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Viscosity, the internal friction of fluids, is among the most consequential yet underappreciated properties in physics. This paper explores what would happen if viscosity vanished from all fluids while other material properties remained unchanged. The consequences are catastrophic and universal. Aircraft cannot generate lift because circulation around wings requires viscous action. Rotating machinery seizes without lubricating fluid films. Cardiovascular systems lose the resistance necessary for pressure regulation. Rivers become violent torrents, aquifers drain in hours, and storms persist indefinitely without frictional dissipation. The pedagogical value lies in illuminating viscosity's role providing resistance, damping, and control across all scales - from cellular interiors to planetary atmospheres. Evolution, engineering, and climate have exploited viscous dissipation for billions of years; its absence would render complex life impossible and Earth uninhabitable. By imagining a world without viscosity, we better understand the viscous world we inhabit.

In this article, we consider a sufficient condition that a knot-surgery or log-transformation of $E(n)$ admits a handle decomposition without 1-handles. We show that if $K$ is a knot that the bridge number is $b(K)\le 9n$, then the knot-surgery $E(n)_K$ of the elliptic surface $E(n)$ admits a handle decomposition without 1-handles. This means that if $\gcd(p,q)=1$, and $\min\{p,q\}\le 9$, then $E(1)_{p,q}$ admits a handle decomposition without 1-handles. We also show that if $\gcd (p,q)=1$, $\min\{p,q\}\le 4$, then the double log-transformation $E(n)_{p,q}$ admits a handle decomposition without 1-handles for any positive integer $n$.

Normalization layers are ubiquitous in modern neural networks and have long been considered essential. This work demonstrates that Transformers without normalization can achieve the same or better performance using a remarkably simple technique. We introduce Dynamic Tanh (DyT), an element-wise operation $DyT($x$) = \tanh(α$x$)$, as a drop-in replacement for normalization layers in Transformers. DyT is inspired by the observation that layer normalization in Transformers often produces tanh-like, $S$-shaped input-output mappings. By incorporating DyT, Transformers without normalization can match or exceed the performance of their normalized counterparts, mostly without hyperparameter tuning. We validate the effectiveness of Transformers with DyT across diverse settings, ranging from recognition to generation, supervised to self-supervised learning, and computer vision to language models. These findings challenge the conventional understanding that normalization layers are indispensable in modern neural networks, and offer new insights into their role in deep networks.

We glue together two copies of pure AdS spacetime along their conformal boundaries creating a manifold without boundaries. The resulting space, which in dimension $d+2$ we denote by $AdS^{d+2}_\pm$, has the topology of $S^2\timesΣ^d$, where $Σ^d$ is a $d$-manifold without boundary. Acting with $\mathbb Z_n$ on the $S^2$ factor amounts to coupling a pair of membranes at the north and south poles of the 2-sphere. Moreover, extending the domain of the 2-sphere polar coordinate from $[0, π]$ to the interval $[0, (2N-1)π]$, where $N>1$, enables the coupling of one stack of $N$ coincident membranes at each pole of the 2-sphere ($2N$ membranes in total). Assuming the existence of a quantum gravity theory on the glued spacetime, we compute the classical approximation of the entanglement entropy across an entangling surface consisting of the two antipodal stacks of membranes. We find that the resulting entropy exhibits a boundary cutoff divergence that can be canceled by taking the limit of an infinite number of membranes. This large-$N$ cancellation -- possible only in the doubled, extended geometry without boundaries -- yields a finite, universal quarter-area law. The calculation does

