Recent measurements of Jupiter's gravitational moments by the Juno spacecraft and seismology of Saturn's rings suggest that the primordial composition gradients in the deep interior of these planets have persisted since their formation. One possible explanation is the presence of a double-diffusive staircase below the planet's outer convection zone, which inhibits mixing across the deeper layers. However, hydrodynamic simulations have shown that these staircases are not long-lasting and can be disrupted by overshooting convection. In this paper we suggests that planetary rotation could be another factor for the longevity of primordial composition gradients. Using rotational mixing-length theory and 3D hydrodynamic simulations, we demonstrate that rotation significantly reduces both the convective velocity and the mixing of primordial composition gradients. In particular, for Jovian conditions at $t\sim10^{8}~\mathrm{yrs}$ after formation, rotation reduces the convective velocity by a factor of 6, and in turn, the kinetic energy flux available for mixing gets reduced by a factor of $6^3\sim 200$. This leads to an entrainment timescale that is more than two orders of magnitude longer
Introduced by Hinton et al. in 2012, dropout has stood the test of time as a regularizer for preventing overfitting in neural networks. In this study, we demonstrate that dropout can also mitigate underfitting when used at the start of training. During the early phase, we find dropout reduces the directional variance of gradients across mini-batches and helps align the mini-batch gradients with the entire dataset's gradient. This helps counteract the stochasticity of SGD and limit the influence of individual batches on model training. Our findings lead us to a solution for improving performance in underfitting models - early dropout: dropout is applied only during the initial phases of training, and turned off afterwards. Models equipped with early dropout achieve lower final training loss compared to their counterparts without dropout. Additionally, we explore a symmetric technique for regularizing overfitting models - late dropout, where dropout is not used in the early iterations and is only activated later in training. Experiments on ImageNet and various vision tasks demonstrate that our methods consistently improve generalization accuracy. Our results encourage more research o
Abstractive summarization aims at generating natural language summaries of a source document that are succinct while preserving the important elements. Despite recent advances, neural text summarization models are known to be susceptible to hallucinating (or more correctly confabulating), that is to produce summaries with details that are not grounded in the source document. In this paper, we introduce a simple yet efficient technique, CoBa, to reduce hallucination in abstractive summarization. The approach is based on two steps: hallucination detection and mitigation. We show that the former can be achieved through measuring simple statistics about conditional word probabilities and distance to context words. Further, we demonstrate that straight-forward backtracking is surprisingly effective at mitigation. We thoroughly evaluate the proposed method with prior art on three benchmark datasets for text summarization. The results show that CoBa is effective and efficient in reducing hallucination, and offers great adaptability and flexibility. Code can be found at https://github.com/zhenzhel/CoBa.
Pre-trained language models (LMs) store knowledge in their parameters and can generate informative responses when used in conversational systems. However, LMs suffer from the problem of "hallucination:" they may generate plausible-looking statements that are irrelevant or factually incorrect. To address this problem, we propose a contrastive learning scheme, named MixCL. A novel mixed contrastive objective is proposed to explicitly optimize the implicit knowledge elicitation process of LMs, and thus reduce their hallucination in conversations. We also examine negative sampling strategies of retrieved hard negatives and model-generated negatives. We conduct experiments on Wizard-of-Wikipedia, a public, open-domain knowledge-grounded dialogue benchmark, and assess the effectiveness of MixCL. MixCL effectively reduces the hallucination of LMs in conversations and achieves the highest performance among LM-based dialogue agents in terms of relevancy and factuality. We show that MixCL achieves comparable performance to state-of-the-art KB-based approaches while enjoying notable advantages in terms of efficiency and scalability.
The optimal price of each firm falls in the search cost of consumers, in the limit to the monopoly price, despite the exit of lower-value consumers in response to costlier search. Exit means that fewer inframarginal consumers remain. The decrease in marginal buyers is smaller, because part of demand is composed of customers coming from rival firms. These buyers can be held up and are not marginal. Higher search cost reduces the fraction of incoming switchers among buyers, which decreases the hold-up motive, thus the price.
