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. We suspect that for large values of subscript d_{k} , the dot products grow large in magnitude, pushing the softmax function into regions where it has extremely small gradients To illustrate why the dot products get large, assume that the components of and are independent random variables with mean and variance . The... |
3.2.2 Multi-Head Attention Instead of performing a single attention function with model subscript model d_{\text{model}} -dimensional keys, values and queries, we found it beneficial to linearly project the queries, keys and values times with different, learned linear projections to subscript d_{k} subscript d_{k} and ... |
Multi-head attention allows the model to jointly attend to information from different representation subspaces at different positions. With a single attention head, averaging inhibits this. |
MultiHead MultiHead \displaystyle\mathrm{MultiHead}(Q,K,V) Concat head head absent Concat subscript head subscript head superscript \displaystyle=\mathrm{Concat}(\mathrm{head_{1}},...,\mathrm{head_{h}})W^{O} |
where head where subscript head \displaystyle\text{where}~{}\mathrm{head_{i}} Attention absent Attention subscript superscript subscript superscript subscript superscript \displaystyle=\mathrm{Attention}(QW^{Q}_{i},KW^{K}_{i},VW^{V}_{i}) |
Where the projections are parameter matrices model subscript superscript superscript subscript model subscript W^{Q}_{i}\in\mathbb{R}^{d_{\text{model}}\times d_{k}} model subscript superscript superscript subscript model subscript W^{K}_{i}\in\mathbb{R}^{d_{\text{model}}\times d_{k}} model subscript superscript supersc... |
In this work we employ h=8 parallel attention layers, or heads. For each of these we use model 64 subscript subscript subscript model 64 d_{k}=d_{v}=d_{\text{model}}/h=64 Due to the reduced dimension of each head, the total computational cost is similar to that of single-head attention with full dimensionality. |
3.2.3 Applications of Attention in our Model The Transformer uses multi-head attention in three different ways: In "encoder-decoder attention" layers, the queries come from the previous decoder layer, and the memory keys and values come from the output of the encoder. This allows every position in the decoder to attend... |
The encoder contains self-attention layers. In a self-attention layer all of the keys, values and queries come from the same place, in this case, the output of the previous layer in the encoder. Each position in the encoder can attend to all positions in the previous layer of the encoder. |
Similarly, self-attention layers in the decoder allow each position in the decoder to attend to all positions in the decoder up to and including that position. We need to prevent leftward information flow in the decoder to preserve the auto-regressive property. We implement this inside of scaled dot-product attention b... |
3.3 Position-wise Feed-Forward Networks In addition to attention sub-layers, each of the layers in our encoder and decoder contains a fully connected feed-forward network, which is applied to each position separately and identically. This consists of two linear transformations with a ReLU activation in between. |
FFN max FFN subscript subscript subscript subscript \mathrm{FFN}(x)=\max(0,xW_{1}+b_{1})W_{2}+b_{2} (2) While the linear transformations are the same across different positions, they use different parameters from layer to layer. Another way of describing this is as two convolutions with kernel size 1. The dimensionalit... |
3.4 Embeddings and Softmax Similarly to other sequence transduction models, we use learned embeddings to convert the input tokens and output tokens to vectors of dimension model subscript model d_{\text{model}} . We also use the usual learned linear transformation and softmax function to convert the decoder output to p... |
. In the embedding layers, we multiply those weights by model subscript model \sqrt{d_{\text{model}}} 3.5 Positional Encoding Since our model contains no recurrence and no convolution, in order for the model to make use of the order of the sequence, we must inject some information about the relative or absolute positio... |
In this work, we use sine and cosine functions of different frequencies: 10000 model subscript superscript 10000 subscript model \displaystyle PE_{(pos,2i)}=sin(pos/10000^{2i/d_{\text{model}}}) |
10000 model subscript superscript 10000 subscript model \displaystyle PE_{(pos,2i+1)}=cos(pos/10000^{2i/d_{\text{model}}}) where pos is the position and is the dimension. That is, each dimension of the positional encoding corresponds to a sinusoid. The wavelengths form a geometric progression from 2\pi to 10000 10000 1... |
