Anthropic has usurped OpenAI as the world's most valuable artificial intelligence startup, soaring to a $965bn valuation ahead of expected public listings by the rival firms. Anthropic, the maker of the Claude family of chatbots, said on Thursday that it had raised $65bn from private investors after a fundraising round led by Altimeter Capital, Greenoaks, Dragoneer and Sequoia Capital. "This funding will help us serve the historic demand we are experiencing, stay at the research frontier, and bring Claude to more of the places where work happens," Anthropic's Chief Financial Officer Krishna Rao said in a statement. Altimeter Capital CEO Brad Gerstner hailed the adoption of Claude among the "world's most demanding organisations" as evidence of Anthropic's command in the field. "This momentum positions Anthropic to lead the next phase of AI innovation and capture the enormous opportunity ahead," Gerstner said.

Taiyo Yuden sees'scary' levels of AI parts demand risking supply chain Multilayer ceramic capacitors, which are tiny components that regulate and stabilize power flow in electronic devices, are becoming a growing bottleneck in the construction of artificial intelligence data centers. Taiyo Yuden is fielding "scary" levels of demand for its high-end artificial intelligence server components, stretching capacity and increasing the risk of supply chain hiccups. The Tokyo-based company, which makes multilayer ceramic capacitors, will likely need to accelerate spending to expand output capacity, Chief Executive Officer Katsuya Sase said in an interview. MLCCs, which are tiny components that regulate and stabilize power flow in electronic devices, are becoming a growing bottleneck in the construction of artificial intelligence data centers. Taiyo Yuden and Murata Manufacturing comprise the bulk of the world's supplies of high-end MLCCs. "The volumes we are seeing today -- it's scary," Sase said.

Saddle-point models arise throughout optimization, optimal transport, robust learning, and control. In many applications, the relevant function f(x,y) is convex in x and concave in y, and preserving this geometry is essential for obtaining tractable min--max formulations and reliable certificates. We introduce a structured separable decomposition that preserves the convex-concave geometry and prove a complete one-dimensional approximation theorem under a mixed Monge-type convexity condition. We then describe practical saddle network architectures that preserve convexity in x and concavity in y by construction. The proposed architectures require only convexity-preserving neural networks, together with simple output transformations enforcing sign and concavity constraints. Finally, we report numerical benchmarks in dimension 1 and 5, showing that the proposed saddle networks achieve high accuracy on smooth, nonsmooth, and high-rank convex--concave test functions.

Model-based reinforcement learning (MBRL) agents typically learn world models by minimizing predictive loss. However, powerful RL optimizers inevitably exploit minor model inaccuracies, leading to simulator exploitation and a reality gap where policies succeed in simulation but fail in the real world. We propose that the objective for learning simulators should be strategic robustness rather than predictive accuracy, and formulate this as a zero-sum minimax game between a model player and an adversarial policy player. We provide a comprehensive theoretical analysis: (1) an online learning guarantee showing the game is learnable with sublinear regret bounds; (2) a tractable critic-based simplification bounding the global policy-value gap by the local critic's loss; and (3) an Error-MDP duality, proving that finding the worst-case policy is formally dual to a standard RL problem where the reward is the one-step critic error. This duality yields a provably convergent active data selection algorithm. Experiments on continuous control tasks demonstrate that our approach reduces prediction error in strategically important regions by $1.5$-$2.2\times$ and enables policies trained purely in simulation to match near-optimal real-world performance.

Conformal prediction (CP) and its extension, conformal risk control (CRC), are established frameworks for quantifying uncertainty in supervised machine learning through formal guarantees. However, recent breakthroughs in artificial intelligence (AI) have been driven by unsupervised generative models, such as large language models (LLMs) and image generators, which are not directly compatible with CP or CRC. In this work we introduce conformal generation (Conf-Gen), a general framework adapting CRC to generative tasks while relaxing its theoretical assumptions. Conf-Gen unifies and generalizes previous attempts to apply CP to LLMs, and extends conformal methodology to entirely new domains. We demonstrate the flexibility of Conf-Gen through some novel applications, including obtaining conformal guarantees on: image generators producing non-memorized images, conversational AI systems having asked enough clarifying questions, and the output of AI agents being correct.

Federated Conformal RAG (FC-RAG) provides distribution-free coverage for a bandwidth-limited swarm of weak language models, but only at a fixed horizon. We extend it to anytime-valid sequential coverage: validity at every stopping time, preserved under predictable adaptive control (recalibration, per-node bandwidth escalation, distilled-student refresh), at no extra cost in assumptions over fixed-horizon FC-RAG. Naive composition fails because FC-RAG's marginal coverage bound makes the betting e-process a non-supermartingale on adverse calibration draws, and Ville's inequality cannot be invoked. We give Anytime-FC-RAG, a sequential extension built on a summable per-step calibration-deviation budget that converts the marginal bound into a strict conditional bound on a calibration-good event, paired with a truncated betting e-process that is a nonnegative supermartingale on the entire probability space. From these two ingredients, we obtain four guarantees: time-uniform alarm validity $\mathbb{P}(\sup_t E_t \ge 1/δ_e) \le δ_e + δ_{\mathrm{cal}}$, a Hoeffding-stitched cumulative-miscoverage envelope at the same total budget, safety under any predictable controller (recalibration, bandwidth escalation, student refresh), and training-side error propagation across an unbounded sequence of Federated Probe-Logit Distillation (FPLD) refreshes via a summable training budget. As a practical consequence, an adaptive controller that escalates retrieval bandwidth only when the e-process crosses a warning threshold matches the alarm rate of a fixed-high-bandwidth schedule at substantially lower communication cost. Experiments on a GPT-2-small + MiniLM swarm across MMLU, DBpedia, and AG News verify the predicted alarm rate, detection delay, envelope coverage, and $14$-$57\%$ bandwidth savings; the alarm fires when and only when coverage genuinely breaks.