A drug originally developed for spinal cord injury may offer a fresh approach to treating Alzheimer’s disease。 In mouse studies, KCL-286 repaired dangerous DNA damage, reduced inflammation, and targeted multiple disease-related pathways instead of focusing on just amyloid or tau。 Since it has already cleared an initial human safety trial, researche
Guessing Random Additive Noise Decoding (GRAND) is a universal framework for decoding all block codes by testing candidate error patterns (EPs). Ordered Reliability Bits GRAND (ORBGRAND) facilitates parallel implementation of GRAND by exploiting log-likelihood ratio (LLR) rankings but still suffers from high tail latency under unfavorable channel conditions, limiting its use in real-time systems. We propose an elimination-aided ORBGRAND scheme that reduces decoding latency by integrating the Rank of the Most Reliable Erroneous (RMRE) bit with a partial Gaussian-elimination (GE) filtering mechanism. The scheme groups and jointly verifies EPs that share the same RMRE, and once a valid EP is identified, the ORBGRAND search is resumed. By leveraging prior GE steps to filter out unnecessary guesses, this approach significantly reduces the number of EPs to be tested, thereby lowering both average and worst-case latency while maintaining error-correction performance. Simulation results show that compared to the original ORBGRAND, the elimination-aided ORBGRAND filters out more than 50\% of EPs and correspondingly reduce overall computational complexity, all with no loss in block error rat
The standard taxonomy of predictive uncertainty defines epistemic uncertainty as the part removable by collecting more data, while the standard measure identifies it with a mutual-information term. We prove the definition and the measure are extensionally inconsistent. On an explicit construction, the measure assigns all uncertainty to the epistemic class, yet no quantity of training data reduces it. Reducibility is instead a property of the pair (uncertainty, acquisition class), and the dichotomy resolves into three parts: aleatoric, sample-reducible epistemic, and mechanism-reducible epistemic uncertainty. An exact identity for the value of an observation shows that in-distribution data never reduces mechanism-irreducible uncertainty and generically increases it. Ensemble disagreement, the deployed epistemic estimate, tracks the training procedure rather than the epistemic term. It collapses to zero beneath a positive truth under consistent training, and equals hyperparameter-scaled initialization noise under interpolation. A finite-sample falsification test and seed-swept experiments confirm the theory.
The rise of reasoning models and agentic systems has made LLM token-generation latency a key bottleneck. Unlike chatbots, whose latency gains saturate at human reading speed, these systems generate intermediate reasoning tokens not consumed by humans. Thus, per-token latency directly determines end-to-end response time. Low-latency inference uses minimal batching, making token generation bandwidth-bound. Tensor Parallelism addresses this by sharding model weights across GPUs and loading them in parallel. However, scaling to more GPUs introduces All-Reduce overheads that grow with GPU count. Removing All-Reduce improves token throughput by 43% for Llama-3.1-8B on 8 H200 GPUs. We propose Synchronization-Free All-Reduce (SiFAR), which reduces synchronization overhead during low-latency inference. Existing oneshot and twoshot algorithms incur overheads from barriers before and after communication. First, we find that the bottom barrier in oneshot enforces a WAW dependency and eliminate it by co-designing communication and model execution to enable dual buffering. However, oneshot scales poorly with GPU count. Twoshot performs better at higher TP degrees but incurs an unavoidable bottom
Large language models (LLMs) exhibit systematic political bias across a variety of sensitive contexts. We find that LLMs handle counterpart topics from opposing political sides asymmetrically. We refer to this phenomenon as covert political bias and identify 7 categories of techniques through which it operates. We propose two metrics for covert bias: Sentiment Consistency measures symmetry in rhetoric and framing across paired political prompts; Helpfulness Consistency measures symmetric depth and engagement. To reduce both types of covert bias, we introduce Political Consistency Training (PCT), an RL training method with two complementary paradigms: Sentiment Consistency Training and Helpfulness Consistency Training. We show that PCT preserves overall helpfulness, substantially reduces covert political bias, and generalizes to held-out benchmarks. We release our work at https://political-manipulation.ai
Given a positive integer $k$, we investigate the $k$-redcibility of self-maps in the monoid $Å^k(X\vee Y)$, consisting of self-maps that induce isomorphisms on homology groups up to degree $k$. In general, verifying $k$-reducibility is a subtle problem. We show that the $k$-reducibility of a self-map is determine through its induced endomorphisms on homology or cohomology groups. Moreover, under the k-reducibility assumption, the computation of the homology self-closeness number of the wedge sum of spaces essentially reduces to the computation of the homology self-closeness numbers of the individual wedge summands. We generalize the notion of an atomic space to that of an $n$-atomic space and establish some of its fundamental properties. We show that the $k$-reducibility criteria for self-maps in a monoid $Å^k(X)$ is satisfied when the space $X$ decomposes as a wedge sum of distinct $n$-atomic spaces. Finally, we determine the homology self-closeness numbers of wedge sums of distinct $n$-atomic spaces.
Tokenization directly affects the inference efficiency of large language models, since fragmented tokenization increases sequence length and generation cost. Although longer, multi-word tokens can reduce fertility, naively adding them often degrades language model performance. We propose Thunder-Tok, a subword tokenizer that reduces fertility while preserving downstream performance. Thunder-Tok first constructs a large seed vocabulary from corpus substrings and filters structurally incomplete candidates, including invalid Unicode byte fragments and word-boundary violations. It then prunes the seed vocabulary using a likelihood-based token score derived from a uniform Jensen lower bound of the training-data probability. Experiments show that Thunder-Tok reduces fertility by approximately 25% in English and 9% in Korean compared with the standard BPE tokenizer while maintaining competitive performance.
SJT reducibility between sets $A,B \subseteq \mathbb N$ is defined by $A \le_{SJT} B$ if for each computable function $h$ that is unbounded and nondecreasing, there is an $h$-bounded uniformly $B$-c.e.\ trace $(T_n)_{n \in \mathbb N} $ such that for each $n$, the value $J^A(n)$ of the jump is in $T_n$, if defined. This reducibility is slightly weaker than Turing reducibility. We study SJT reducibility, and as a main result give several characterisations of it on the $K$-trivial sets. This is the first case of extending the three lowness paradigms, weak as an oracle, computed by many, and inert, to the setting of weak reducibilities.
