSB matches the sample quality of existing baselines, requiring substantially less time. Code and data are available at github.com/mathefuchs/qdsb.