Grokking as Compression: A Nonlinear Complexity Perspective

We attribute grokking, the phenomenon where generalization is much delayed after memorization, to compression. To do so, we define linear mapping number (LMN) to measure network complexity, which is a generalized version of linear region number for ReLU networks. LMN can nicely characterize neural network compression before generalization. Although the $L_2$ norm has been a popular choice for characterizing model complexity, we argue in favor of LMN for a number of reasons: (1) LMN can be naturally interpreted as information/computation, while $L_2$ cannot. (2) In the compression phase, LMN has linear relations with test losses, while $L_2$ is correlated with test losses in a complicated nonlinear way. (3) LMN also reveals an intriguing phenomenon of the XOR network switching between two generalization solutions, while $L_2$ does not. Besides explaining grokking, we argue that LMN is a promising candidate as the neural network version of the Kolmogorov complexity since it explicitly considers local or conditioned linear computations aligned with the nature of modern artificial neural networks

Technical advancements and protocol optimization of diffusion-weighted imaging (DWI) in liver

An area of rapid advancement in abdominal MRI is diffusion-weighted imaging (DWI). By measuring diffusion properties of water molecules, DWI is capable of non-invasively probing tissue properties and physiology at cellular and macromolecular level. The integration of DWI as part of abdominal MRI exam allows better lesion characterization and therefore more accurate initial diagnosis and treatment monitoring. One of the most technical challenging, but also most useful abdominal DWI applications is in liver and therefore requires special attention and careful optimization. In this article, the latest technical developments of DWI and its liver applications are reviewed with the explanations of the technical principles, recommendations of the imaging parameters, and examples of clinical applications. More advanced DWI techniques, including Intra-Voxel Incoherent Motion (IVIM) diffusion imaging, anomalous diffusion imaging, and Diffusion Kurtosis Imaging (DKI) are discussed

Disentangling the effects of vapor pressure deficit on northern terrestrial vegetation productivity

The impact of atmospheric vapor pressure deficit (VPD) on plant photosynthesis has long been acknowledged, but large interactions with air temperature (T) and soil moisture (SM) still hinder a complete understanding of the influence of VPD on vegetation production across various climate zones. Here, we found a diverging response of productivity to VPD in the Northern Hemisphere by excluding interactive effects of VPD with T and SM. The interactions between VPD and T/SM not only offset the potential positive impact of warming on vegetation productivity but also amplifies the negative effect of soil drying. Notably, for high-latitude ecosystems, there occurs a pronounced shift in vegetation productivity\u27s response to VPD during the growing season when VPD surpasses a threshold of 3.5 to 4.0 hectopascals. These results yield previously unknown insights into the role of VPD in terrestrial ecosystems and enhance our comprehension of the terrestrial carbon cycle\u27s response to global warming

New Lower Bounds and Upper Bounds for Listing Avoidable Vertices

We consider the problem of listing all avoidable vertices in a given n vertex graph. A vertex is avoidable if every pair of its neighbors is connected by a path whose internal vertices are not neighbors of the vertex or the vertex itself. Recently, Papadopolous and Zisis showed that one can list all avoidable vertices in O(n^{?+1}) time, where ? < 2.373 is the square matrix multiplication exponent, and conjectured that a faster algorithm is not possible. In this paper we show that under the 3-OV Hypothesis, and thus the Strong Exponential Time Hypothesis, n^{3-o(1)} time is needed to list all avoidable vertices, and thus the current best algorithm is conditionally optimal if ? = 2. We then show that if ? > 2, one can obtain an improved algorithm that for the current value of ? runs in O(n^3.32) time. We also show that our conditional lower bound is actually higher and supercubic, under a natural High Dimensional 3-OV hypothesis, implying that for our current knowledge of rectangular matrix multiplication, the avoidable vertex listing problem likely requires ?(n^3.25) time. We obtain further algorithmic improvements for sparse graphs and bounded degree graphs