Modern network intrusion detection systems (NIDS) are caught in a structural contradiction: the protocols carrying the highest threat intelligence are precisely those encrypted under TLS 1.3 and QUIC, where payload inspection yields nothing. We ask a simpler question -- what if the attack signature is not in the bytes, but in the rhythm? -- and answer it by treating network flows as a language whose grammar is written entirely in L3/L4 packet metadata: length, inter-arrival time, TTL, TCP flags, and hashed port numbers. We present PLM-NIDS, which proves three claims in sequence. (1) The grammar exists and is learnable: a RWKV-4 state-space model trained on 344,232 unlabelled Monday flows achieves a causal LM validation loss of 0.204, demonstrating that benign traffic has predictable, statistically consistent structure. (2) Attacks violate this grammar: the per-flow perplexity score cleanly separates benign from attack flows with PR-AUC = 0.93 using zero attack labels at training time. (3) This separation is architecturally nontrivial: an LSTM trained on identical token sequences degenerates to a majority-class predictor (ROC-AUC approximately 0.50, F1 = 0.91 by always predicting "a

We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for new ones. Existing implementations of QSVT rely on block encoding, incurring an intrinsic $O(\log L)$ ancilla overhead and circuit depth $\widetilde{O}(L dλ)$ for polynomial transformations of a Hamiltonian $H=\sum_{k=1}^L H_k$, where $d$ is the polynomial degree and $λ=\sum_{k}\|H_k\|$. We introduce a simple yet powerful approach that utilizes only basic Hamiltonian simulation techniques, namely, Trotter methods, to: (i) eliminate the need for block encoding, (ii) reduce the ancilla overhead to only a single qubit, and (iii) still maintain near-optimal complexity. Our method achieves a circuit depth of $\widetilde{O}(L(dλ_{\mathrm{comm}})^{1+o(1)})$, without requiring any complicated multi-qubit controlled gates. Moreover, $λ_{\mathrm{comm}}$ depends on the nested commutators of the terms of $H$ and can be substantially smaller than $λ$ for many physically relevant Hamiltonians, a feature absent in standard QSVT. To achieve these results, we make use of Richardson extrapolation in a novel way, systematical

Can one perceive a video's content without seeing its pixels, just from the camera trajectory-the path it carves through space? This paper is the first to systematically investigate this seemingly implausible question. Towards this end, we propose a contrastive learning framework to train CamFormer, a dedicated encoder that projects camera pose trajectories into a joint embedding space, aligning them with natural language. We find that, contrary to its apparent simplicity, the camera trajectory is a remarkably informative signal to uncover video content. In other words, "how you move" can indeed provide valuable cues about "what you are doing" (egocentric) or "observing" (exocentric). We demonstrate the versatility of our learned CamFormer embeddings on a diverse suite of downstream tasks, ranging from cross-modal alignment to classification and temporal analysis. Importantly, our representations are robust across diverse camera pose estimation methods, including both high-fidelity multi-sensored and standard RGB-only estimators. Our findings establish camera trajectory as a lightweight, robust, and versatile modality for perceiving video content.

There can be many competing and contradictory explanations for a single model prediction, making it difficult to select which one to use. Current explanation evaluation frameworks measure quality by comparing against ideal "ground-truth" explanations, or by verifying model sensitivity to important inputs. We outline the limitations of these approaches, and propose three desirable principles to ground the future development of explanation evaluation strategies for local feature importance explanations. We propose a ground-truth Agnostic eXplanation Evaluation framework (AXE) for evaluating and comparing model explanations that satisfies these principles. Unlike prior approaches, AXE does not require access to ideal ground-truth explanations for comparison, or rely on model sensitivity - providing an independent measure of explanation quality. We verify AXE by comparing with baselines, and show how it can be used to detect explanation fairwashing. Our code is available at https://github.com/KaiRawal/Evaluating-Model-Explanations-without-Ground-Truth.

Large Language Models (LLMs), when paired with prompt-based tasks, have significantly reduced data annotation costs and reliance on human annotators. However, evaluating the quality of their annotations remains challenging in dynamic, unsupervised environments where oracle feedback is scarce and conventional methods fail. To address this challenge, we propose a novel agentic annotation paradigm, where a student model collaborates with a noisy teacher (the LLM) to assess and refine annotation quality without relying on oracle feedback. The student model, acting as an unsupervised feedback mechanism, employs a user preference-based majority voting strategy to evaluate the consistency of the LLM outputs. To systematically measure the reliability of LLM-generated annotations, we introduce the Consistent and Inconsistent (CAI) Ratio, a novel unsupervised evaluation metric. The CAI Ratio not only quantifies the annotation quality of the noisy teacher under limited user preferences but also plays a critical role in model selection, enabling the identification of robust LLMs in dynamic, unsupervised environments. Applied to ten open-domain NLP datasets across four LLMs, the CAI Ratio demon

