[HTML payload içeriği buraya]
28 C
Jakarta
Wednesday, November 27, 2024
HomeArtificial Intelligence
Artificial Intelligence

Posit AI Weblog: Variational convnets with tfprobability

By Admin
0
29


A bit greater than a 12 months in the past, in his stunning visitor publish, Nick Strayer confirmed the way to classify a set of on a regular basis actions utilizing smartphone-recorded gyroscope and accelerometer information. Accuracy was excellent, however Nick went on to examine classification outcomes extra carefully. Have been there actions extra vulnerable to misclassification than others? And the way about these faulty outcomes: Did the community report them with equal, or much less confidence than those who have been appropriate?

Technically, after we converse of confidence in that method, we’re referring to the rating obtained for the “profitable” class after softmax activation. If that profitable rating is 0.9, we’d say “the community is certain that’s a gentoo penguin”; if it’s 0.2, we’d as a substitute conclude “to the community, neither possibility appeared becoming, however cheetah appeared greatest.”

This use of “confidence” is convincing, but it surely has nothing to do with confidence – or credibility, or prediction, what have you ever – intervals. What we’d actually like to have the ability to do is put distributions over the community’s weights and make it Bayesian. Utilizing tfprobability’s variational Keras-compatible layers, that is one thing we truly can do.

Including uncertainty estimates to Keras fashions with tfprobability reveals the way to use a variational dense layer to acquire estimates of epistemic uncertainty. On this publish, we modify the convnet utilized in Nick’s publish to be variational all through. Earlier than we begin, let’s shortly summarize the duty.

The duty

To create the Smartphone-Based mostly Recognition of Human Actions and Postural Transitions Knowledge Set (Reyes-Ortiz et al. 2016), the researchers had topics stroll, sit, stand, and transition from a type of actions to a different. In the meantime, two varieties of smartphone sensors have been used to file movement information: Accelerometers measure linear acceleration in three dimensions, whereas gyroscopes are used to trace angular velocity across the coordinate axes. Listed here are the respective uncooked sensor information for six varieties of actions from Nick’s unique publish:

Identical to Nick, we’re going to zoom in on these six varieties of exercise, and attempt to infer them from the sensor information. Some information wrangling is required to get the dataset right into a type we will work with; right here we’ll construct on Nick’s publish, and successfully begin from the info properly pre-processed and break up up into coaching and check units:

Observations: 289
Variables: 6
$ experiment    <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 18, 19, 2…
$ userId        <int> 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 7, 9, 9, 10, 10, 11…
$ exercise      <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7…
$ information          <record> [<data.frame[160 x 6]>, <information.body[206 x 6]>, <dat…
$ activityName  <fct> STAND_TO_SIT, STAND_TO_SIT, STAND_TO_SIT, STAND_TO_S…
$ observationId <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 18, 19, 2…
Observations: 69
Variables: 6
$ experiment    <int> 11, 12, 15, 16, 32, 33, 42, 43, 52, 53, 56, 57, 11, …
$ userId        <int> 6, 6, 8, 8, 16, 16, 21, 21, 26, 26, 28, 28, 6, 6, 8,…
$ exercise      <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8…
$ information          <record> [<data.frame[185 x 6]>, <information.body[151 x 6]>, <dat…
$ activityName  <fct> STAND_TO_SIT, STAND_TO_SIT, STAND_TO_SIT, STAND_TO_S…
$ observationId <int> 11, 12, 15, 16, 31, 32, 41, 42, 51, 52, 55, 56, 71, …

The code required to reach at this stage (copied from Nick’s publish) could also be discovered within the appendix on the backside of this web page.

Coaching pipeline

The dataset in query is sufficiently small to slot in reminiscence – however yours won’t be, so it could possibly’t damage to see some streaming in motion. Apart from, it’s most likely secure to say that with TensorFlow 2.0, tfdatasets pipelines are the approach to feed information to a mannequin.