Fixed Fiber Light Guide System with Concave Outlet Concentrators

Because a traditional optical fiber light guiding system includes a tracking device, it also inevitably has a complex structure, high construction and maintenance costs, short life span and low reliability. Although several types have been developed for decades, there are no successful products on the market. The biggest cause of the problem is that all traditional optical fiber light guiding systems must have a tracking device. This paper studies a solar fiber optic guide system without a tracking device, hoping to solve this problem. A fixed fiber light guide system using concave outlet concentrators as its receiving unit is proposed. The structure and working principle of the concave outlet concentrator, the receiving unit and the light guide system are introduced. With optical simulation software and the actual sunlight experimental method, this paper first discusses the conceptual design of the concentrator, then studies the transmission efficiency curve of the receiving unit with different angles of incident light, and finally tests the output illuminance of the whole system in actual sunlight. Field test results show that when the average sunshine intensity is about 800 W/m2, the system has an output of nearly 300 lux at 0.4 m in front of the outlet end of the fiber bundle with only 3.11×10−2 m2 receiving area. This illumination has been able to meet people’s daily lighting requirements. The results of computer simulation and actual sunlight experiments show that this fixed optical fiber light guide system with non-tracing structure is feasible. The absence of a tracking structure means that all moving parts of the system are completely discarded. This greatly improves the working reliability and operation life of the light guide system, and greatly reduces the maintenance and operating costs

Fixed Fiber Light Guide System with Concave Outlet Concentrators

Because a traditional optical fiber light guiding system includes a tracking device, it also inevitably has a complex structure, high construction and maintenance costs, short life span and low reliability. Although several types have been developed for decades, there are no successful products on the market. The biggest cause of the problem is that all traditional optical fiber light guiding systems must have a tracking device. This paper studies a solar fiber optic guide system without a tracking device, hoping to solve this problem. A fixed fiber light guide system using concave outlet concentrators as its receiving unit is proposed. The structure and working principle of the concave outlet concentrator, the receiving unit and the light guide system are introduced. With optical simulation software and the actual sunlight experimental method, this paper first discusses the conceptual design of the concentrator, then studies the transmission efficiency curve of the receiving unit with different angles of incident light, and finally tests the output illuminance of the whole system in actual sunlight. Field test results show that when the average sunshine intensity is about 800 W/m2, the system has an output of nearly 300 lux at 0.4 m in front of the outlet end of the fiber bundle with only 3.11&times;10&minus;2&nbsp;m2 receiving area. This illumination has been able to meet people&rsquo;s daily lighting requirements. The results of computer simulation and actual sunlight experiments show that this fixed optical fiber light guide system with non-tracing structure is feasible. The absence of a tracking structure means that all moving parts of the system are completely discarded. This greatly improves the working reliability and operation life of the light guide system, and greatly reduces the maintenance and operating costs

Efficacy and tolerability of minocycline in depressive patients with or without treatment-resistant: a meta-analysis of randomized controlled trials

BackgroundMinocycline, an antibiotic with anti-inflammatory, antioxidant, and neuroprotective properties, has been used for treating psychiatric disorders in research. This systematic review aimed to evaluate the efficacy and tolerability of minocycline in patients having depression with or without treatment-resistance.MethodsElectronic databases including Embase, PubMed, and the Cochrane library were searched for relevant studies published up to October 17, 2022. The primary efficacy outcome was the change in depression severity scores and the secondary efficacy outcomes included the changes in Clinical Global Impression (CGI) and Beck Depression Inventory (BDI) scores and the incidence of response and partial response. Safety outcomes were evaluated based on the incidence of classified adverse events and all-cause discontinuation.ResultsFive studies with 374 patients were selected for analysis. The minocycline group demonstrated a significant reduction in depression severity scale (standardized mean difference [SMD]: −0.59, 95% confidence interval [CI]: −0.98 to −0.20, P = 0.003) and CGI (SMD: −0.28, 95% CI: −0.56 to −0.01, P = 0.042) scores; however, no statistical difference was found in terms of the BDI score, response, and partial response. No significant differences were found between the groups in terms of adverse events (other than dizziness) and discontinuation rates. Subgroup analysis showed that minocycline was also effective in reducing depression severity scores in treatment-resistant depression (SMD: −0.36, 95% CI: −0.64 to −0.09, P = 0.010). Subgroup analysis of Hamilton Depression Rating Scale (17-item) scores showed a statistical difference in response in patients with depression (relative risk: 2.51, 95% CI: 1.13 to 5.57, P = 0.024).ConclusionsMinocycline may improve depressive symptoms and augment response to treatment in patients with depression irrespective of treatment-resistance. However, clinical trials with large sample sizes are warranted for evaluating long-term outcomes with minocycline.Systematic review registrationhttps://inplasy.com/inplasy-2022-12-0051/