We study stochastic decision-theoretic online learning with full information and event-level pure differential privacy. A COLT open problem of Hu and Mehta asks to determine the optimal gap-dependent regret rate for stochastic decision-theoretic online learning under pure event-level differential privacy. For $K$ actions, losses in $[0,1]$, and a unique best action separated from the second-best action by gap $Δ_{\min}$, the known lower bound is of order $ \frac{\log K}{\min\{Δ_{\min},\varepsilon\}}, $ or equivalently, up to universal constants, of order \[ \frac{\log K}{Δ_{\min}}+\frac{\log K}{\varepsilon}. \] We give a horizon-free pure-DP algorithm and prove the explicit regret bound \[ \operatorname{Reg}_T \le 1000 \cdot \left(\frac{\log K}{Δ_{\min}}+\frac{\log K}{\varepsilon}\right) \] for every horizon $T$. The numerical constant is not optimized. The algorithm partitions time into blocks of exponentially increasing size, plays a single action throughout each block, and chooses the next action by an exponential mechanism applied to a data-independent random prefix of the previous block. The random prefix converts block regret into a sum, over all prefix lengths, of softmax selection errors. A single entropy-potential argument controls all privacy-dominated large-gap actions at cost $\log K/\varepsilon$.

Randomly initialized neural networks induce a prior over functions, but the predictor used in practice is produced only after training. We ask how much of this initial bias survives the training pipeline. To make the question measurable, we introduce initialization memory: the dependence of the validation-selected predictor on the scale of the random initialization. We perform controlled CIFAR-10 experiments on ResNets where initialization memory already sharply separates training regimes. Low-learning-rate SGD can interpolate while still remembering its initialization: on ResNet-9 with batch size $b=128$, test accuracy varies by $26.5$ percentage points across initialization scales despite $\ge99.5\%$ training accuracy. This is not undertraining: extending the same low-learning-rate regime to $5{,}000$ epochs leaves the spread essentially unchanged. In contrast, Adam-family methods largely erase the dependence. SGD can also be made to forget when larger learning rates are paired with explicit $L_2$ norm control. We interpret these findings in terms of the time scale of forgetting: gradient-flow-like dynamics can preserve initialization memory, whereas stochastic finite-step effects, explicit norm decay, and adaptive preconditioning erase it on scales governed by the size of explicit or implicit regularization. The practical inductive bias of a trained network is therefore not the architectural prior alone, but the architectural prior after being filtered by the forgetting dynamics of the training pipeline; and the same regularizers that improve generalization are precisely those that erase memory of initialization.

We develop a natural Bayesian multiplicity-correcting prior distribution within the probabilistic forward stepwise representation of model space priors for regression problems. The proposed prior, obtained from making an analogy to the Holm procedure, exhibits behavior closely aligned with that of the Matryoshka doll prior. We compare both priors to several other priors, including some recently put forward as objective choices for model space prior probabilities. Our comparisons indicate that adequate multiplicity correction requires a degree of sparsity that many recommended priors do not provide, and we argue that multiplicity correction itself offers a principled and transparent criterion for specifying model space priors in regression.

Fraud detection models in payment networks train on chargeback labels that are systematically biased. Every label must survive three sequential gates: authorization (declined transactions generate no labels), issuer reporting (unreported fraud is invisible), and delay (pending chargebacks are missing at training time). Labels that do arrive may be corrupted by first-party misuse or issuer misclassification. A companion paper [arXiv:2605.27557] proved that these four impairments impose a minimax lower bound on detection performance. This paper asks: can that bound be achieved? We formalize the observation pipeline as a sequential missing-data problem with three propensity stages and a corruption layer, and construct the Sequential Triply Robust (STR) estimator. The STR corrects for all four impairments simultaneously and achieves the semiparametric efficiency bound -- no estimator can have lower asymptotic variance. It is sequentially triply robust: at each gate, consistency requires only that either the propensity model or the outcome regression is correctly specified, not both. We provide corruption correction via noise-rate-adjusted pseudo-labels, empirical Bayes shrinkage to stabilize inverse-propensity weights for small issuers, a plug-in variance estimator yielding valid confidence intervals, and a Bernstein concentration inequality for finite-sample guarantees. On the operational side, we derive the optimal training delay -- the maturity window that minimizes the sum of label-quality loss and model staleness -- and prove that the STR permits training on data that is days old rather than months old, decoupling model freshness from the chargeback maturity cycle. The STR provably dominates naive chargeback-based training in mean squared error for any sample size.