We also experimented with using learned positional embeddings instead, and found that the two versions produced nearly identical results (see Table row (E)). We chose the sinusoidal version because it may allow the model to extrapolate to sequence lengths longer than the ones encountered during training. |
Why Self-Attention In this section we compare various aspects of self-attention layers to the recurrent and convolutional layers commonly used for mapping one variable-length sequence of symbol representations subscript subscript (x_{1},...,x_{n}) to another sequence of equal length subscript subscript (z_{1},...,z_{n}... |
One is the total computational complexity per layer. Another is the amount of computation that can be parallelized, as measured by the minimum number of sequential operations required. |
The third is the path length between long-range dependencies in the network. Learning long-range dependencies is a key challenge in many sequence transduction tasks. One key factor affecting the ability to learn such dependencies is the length of the paths forward and backward signals have to traverse in the network. T... |
. Hence we also compare the maximum path length between any two input and output positions in networks composed of the different layer types. |
As noted in Table , a self-attention layer connects all positions with a constant number of sequentially executed operations, whereas a recurrent layer requires O(n) sequential operations. In terms of computational complexity, self-attention layers are faster than recurrent layers when the sequence length is smaller th... |
and byte-pair representations. To improve computational performance for tasks involving very long sequences, self-attention could be restricted to considering only a neighborhood of size in the input sequence centered around the respective output position. This would increase the maximum path length to O(n/r) . We plan... |
A single convolutional layer with kernel width k<n does not connect all pairs of input and output positions. Doing so requires a stack of O(n/k) convolutional layers in the case of contiguous kernels, or subscript O(log_{k}(n)) in the case of dilated convolutions |
, increasing the length of the longest paths between any two positions in the network. Convolutional layers are generally more expensive than recurrent layers, by a factor of . Separable convolutions |
, however, decrease the complexity considerably, to superscript O(k\cdot n\cdot d+n\cdot d^{2}) . Even with k=n , however, the complexity of a separable convolution is equal to the combination of a self-attention layer and a point-wise feed-forward layer, the approach we take in our model. |
As side benefit, self-attention could yield more interpretable models. We inspect attention distributions from our models and present and discuss examples in the appendix. Not only do individual attention heads clearly learn to perform different tasks, many appear to exhibit behavior related to the syntactic and semant... |
Training This section describes the training regime for our models. 5.1 Training Data and Batching We trained on the standard WMT 2014 English-German dataset consisting of about 4.5 million sentence pairs. Sentences were encoded using byte-pair encoding |
, which has a shared source-target vocabulary of about 37000 tokens. For English-French, we used the significantly larger WMT 2014 English-French dataset consisting of 36M sentences and split tokens into a 32000 word-piece vocabulary |
. Sentence pairs were batched together by approximate sequence length. Each training batch contained a set of sentence pairs containing approximately 25000 source tokens and 25000 target tokens. |
5.2 Hardware and Schedule We trained our models on one machine with 8 NVIDIA P100 GPUs. For our base models using the hyperparameters described throughout the paper, each training step took about 0.4 seconds. We trained the base models for a total of 100,000 steps or 12 hours. For our big models,(described on the botto... |
5.3 Optimizer We used the Adam optimizer with 0.9 subscript 0.9 \beta_{1}=0.9 0.98 subscript 0.98 \beta_{2}=0.98 and 10 italic-ϵ superscript 10 \epsilon=10^{-9} . We varied the learning rate over the course of training, according to the formula: |
model 0.5 min 0.5 1.5 superscript subscript model 0.5 superscript 0.5 superscript 1.5 lrate=d_{\text{model}}^{-0.5}\cdot\min({step\_num}^{-0.5},{step\_num}\cdot{warmup\_steps}^{-1.5}) |