As soon as the code listed within the appendix has run, the sensor information is to be present in trainData$information, an inventory column containing information.bodys the place every row corresponds to a degree in time and every column holds one of many measurements. Nevertheless, not all time sequence (recordings) are of the identical size; we thus observe the unique publish to pad all sequence to size pad_size (= 338). The anticipated form of coaching batches will then be (batch_size, pad_size, 6).

We initially create our coaching dataset:

train_x <- train_data$information %>% 
  map(as.matrix) %>%
  pad_sequences(maxlen = pad_size, dtype = "float32") %>%
  tensor_slices_dataset() 

train_y <- train_data$exercise %>% 
  one_hot_classes() %>% 
  tensor_slices_dataset()

train_dataset <- zip_datasets(train_x, train_y)
train_dataset
<ZipDataset shapes: ((338, 6), (6,)), sorts: (tf.float64, tf.float64)>

Then shuffle and batch it:

n_train <- nrow(train_data)
# the very best doable batch measurement for this dataset
# chosen as a result of it yielded the very best efficiency
# alternatively, experiment with e.g. totally different studying charges, ...
batch_size <- n_train

train_dataset <- train_dataset %>% 
  dataset_shuffle(n_train) %>%
  dataset_batch(batch_size)
train_dataset
<BatchDataset shapes: ((None, 338, 6), (None, 6)), sorts: (tf.float64, tf.float64)>

Identical for the check information.

test_x <- test_data$information %>% 
  map(as.matrix) %>%
  pad_sequences(maxlen = pad_size, dtype = "float32") %>%
  tensor_slices_dataset() 

test_y <- test_data$exercise %>% 
  one_hot_classes() %>% 
  tensor_slices_dataset()

n_test <- nrow(test_data)
test_dataset <- zip_datasets(test_x, test_y) %>%
  dataset_batch(n_test)

Utilizing tfdatasets doesn’t imply we can’t run a fast sanity test on our information:

first <- test_dataset %>% 
  reticulate::as_iterator() %>% 
  # get first batch (= entire check set, in our case)
  reticulate::iter_next() %>%
  # predictors solely
  .[[1]] %>% 
  # first merchandise in batch
  .[1,,]
first
tf.Tensor(
[[ 0.          0.          0.          0.          0.          0.        ]
 [ 0.          0.          0.          0.          0.          0.        ]
 [ 0.          0.          0.          0.          0.          0.        ]
 ...
 [ 1.00416672  0.2375      0.12916666 -0.40225476 -0.20463985 -0.14782938]
 [ 1.04166663  0.26944447  0.12777779 -0.26755899 -0.02779437 -0.1441642 ]
 [ 1.0250001   0.27083334  0.15277778 -0.19639318  0.35094208 -0.16249016]],
 form=(338, 6), dtype=float64)

Now let’s construct the community.

A variational convnet

We construct on the simple convolutional structure from Nick’s publish, simply making minor modifications to kernel sizes and numbers of filters. We additionally throw out all dropout layers; no extra regularization is required on high of the priors utilized to the weights.

Be aware the next concerning the “Bayesified” community.

  • Every layer is variational in nature, the convolutional ones (layer_conv_1d_flipout) in addition to the dense layers (layer_dense_flipout).

  • With variational layers, we will specify the prior weight distribution in addition to the type of the posterior; right here the defaults are used, leading to a typical regular prior and a default mean-field posterior.

  • Likewise, the consumer might affect the divergence perform used to evaluate the mismatch between prior and posterior; on this case, we truly take some motion: We scale the (default) KL divergence by the variety of samples within the coaching set.