The classic newsvendor model yields an optimal decision for a ``newsvendor'' selecting a quantity of inventory, under the assumption that the demand is drawn from a known distribution. Motivated by applications such as cloud provisioning and staffing, we consider a setting in which newsvendor-type decisions must be made sequentially, in the face of demand drawn from a stochastic process that is both unknown and nonstationary. All prior work on this problem either (a) assumes that the level of nonstationarity is known, or (b) imposes additional statistical assumptions that enable accurate predictions of the unknown demand. Our research tackles the Nonstationary Newsvendor without these assumptions, both with and without predictions. We first, in the setting without predictions, design a policy which we prove achieves order-optimal regret -- ours is the first policy to accomplish this without being given the level of nonstationarity of the underlying demand. We then, for the first time, introduce a model for generic (i.e. with no statistical assumptions) predictions with arbitrary accuracy, and propose a policy that incorporates these predictions without being given their accuracy. W

We construct rigid Poisson suspensions without roots. The discrete rational component in spectrum of an ergodic automorphism S prevents some roots from existing. If S is tensorly multiplied by an ergodic automorphism of the space with a sigma-finite measure, discrete spectrum disappears in this product, but like the smile of Cheshire Cat, the memory of it can remain in the form of the absence of roots. In additional conditions, this effect is inherited by the Poisson suspension over the above product. Starting from this idea, but without using the tensor product, we describe simple rank-one constructions for which the Poisson suspensions are rigid and have no roots.

This article examines the implicit regularization effect of Stochastic Gradient Descent (SGD). We consider the case of SGD without replacement, the variant typically used to optimize large-scale neural networks. We analyze this algorithm in a more realistic regime than typically considered in theoretical works on SGD, as, e.g., we allow the product of the learning rate and Hessian to be $O(1)$ and we do not specify any model architecture, learning task, or loss (objective) function. Our core theoretical result is that optimizing with SGD without replacement is locally equivalent to making an additional step on a novel regularizer. This implies that the expected trajectories of SGD without replacement can be decoupled in (i) following SGD with replacement (in which batches are sampled i.i.d.) along the directions of high curvature, and (ii) regularizing the trace of the noise covariance along the flat ones. As a consequence, SGD without replacement travels flat areas and may escape saddles significantly faster than SGD with replacement. On several vision tasks, the novel regularizer penalizes a weighted trace of the Fisher Matrix, thus encouraging sparsity in the spectrum of the Hes

Typically, the period-doubling bifurcations exhibited by nonlinear dissipative systems are observed when varying systems' parameters. In contrast, the period-doubling bifurcations considered in the current research are induced by changing the initial conditions whereas parameter values are fixed. Thus, the studied bifurcations can be classified as the period-doubling bifurcations without parameters. Moreover, we show a cascade of the period-doubling bifurcations without parameters resulting in transition to deterministic chaos. The explored effects are demonstrated by means of numerical modelling on an example of a modified Anishchenko-Astakhov self-oscillator where the ability to exhibit bifurcations without parameters is associated with the properties of a memristor. Finally, we compare the dynamics of the ideal-memristor-based oscillator with the behaviour of a model taking into account the memristor forgetting effect.