(3) This corresponds to increasing the learning rate linearly for the first warmup\_steps training steps, and decreasing it thereafter proportionally to the inverse square root of the step number. We used 4000 4000 warmup\_steps=4000 |
5.4 Regularization We employ three types of regularization during training: Residual Dropout We apply dropout to the output of each sub-layer, before it is added to the sub-layer input and normalized. In addition, we apply dropout to the sums of the embeddings and the positional encodings in both the encoder and decode... |
Label Smoothing During training, we employed label smoothing of value 0.1 subscript italic-ϵ 0.1 \epsilon_{ls}=0.1 . This hurts perplexity, as the model learns to be more unsure, but improves accuracy and BLEU score. |
Results 6.1 Machine Translation On the WMT 2014 English-to-German translation task, the big transformer model (Transformer (big) in Table ) outperforms the best previously reported models (including ensembles) by more than 2.0 2.0 2.0 BLEU, establishing a new state-of-the-art BLEU score of 28.4 28.4 28.4 . The configur... |
On the WMT 2014 English-to-French translation task, our big model achieves a BLEU score of 41.0 41.0 41.0 , outperforming all of the previously published single models, at less than 1/4 the training cost of the previous state-of-the-art model. The Transformer (big) model trained for English-to-French used dropout rate ... |
For the base models, we used a single model obtained by averaging the last 5 checkpoints, which were written at 10-minute intervals. For the big models, we averaged the last 20 checkpoints. We used beam search with a beam size of and length penalty 0.6 0.6 \alpha=0.6 |
. These hyperparameters were chosen after experimentation on the development set. We set the maximum output length during inference to input length + 50 50 50 , but terminate early when possible |
Table summarizes our results and compares our translation quality and training costs to other model architectures from the literature. We estimate the number of floating point operations used to train a model by multiplying the training time, the number of GPUs used, and an estimate of the sustained single-precision fl... |
6.2 Model Variations To evaluate the importance of different components of the Transformer, we varied our base model in different ways, measuring the change in performance on English-to-German translation on the development set, newstest2013. We used beam search as described in the previous section, but no checkpoint a... |
In Table rows (A), we vary the number of attention heads and the attention key and value dimensions, keeping the amount of computation constant, as described in Section 3.2.2 . While single-head attention is 0.9 BLEU worse than the best setting, quality also drops off with too many heads. |
In Table rows (B), we observe that reducing the attention key size subscript d_{k} hurts model quality. This suggests that determining compatibility is not easy and that a more sophisticated compatibility function than dot product may be beneficial. We further observe in rows (C) and (D) that, as expected, bigger model... |
, and observe nearly identical results to the base model. 6.3 English Constituency Parsing To evaluate if the Transformer can generalize to other tasks we performed experiments on English constituency parsing. This task presents specific challenges: the output is subject to strong structural constraints and is signific... |
We trained a 4-layer transformer with 1024 subscript 1024 d_{model}=1024 on the Wall Street Journal (WSJ) portion of the Penn Treebank |
, about 40K training sentences. We also trained it in a semi-supervised setting, using the larger high-confidence and BerkleyParser corpora from with approximately 17M sentences |
. We used a vocabulary of 16K tokens for the WSJ only setting and a vocabulary of 32K tokens for the semi-supervised setting. We performed only a small number of experiments to select the dropout, both attention and residual (section 5.4 ), learning rates and beam size on the Section 22 development set, all other param... |
Our results in Table show that despite the lack of task-specific tuning our model performs surprisingly well, yielding better results than all previously reported models with the exception of the Recurrent Neural Network Grammar |
In contrast to RNN sequence-to-sequence models , the Transformer outperforms the BerkeleyParser even when training only on the WSJ training set of 40K sentences. |