  • One very last thing to notice is the output layer. It’s a distribution layer, that’s, a layer wrapping a distribution – the place wrapping means: Coaching the community is enterprise as common, however predictions are distributions, one for every information level.

library(tfprobability)

num_classes <- 6

# scale the KL divergence by variety of coaching examples
n <- n_train %>% tf$forged(tf$float32)
kl_div <- perform(q, p, unused)
  tfd_kl_divergence(q, p) / n

mannequin <- keras_model_sequential()
mannequin %>% 
  layer_conv_1d_flipout(
    filters = 12,
    kernel_size = 3, 
    activation = "relu",
    kernel_divergence_fn = kl_div
  ) %>%
  layer_conv_1d_flipout(
    filters = 24,
    kernel_size = 5, 
    activation = "relu",
    kernel_divergence_fn = kl_div
  ) %>%
  layer_conv_1d_flipout(
    filters = 48,
    kernel_size = 7, 
    activation = "relu",
    kernel_divergence_fn = kl_div
  ) %>%
  layer_global_average_pooling_1d() %>% 
  layer_dense_flipout(
    models = 48,
    activation = "relu",
    kernel_divergence_fn = kl_div
  ) %>% 
  layer_dense_flipout(
    num_classes, 
    kernel_divergence_fn = kl_div,
    title = "dense_output"
  ) %>%
  layer_one_hot_categorical(event_size = num_classes)

We inform the community to attenuate the unfavourable log chance.

nll <- perform(y, mannequin) - (mannequin %>% tfd_log_prob(y))

It will develop into a part of the loss. The best way we arrange this instance, this isn’t its most substantial half although. Right here, what dominates the loss is the sum of the KL divergences, added (robotically) to mannequin$losses.

In a setup like this, it’s fascinating to watch each components of the loss individually. We will do that by the use of two metrics:

# the KL a part of the loss
kl_part <-  perform(y_true, y_pred) {
    kl <- tf$reduce_sum(mannequin$losses)
    kl
}

# the NLL half
nll_part <- perform(y_true, y_pred) {
    cat_dist <- tfd_one_hot_categorical(logits = y_pred)
    nll <- - (cat_dist %>% tfd_log_prob(y_true) %>% tf$reduce_mean())
    nll
}

We practice considerably longer than Nick did within the unique publish, permitting for early stopping although.

mannequin %>% compile(
  optimizer = "rmsprop",
  loss = nll,
  metrics = c("accuracy", 
              custom_metric("kl_part", kl_part),
              custom_metric("nll_part", nll_part)),
  experimental_run_tf_function = FALSE
)

train_history <- mannequin %>% match(
  train_dataset,
  epochs = 1000,
  validation_data = test_dataset,
  callbacks = record(
    callback_early_stopping(persistence = 10)
  )
)

Whereas the general loss declines linearly (and possibly would for a lot of extra epochs), this isn’t the case for classification accuracy or the NLL a part of the loss:

Last accuracy isn’t as excessive as within the non-variational setup, although nonetheless not dangerous for a six-class drawback. We see that with none extra regularization, there may be little or no overfitting to the coaching information.

Now how will we get hold of predictions from this mannequin?

Probabilistic predictions

Although we received’t go into this right here, it’s good to know that we entry extra than simply the output distributions; by their kernel_posterior attribute, we will entry the hidden layers’ posterior weight distributions as effectively.

Given the small measurement of the check set, we compute all predictions directly. The predictions at the moment are categorical distributions, one for every pattern within the batch:

test_data_all <- dataset_collect(test_dataset) %>% { .[[1]][[1]]}

one_shot_preds <- mannequin(test_data_all) 

one_shot_preds
tfp.distributions.OneHotCategorical(
 "sequential_one_hot_categorical_OneHotCategorical_OneHotCategorical",
 batch_shape=[69], event_shape=[6], dtype=float32)

We prefixed these predictions with one_shot to point their noisy nature: These are predictions obtained on a single cross by the community, all layer weights being sampled from their respective posteriors.

