We provide an improved analysis of normalized SGD showing that adding momentum provably removes the need for large batch sizes on non-convex objectives. Then, we consider the case of objectives with bounded second derivative and show that in this case a small tweak to the momentum formula allows normalized SGD with momentum to find an -critical point in O(1/ 3.5 ) iterations, matching the best-known rates without accruing any logarithmic factors or dependence on dimension. We also provide an adaptive method that automatically improves convergence rates when the variance in the gradients is small. Finally, we show that our method is effective when employed on popular large scale tasks such as ResNet-50 and BERT pretraining, matching the performance of the disparate methods used to get state-of-the-art results on both tasks.

Due to extensive root system, connected rhizome bamboos are considered suitable for improving soil properties within a short period, though most of the claims are anecdotal and need to be supported with quantified data. The study evaluates seven bamboo species viz., Bambusa balcooa, Bambusa bambos, Bambusa vulgaris, Bambusa nutans, Dendrocalamus hamiltonii, Dendrocalamus stocksii and Dendrocalamus strictus for their rooting pattern and impact on soil health properties. Coarse and fine root intensity was maximum in B. vulgaris. Coarse root biomass ranged from 0.6 kg m −3 in B. nutans to 2.0 kg m −3 in B. vulgaris and B. bambos. Fine root biomass ranged from 1.1 kg m −3 in B. nutans to 4.5 kg m −3 in D. hamiltonii. Contribution of fine roots in terms of intensity and biomass was much higher than coarse roots. Fine root biomass showed declining trend with increase in soil depth in all the species. During sixth year, the litter fall ranged from 8.1 Mg ha −1 in D. stocksii to 12.4 Mg ha −1 in D. hamiltonii. Among soil physical properties significant improvement were recorded in hydraulic conductivity, water stable aggregates and mean weight diameter. Soil pH, organic carbon and available phosphorus under different species did not reveal any significant changes, while significant reduction was observed in total nitrogen and potassium. Significant positive correlation was observed between WSA and iron content. Soil microbial population and enzyme activities were higher in control plot. Considering root distribution, biomass, soil hydraulic conductivity and water stable aggregates, B. bambos, B. vulgaris and D. hamiltonii are recommended for rehabilitation of degraded lands prone to soil erosion. Bamboo grows worldwide in at least 37 million ha and covers 3.2 percent of forest areas of their host countries, or about 1 percent of the global forest area 1. Bamboo being an annual yielding crop with multipurpose utility has proven potential for contributing to poverty reduction, environmental protection and achievement of United Nations Sustainable Development Goals-SDG1, SDG7, SDG 11, SDG 12, SDG 13, SDG 15, and SDG 17 2. Many countries are now exploring options for achieving land degradation neutrality through the use of bamboo. Bamboo also contributes to the Bonn Challenge, the global initiative targeting the restoration of 200 million hectares of the planet's degraded lands, to which International Bamboo and Rattan Organization (INBAR) member states have agreed to contribute about five million hectares of bamboo plantations 3. India is the second richest country of the world, after China, in terms of bamboo genetic resources 4. The bamboo area of the country is estimated to be 15.69 million hectare with total standing stock of 189 million tons 5. Raising of bamboo on degraded soils improves soil quality and sequesters carbon in the soil 6,7. Bamboo due to its fast growth and extensive root system improves soil physical, chemical and biological properties; controls soil erosion; filters sediment and is considered suitable...

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In this paper, we demonstrate that information retrieval can be accomplished with a single Transformer, in which all information about the corpus is encoded in the parameters of the model. To this end, we introduce the Differentiable Search Index (DSI), a new paradigm that learns a text-to-text model that maps string queries directly to relevant docids; in other words, a DSI model answers queries directly using only its parameters, dramatically simplifying the whole retrieval process. We study variations in how documents and their identifiers are represented, variations in training procedures, and the interplay between models and corpus sizes. Experiments demonstrate that given appropriate design choices, DSI significantly outperforms strong baselines such as dual encoder models. Moreover, DSI demonstrates strong generalization capabilities, outperforming a BM25 baseline in a zero-shot setup.