Conclusion In this work, we presented the Transformer, the first sequence transduction model based entirely on attention, replacing the recurrent layers most commonly used in encoder-decoder architectures with multi-headed self-attention. |
For translation tasks, the Transformer can be trained significantly faster than architectures based on recurrent or convolutional layers. On both WMT 2014 English-to-German and WMT 2014 English-to-French translation tasks, we achieve a new state of the art. In the former task our best model outperforms even all previou... |
We are excited about the future of attention-based models and plan to apply them to other tasks. We plan to extend the Transformer to problems involving input and output modalities other than text and to investigate local, restricted attention mechanisms to efficiently handle large inputs and outputs such as images, au... |
The code we used to train and evaluate our models is available at Acknowledgements We are grateful to Nal Kalchbrenner and Stephan Gouws for their fruitful comments, corrections and inspiration. Attention Visualizations |
# Source: arxiv 1710.02553 # Title: Artificial life, complex systems and cloud computing: a short review # Sections: all # Downloaded: 2026-03-03T01:55:54.423295+00:00 |
Artificial life, complex systems and cloud computing: a short review (September 2nd, 2017) Abstract Cloud computing is the prevailing mode of designing, creating and deploying complex applications nowadays. Its underlying assumptions include distributed computing, but also new concepts that need to be incorporated in t... |
Introduction Cloud computing is currently the dominant computing platform. Even if initially it was a metaphor applied to virtualized resources of any kind that could be accessed in a pay-per-use basis, it has extended itself way beyond its initial and simple translation of data center concepts to create completely new... |
Infrastructure is fully automatized and described by software; there is no hard boundary between software and hardware, which are developed at the same time, with an application accompanied by the description of the resources it needs. |
Applications are a loose collection of resources which interact asynchronously, are independent of each other, and in many cases have their own vendors or product owners. Some resources are ephemeral, appearing when they are needed and vanishing afterwards, some are permanent, but all of them behave reactively, acting ... |
As such a collection, cloud-native applications become organic with parts of it changing without making the application as a whole a different one. There is internal evolution with continuous integration, testing and deployment, as well as evolution in the sense of a progress in fitness, as applications compete with ot... |
All these characteristics make the cloud an environment that is closer to artificial life than single or multidesktop applications. However, cloud computing is relatively new and, being as it is a techno-social system (Vespignani 2009,J. J. Merelo et al. (2016)) it will probably constitute the object of study form the ... |
First steps towards cloud as complex systems One of the most straightforward ways of connecting old algorithms to new technologies is simply to run those algorithms using a straightforward translation of the old technologies. Cloud computing, for instance, offers the possibility of instantiating computing nodes at a co... |
This cloud-based setup does have the disadvantage of needing a permanent connection and possibly a high bandwidth. However, there is an interesting complex-systems approach to this: so-called edge computing (Satyanarayanan 2017) moves cloud resources close to the service client via technologies that allow them to acces... |
surround the user, they receive the denomination of fog computing too (Luan et al. 2015), which is studied mainly in the context of the Internet of Things. The devices and computing nodes constituting this fog are, effectively, a complex adaptive system (Yan and Ji-Hong 2010)(Roca et al. 2018). However, the scale and s... |
Complex cloud systems Complex cloud systems would make use of the underlying physical (or virtual) characteristics of the cloud to implement complex systems. Most cloud systems architectures are based on queues, which usually form the backbone of the whole system and are used to deliver information as well as activate ... |