From the expected distributions, we calculate imply and commonplace deviation per (check) pattern.

one_shot_means <- tfd_mean(one_shot_preds) %>% 
  as.matrix() %>%
  as_tibble() %>% 
  mutate(obs = 1:n()) %>% 
  collect(class, imply, -obs) 

one_shot_sds <- tfd_stddev(one_shot_preds) %>% 
  as.matrix() %>%
  as_tibble() %>% 
  mutate(obs = 1:n()) %>% 
  collect(class, sd, -obs)

The usual deviations thus obtained might be mentioned to replicate the general predictive uncertainty. We will estimate one other type of uncertainty, referred to as epistemic, by making a lot of passes by the community after which, calculating – once more, per check pattern – the usual deviations of the expected means.

mc_preds <- purrr::map(1:100, perform(x) {
  preds <- mannequin(test_data_all)
  tfd_mean(preds) %>% as.matrix()
})

mc_sds <- abind::abind(mc_preds, alongside = 3) %>% 
  apply(c(1,2), sd) %>% 
  as_tibble() %>%
  mutate(obs = 1:n()) %>% 
  collect(class, mc_sd, -obs)

Placing all of it collectively, we’ve got

pred_data <- one_shot_means %>%
  inner_join(one_shot_sds, by = c("obs", "class")) %>% 
  inner_join(mc_sds, by = c("obs", "class")) %>% 
  right_join(one_hot_to_label, by = "class") %>% 
  prepare(obs)

pred_data
# A tibble: 414 x 6
     obs class       imply      sd    mc_sd label       
   <int> <chr>      <dbl>   <dbl>    <dbl> <fct>       
 1     1 V1    0.945      0.227   0.0743   STAND_TO_SIT
 2     1 V2    0.0534     0.225   0.0675   SIT_TO_STAND
 3     1 V3    0.00114    0.0338  0.0346   SIT_TO_LIE  
 4     1 V4    0.00000238 0.00154 0.000336 LIE_TO_SIT  
 5     1 V5    0.0000132  0.00363 0.00164  STAND_TO_LIE
 6     1 V6    0.0000305  0.00553 0.00398  LIE_TO_STAND
 7     2 V1    0.993      0.0813  0.149    STAND_TO_SIT
 8     2 V2    0.00153    0.0390  0.102    SIT_TO_STAND
 9     2 V3    0.00476    0.0688  0.108    SIT_TO_LIE  
10     2 V4    0.00000172 0.00131 0.000613 LIE_TO_SIT  
# … with 404 extra rows

Evaluating predictions to the bottom reality:

eval_table <- pred_data %>% 
  group_by(obs) %>% 
  summarise(
    maxprob = max(imply),
    maxprob_sd = sd[mean == maxprob],
    maxprob_mc_sd = mc_sd[mean == maxprob],
    predicted = label[mean == maxprob]
  ) %>% 
  mutate(
    reality = test_data$activityName,
    appropriate = reality == predicted
  ) 

eval_table %>% print(n = 20)
# A tibble: 69 x 7
     obs maxprob maxprob_sd maxprob_mc_sd predicted    reality        appropriate
   <int>   <dbl>      <dbl>         <dbl> <fct>        <fct>        <lgl>  
 1     1   0.945     0.227         0.0743 STAND_TO_SIT STAND_TO_SIT TRUE   
 2     2   0.993     0.0813        0.149  STAND_TO_SIT STAND_TO_SIT TRUE   
 3     3   0.733     0.443         0.131  STAND_TO_SIT STAND_TO_SIT TRUE   
 4     4   0.796     0.403         0.138  STAND_TO_SIT STAND_TO_SIT TRUE   
 5     5   0.843     0.364         0.358  SIT_TO_STAND STAND_TO_SIT FALSE  
 6     6   0.816     0.387         0.176  SIT_TO_STAND STAND_TO_SIT FALSE  
 7     7   0.600     0.490         0.370  STAND_TO_SIT STAND_TO_SIT TRUE   
 8     8   0.941     0.236         0.0851 STAND_TO_SIT STAND_TO_SIT TRUE   
 9     9   0.853     0.355         0.274  SIT_TO_STAND STAND_TO_SIT FALSE  
10    10   0.961     0.195         0.195  STAND_TO_SIT STAND_TO_SIT TRUE   
11    11   0.918     0.275         0.168  STAND_TO_SIT STAND_TO_SIT TRUE   
12    12   0.957     0.203         0.150  STAND_TO_SIT STAND_TO_SIT TRUE   
13    13   0.987     0.114         0.188  SIT_TO_STAND SIT_TO_STAND TRUE   
14    14   0.974     0.160         0.248  SIT_TO_STAND SIT_TO_STAND TRUE   
15    15   0.996     0.0657        0.0534 SIT_TO_STAND SIT_TO_STAND TRUE   
16    16   0.886     0.318         0.0868 SIT_TO_STAND SIT_TO_STAND TRUE   
17    17   0.773     0.419         0.173  SIT_TO_STAND SIT_TO_STAND TRUE   
18    18   0.998     0.0444        0.222  SIT_TO_STAND SIT_TO_STAND TRUE   
19    19   0.885     0.319         0.161  SIT_TO_STAND SIT_TO_STAND TRUE   
20    20   0.930     0.255         0.271  SIT_TO_STAND SIT_TO_STAND TRUE   
# … with 49 extra rows