We propose a quantum programming paradigm where all data are familiar classical data, and the only non-classical element is a random number generator that can return results with negative probability. Currently, the vast majority of quantum programming languages instead work with quantum data types made up of qubits. The description of their behavior relies on heavy linear algebra and many interdependent concepts and intuitions from quantum physics, which takes dedicated study to understand. We demonstrate that the proposed view of quantum programming explains its central concepts and constraints in more accessible, computationally relevant terms. This is achieved by systematically reducing everything to the existence of that negative-probability random generator, avoiding mention of advanced physics as much as possible. This makes quantum programming more accessible to programmers without a deep background in physics or linear algebra. The bulk of this paper is written with such an audience in mind. As a working vehicle, we lay out a simple quantum programming language under this paradigm, showing that not only can it express all quantum programs, it also naturally captures the se

Recently, we introduced a configuration space with interaction structure and a uniform local cohomology on it with co-authors in arXiv:2009.04699. The notion is used to understand a common structure of infinite product spaces appeared in the proof of Varadhan's non-gradient method. For this, the cohomology of the configuration space with a group action is the main target to study, but the cohomology is easily obtained from that of the configuration space without a group action by applying a well-known property on the group cohomology. In fact, the analysis of the cohomology of the configuration space without a group action is the essential part of arXiv:2009.04699. In this article, we give an elementary and direct proof to obtain the cohomology of a space with a group action from that without a group action under a certain condition including the setting of the configuration space with interaction structure. In particular, no knowledge of group cohomology is required.

Adversarial robustness poses a critical challenge in the deployment of deep learning models for real-world applications. Traditional approaches to adversarial training and supervised detection rely on prior knowledge of attack types and access to labeled training data, which is often impractical. Existing unsupervised adversarial detection methods identify whether the target model works properly, but they suffer from bad accuracies owing to the use of common cross-entropy training loss, which relies on unnecessary features and strengthens adversarial attacks. We propose new training losses to reduce useless features and the corresponding detection method without prior knowledge of adversarial attacks. The detection rate (true positive rate) against all given white-box attacks is above 93.9% except for attacks without limits (DF($\infty$)), while the false positive rate is barely 2.5%. The proposed method works well in all tested attack types and the false positive rates are even better than the methods good at certain types.

We provide a powerful machinery to prove fully smooth one shot multipartite covering, aka convex split, type results for quantum states. In the important case of smooth multipartite convex split for classical quantum states, aka smooth multipartite soft covering, our machinery works even when certain marginals of these states do not satisfy pairwise independence. The recent paper (arXiv:2410.17893) gave the first proof of fully smooth multipartite convex split by simplifying and extending a technique called telescoping, developed originally for convex split by (arXiv:2304.12056). However, that work as well as all earlier works on convex split assumed pairwise or even more independence amongst suitable marginals of the quantum states. We develop our machinery by leveraging known results from (arXiv:1806.07278) involving tilting and augmentation smoothing of quantum states, combined with a novel observation that a natural quantum operation `flattening' quantum states actually preserves the fidelity. This machinery is powerful enough to lead to non pairwise independent results as mentioned above. As an application of our soft covering lemma without pairwise independence, we prove the

Learning from changing tasks and sequential experience without forgetting the obtained knowledge is a challenging problem for artificial neural networks. In this work, we focus on two challenging problems in the paradigm of Continual Learning (CL) without involving any old data: (i) the accumulation of catastrophic forgetting caused by the gradually fading knowledge space from which the model learns the previous knowledge; (ii) the uncontrolled tug-of-war dynamics to balance the stability and plasticity during the learning of new tasks. In order to tackle these problems, we present Progressive Learning without Forgetting (PLwF) and a credit assignment regime in the optimizer. PLwF densely introduces model functions from previous tasks to construct a knowledge space such that it contains the most reliable knowledge on each task and the distribution information of different tasks, while credit assignment controls the tug-of-war dynamics by removing gradient conflict through projection. Extensive ablative experiments demonstrate the effectiveness of PLwF and credit assignment. In comparison with other CL methods, we report notably better results even without relying on any raw data.

This article examines Hilbert spaces constructed from sets whose existence is incompatible with the Countable Axiom of Choice (CC). Our point of view is twofold: (1) We examine what can and cannot be said about Hilbert spaces and operators on them in ZF set theory without any assumptions of Choice axioms, even the CC. (2) We view Hilbert spaces as ``quantized'' sets and obtain some set-theoretic results from associated Hilbert spaces.