It is shown that the first-order term of the asymptotic bias of the posterior mean is removed by a suitable choice of a prior density. In regular statistical models including exponential families, and linear and logistic regression models, such a prior is given by the squared Jeffreys prior. We also explain the relationship between the proposed prior distribution, the moment matching prior, and the prior distribution that reduces the bias term of the posterior mode.
This paper proposes an audio fingerprinting model with holographic reduced representation (HRR). The proposed method reduces the number of stored fingerprints, whereas conventional neural audio fingerprinting requires many fingerprints for each audio track to achieve high accuracy and time resolution. We utilize HRR to aggregate multiple fingerprints into a composite fingerprint via circular convolution and summation, resulting in fewer fingerprints with the same dimensional space as the original. Our search method efficiently finds a combined fingerprint in which a query fingerprint exists. Using HRR's inverse operation, it can recover the relative position within a combined fingerprint, retaining the original time resolution. Experiments show that our method can reduce the number of fingerprints with modest accuracy degradation while maintaining the time resolution, outperforming simple decimation and summation-based aggregation methods.
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient method. The proposed methods use a preconditioned Krylov subspace method for a high-fidelity discretization of one parameter instance to generate orthogonal basis vectors of the reduced basis subspace. Then large-scale discrete parameter-dependent problems are approximately solved in the low-dimensional Krylov subspace. As shown in the theory and experiments, only a small number of Krylov subspace iterations are needed to simultaneously generate approximate solutions of a family of high-fidelity and large-scale systems in the reduced basis subspace. This reduces the computational cost dramatically because (1) to construct the reduced basis vectors, we only solve one large-scale problem in the high-fidelity level; and (2) the family of large-scale problems restricted to the reduced basis subspace have much smaller sizes.
In the recent papers ``The fast reduced QMC matrix-vector product'' (J. Comput. Appl. Math. 440, 115642, 2024) and ``Column reduced digital nets'' (submitted), it was proposed to use QMC rules based on reduced digital nets which provide a speed-up in the computation of QMC vector-matrix products that may occur in practical applications. In this paper, we provide upper bounds on the quality parameter of row reduced and column-row reduced digital nets, which are helpful for the error analysis of using reduced point sets as integration nodes in a QMC rule. We also give remarks on further aspects and comparisons of row reduced, column reduced, and column-row reduced digital net.
Recurrent neural network (RNNs) that are capable of modeling long-distance dependencies are widely used in various speech tasks, eg., keyword spotting (KWS) and speech enhancement (SE). Due to the limitation of power and memory in low-resource devices, efficient RNN models are urgently required for real-world applications. In this paper, we propose an efficient RNN architecture, GhostRNN, which reduces hidden state redundancy with cheap operations. In particular, we observe that partial dimensions of hidden states are similar to the others in trained RNN models, suggesting that redundancy exists in specific RNNs. To reduce the redundancy and hence computational cost, we propose to first generate a few intrinsic states, and then apply cheap operations to produce ghost states based on the intrinsic states. Experiments on KWS and SE tasks demonstrate that the proposed GhostRNN significantly reduces the memory usage (~40%) and computation cost while keeping performance similar.
Outside of the left-c.e. reals, Solovay reducibility is considered to be behaved badly [10.1007/978-0-387-68441-3]. Proposals for variants of Solovay reducibility that are better suited for the investigation of arbitrary, not necessarily left-c.e. reals were made by Rettinger and Zheng [10.1007/978-3-540-27798-9_39], and, recently, by Titov [10.11588/heidok.00034250] and by Kumabe and co-authors [10.4115/jla.2020.12.2; 10.3233/COM-230486]. These variants all coincide with the original version of Solovay reducibility on the left-c.e. reals. Furthermore, they are all defined in terms of translation functions. The latter translate between computable approximations in the case of Rettinger and Zheng, are monotone in the case of Titov, and are functions between reals in the case of Kumabe et al. In what follows, we derive new results on the mentioned variants and their relation to each other. In particular, we obtain that Solovay reducibility defined in terms of translation function on rationals implies Solovay reducibility defined in terms of translation functions on reals, and we show that the original version of Solovay reducibility is strictly weaker than its monotone variant. Solov
This thesis consists of five papers about reduced spherical convex bodies and in particular spherical bodies of constant width on the $d$-dimensional sphere $S^d$. In paper I we present some facts describing the shape of reduced bodies of thickness under $\fracπ{2}$ on $S^2$. We also consider reduced bodies of thickness at least $\fracπ{2}$, which appear to be of constant width. Paper II focuses on bodies of constant width on $S^d$. We present the properties of these bodies and in particular we discuss conections between notions of constant width and of constant diameter. In paper III we estimate the diameter of a reduced convex body. The main theme of paper IV is estimating the radius of the smallest disk that covers a reduced convex body on $S^2$. The result of paper V is showing that every spherical reduced polygon $V$ is contained in a disk of radius equal to the thickness of this body centered at a boundary point of $V$.