Are commonplace deviations greater for misclassifications?

eval_table %>% 
  group_by(reality, predicted) %>% 
  summarise(avg_mean = imply(maxprob),
            avg_sd = imply(maxprob_sd),
            avg_mc_sd = imply(maxprob_mc_sd)) %>% 
  mutate(appropriate = reality == predicted) %>%
  prepare(avg_mc_sd) 
# A tibble: 2 x 5
  appropriate depend avg_mean avg_sd avg_mc_sd
  <lgl>   <int>    <dbl>  <dbl>     <dbl>
1 FALSE      19    0.775  0.380     0.237
2 TRUE       50    0.879  0.264     0.183

They’re; although maybe to not the extent we’d need.

With simply six lessons, we will additionally examine commonplace deviations on the person prediction-target pairings degree.

eval_table %>% 
  group_by(reality, predicted) %>% 
  summarise(cnt = n(),
            avg_mean = imply(maxprob),
            avg_sd = imply(maxprob_sd),
            avg_mc_sd = imply(maxprob_mc_sd)) %>% 
  mutate(appropriate = reality == predicted) %>%
  prepare(desc(cnt), avg_mc_sd) 
# A tibble: 14 x 7
# Teams:   reality [6]
   reality        predicted      cnt avg_mean avg_sd avg_mc_sd appropriate
   <fct>        <fct>        <int>    <dbl>  <dbl>     <dbl> <lgl>  
 1 SIT_TO_STAND SIT_TO_STAND    12    0.935  0.205    0.184  TRUE   
 2 STAND_TO_SIT STAND_TO_SIT     9    0.871  0.284    0.162  TRUE   
 3 LIE_TO_SIT   LIE_TO_SIT       9    0.765  0.377    0.216  TRUE   
 4 SIT_TO_LIE   SIT_TO_LIE       8    0.908  0.254    0.187  TRUE   
 5 STAND_TO_LIE STAND_TO_LIE     7    0.956  0.144    0.132  TRUE   
 6 LIE_TO_STAND LIE_TO_STAND     5    0.809  0.353    0.227  TRUE   
 7 SIT_TO_LIE   STAND_TO_LIE     4    0.685  0.436    0.233  FALSE  
 8 LIE_TO_STAND SIT_TO_STAND     4    0.909  0.271    0.282  FALSE  
 9 STAND_TO_LIE SIT_TO_LIE       3    0.852  0.337    0.238  FALSE  
10 STAND_TO_SIT SIT_TO_STAND     3    0.837  0.368    0.269  FALSE  
11 LIE_TO_STAND LIE_TO_SIT       2    0.689  0.454    0.233  FALSE  
12 LIE_TO_SIT   STAND_TO_SIT     1    0.548  0.498    0.0805 FALSE  
13 SIT_TO_STAND LIE_TO_STAND     1    0.530  0.499    0.134  FALSE  
14 LIE_TO_SIT   LIE_TO_STAND     1    0.824  0.381    0.231  FALSE

Once more, we see greater commonplace deviations for improper predictions, however to not a excessive diploma.