This can be taken further; every module in a cloud system is not adaptive, performing whatever service it has been programmed to do via its description. But lately, some cloud systems are being built with self- principles in mind; as services in the cloud acquire autonomy in what is called autonomic computing adaptatio... |
is not far away and services become adaptive, being able to self-organize and the whole system to self-heal, two agencies that make a cloud system acquire complex adaptive behaviour, such as being able to reconfigure connections, spawn new copies or eliminate them, all in an autonomic way without needing to rely on a c... |
Conclusions As can be observed by the dearth of references for complex cloud systems or cloud-native artificial life, we are still in the early stages of its development, with the cloud being used mainly as a resource for the straightforward porting of earlier systems. Some steps have been taking in the realization of ... |
Acknowledgements This work has been supported in part by the Spanish Ministry of Economía y Competitividad, projects TIN2014-56494-C4-3-P (UGR-EPHEMECH). |
References Bottone, Michele, Filippo Palumbo, Giuseppe Primiero, Franco Raimondi, and Richard Stocker. 2016. “Implementing Virtual Pheromones in Bdi Robots Using Mqtt and Jason (Short Paper).” In Cloud Networking (Cloudnet), 2016 5th Ieee International Conference on , 196–99. IEEE. |
Chen, Yinong, Zhihui Du, and Marcos García-Acosta. 2010. “Robot as a Service in Cloud Computing.” In Service Oriented System Engineering (Sose), 2010 Fifth Ieee International Symposium on 151–58. IEEE. |
Du, Zhihui, Ligang He, Yinong Chen, Yu Xiao, Peng Gao, and Tongzhou Wang. 2017. “Robot Cloud: Bridging the Power of Robotics and Cloud Computing.” Future Generation Computer Systems 74. Elsevier: 337–48. |
Laredo, Juan Luis J., Carlos Fernandes, Antonio Mora, Pedro A. Castillo, Pablo Garcia-Sanchez, and Juan Julian Merelo. 2009. “Studying the Cache Size in a Gossip-Based Evolutionary Algorithm.” In Proceedings of the 3rd International Symposium on Intelligent Distributed Computing edited by G.A. Papadopoulos and C. Badic... |
Laredo, Juan Luís Jiménez, Pedro Angel Castillo, Ben Paechter, Antonio Miguel Mora, Eva Alfaro-Cid, Anna I. Esparcia-Alcázar, and Juan Julián Merelo. n.d. “Empirical Validation of a Gossiping Communication Mechanism for Parallel EAs.” In, 129–36. |
Luan, Tom H, Longxiang Gao, Zhi Li, Yang Xiang, Guiyi Wei, and Limin Sun. 2015. “Fog Computing: Focusing on Mobile Users at the Edge.” |
arXiv Preprint arXiv:1502.01815 Medel, Victor, Unai Arronategui, José Ángel Bañares, and José-Manuel Colom. 2017. “Distributed Simulation of Complex and Scalable Systems: From Models to the Cloud.” In Economics of Grids, Clouds, Systems, and Services: 13th International Conference, Gecon 2016, Athens, Greece, September... |
Merelo, J. J., Paloma de Las Cuevas, Pablo García-Sánchez, and Mario García-Valdez. 2016. “The Human in the Loop: Volunteer-Based Metacomputers as a Socio-Technical System.” In Proceedings of the Artificial Life Conference 2016 , 648. Complex Adaptive Systems. One Rogers Street Cambridge MA 02142-1209: The MIT Press. d... |
Merelo-Guervós, Juan-Julián, Maribel García Arenas, Antonio Miguel Mora, Pedro A. Castillo, Gustavo Romero, and Juan Luís Jiménez Laredo. 2011. “Cloud-Based Evolutionary Algorithms: An Algorithmic Study.” |
CoRR abs/1105.6205. Roca, Damian, Rodolfo Milito, Mario Nemirovsky, and Mateo Valero. 2018. “Tackling Iot Ultra Large Scale Systems: Fog Computing in Support of Hierarchical Emergent Behaviors.” In Fog Computing in the Internet of Things , 33–48. Springer. |
Satyanarayanan, Mahadev. 2017. “Edge Computing: Vision and Challenges.” USENIX Association. Taylor, Tim, Joshua E Auerbach, Josh Bongard, Jeff Clune, Simon Hickinbotham, Charles Ofria, Mizuki Oka, Sebastian Risi, Kenneth O Stanley, and Jason Yosinski. 2016. “WebAL Comes of Age: A Review of the First 21 Years of Artific... |
Vespignani, Alessandro. 2009. “Predicting the Behavior of Techno-Social Systems.” Science 325 (5939). American Association for the Advancement of Science: 425–28. |
Yan, Chen, and Qiao Ji-Hong. 2010. “Application Analysis of Complex Adaptive Systems for Wsn.” In Computer Application and System Modeling (ICCASM), 2010 International Conference on , 7:V7–328. IEEE. |
# Source: arxiv 1711.06869 # Title: Bio-Inspired Local Information-Based Control for Probabilistic Swarm Distribution Guidance # Sections: all # Downloaded: 2026-03-03T02:01:26.195146+00:00 |
Bio-Inspired Local Information-Based Control for Probabilistic Swarm Distribution Guidance Abstract This paper addresses a task allocation problem for a large-scale robotic swarm, namely swarm distribution guidance problem . Unlike most of the existing frameworks handling this problem, the proposed framework suggests u... |
Index Terms: Swarm robotics, Distributed robot systems, Networked robots, Markov chains. Introduction This paper addresses a task allocation problem for a large-scale multiple-robot system, called a robotic swarm Robotic swarms have attracted lots of attention because they are regarded as promising solutions to handle ... |
Agents in a swarm are assumed to be homogeneous because the swarm is usually realised through mass production In this context, the task allocation problem can be reduced to a problem of how to distribute a swarm of agents into given tasks (or bins), satisfying the desired population fraction (or swarm density) for each... |
For a large number of agents, probabilistic approaches based on Markov chains or differential equations have been widely utilised. Since these approaches focus not on individual agents but instead on the ensemble dynamics, they are also called Eulerian |
or macroscopic frameworks In these approaches, swarm densities for each bin are represented as system states, and a state-transition matrix describes stochastic decision policies , i.e., the probabilities that agents in a bin switch to another. Individual agents in the swarm make decisions based on these policies, but ... |
Initially, open-loop-type frameworks have been proposed . Agents under these frameworks are controlled by time-invariant stochastic decision policies. The policies, which make a swarm converge to a desired distribution, are pre-determined by a central controller and broadcasted to each agent before executing the missio... |
There have been also some other works, called closed-loop-type frameworks . This type of frameworks allows agents to adaptively construct their own stochastic decision policies at the expense of sensing the concurrent swarm status through interactions with other agents. Based on such information, agents can synthesise ... |
, minimising travelling costs , and temporarily adjusting given policies when bins are more overpopulated or underpopulated than certain levels |
In particular, Bandyopadhyay et. al. recently proposed a closed-loop-type algorithm that exhibits faster convergence as well as less undesirable transition behaviours, compared with an open-loop-type algorithm. This algorithm is expected to mitigate the trade-off raised in open-loop-type frameworks. |
To the best of our knowledge, most of the existing closed-loop-type algorithms are based on Global Information Consistency Assumption (GICA) |
GICA implies that necessary information is required to be consistently known by entire agents. We refer to such information as global , because achieving information consistency needs agents to somehow interact with all the others through a multi-hop fashion and thus it “happens on a global communication timescale” |
This paper proposes a framework that requires Local Information Consistency Assumption (LICA) . Unlike GICA-based algorithms, the proposed framework require only local consistency on information with neighbouring agents, not the global consistency. LICA can provide various alternative advantages to the proposed framewo... |
Secondly, LICA enables a foundation on which an asynchronous decentralised decision-making process can be developed. Note that the timescales for achieving the information consistency between the agents can be different depending on their local circumstances. Considering any possibly-extrinsic heterogeneity of agents (... |
Finally, LICA makes the proposed approach additionally robust against dynamical changes in bins and those in agents. Given that inclusions or exclusions of bins are perceived by neighbouring agents, the proposed approach works well even without requiring other far-away agents to know the changes. |
The LICA-based framework developed in this paper utilises local information as its feedback gains, which is motivated from the recent GICA-based work in |
This framework is inspired by the mechanism of decision-making in a fish swarm, in which each of them adjusts its individual behaviour based on those of neighbours |
Similarly, each agent in the framework developed uses its local status, i.e. the current density of its associated bin relative to those of its neighbour bins, to generate its time-varying stochastic decision policies. The agent is not required to know any global information, and hence the aforementioned advantages of ... |
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