Conclusion

We’ve proven the way to construct, practice, and acquire predictions from a totally variational convnet. Evidently, there may be room for experimentation: Various layer implementations exist; a unique prior might be specified; the divergence might be calculated in a different way; and the standard neural community hyperparameter tuning choices apply.

Then, there’s the query of penalties (or: resolution making). What’s going to occur in high-uncertainty instances, what even is a high-uncertainty case? Naturally, questions like these are out-of-scope for this publish, but of important significance in real-world functions.
Thanks for studying!

Appendix

To be executed earlier than working this publish’s code. Copied from Classifying bodily exercise from smartphone information.

library(keras)     
library(tidyverse) 

activity_labels <- learn.desk("information/activity_labels.txt", 
                             col.names = c("quantity", "label")) 

one_hot_to_label <- activity_labels %>% 
  mutate(quantity = quantity - 7) %>% 
  filter(quantity >= 0) %>% 
  mutate(class = paste0("V",quantity + 1)) %>% 
  choose(-quantity)

labels <- learn.desk(
  "information/RawData/labels.txt",
  col.names = c("experiment", "userId", "exercise", "startPos", "endPos")
)

dataFiles <- record.information("information/RawData")
dataFiles %>% head()

fileInfo <- data_frame(
  filePath = dataFiles
) %>%
  filter(filePath != "labels.txt") %>%
  separate(filePath, sep = '_',
           into = c("sort", "experiment", "userId"),
           take away = FALSE) %>%
  mutate(
    experiment = str_remove(experiment, "exp"),
    userId = str_remove_all(userId, "consumer|.txt")
  ) %>%
  unfold(sort, filePath)

# Learn contents of single file to a dataframe with accelerometer and gyro information.
readInData <- perform(experiment, userId){
  genFilePath = perform(sort) {
    paste0("information/RawData/", sort, "_exp",experiment, "_user", userId, ".txt")
  }
  bind_cols(
    learn.desk(genFilePath("acc"), col.names = c("a_x", "a_y", "a_z")),
    learn.desk(genFilePath("gyro"), col.names = c("g_x", "g_y", "g_z"))
  )
}

# Operate to learn a given file and get the observations contained alongside
# with their lessons.
loadFileData <- perform(curExperiment, curUserId) {

  # load sensor information from file into dataframe
  allData <- readInData(curExperiment, curUserId)
  extractObservation <- perform(startPos, endPos){
    allData[startPos:endPos,]
  }

  # get commentary areas on this file from labels dataframe
  dataLabels <- labels %>%
    filter(userId == as.integer(curUserId),
           experiment == as.integer(curExperiment))

  # extract observations as dataframes and save as a column in dataframe.
  dataLabels %>%
    mutate(
      information = map2(startPos, endPos, extractObservation)
    ) %>%
    choose(-startPos, -endPos)
}

# scan by all experiment and userId combos and collect information right into a dataframe.
allObservations <- map2_df(fileInfo$experiment, fileInfo$userId, loadFileData) %>%
  right_join(activityLabels, by = c("exercise" = "quantity")) %>%
  rename(activityName = label)

write_rds(allObservations, "allObservations.rds")

allObservations <- readRDS("allObservations.rds")

desiredActivities <- c(
  "STAND_TO_SIT", "SIT_TO_STAND", "SIT_TO_LIE", 
  "LIE_TO_SIT", "STAND_TO_LIE", "LIE_TO_STAND"  
)

filteredObservations <- allObservations %>% 
  filter(activityName %in% desiredActivities) %>% 
  mutate(observationId = 1:n())

# get all customers
userIds <- allObservations$userId %>% distinctive()

# randomly select 24 (80% of 30 people) for coaching
set.seed(42) # seed for reproducibility
trainIds <- pattern(userIds, measurement = 24)

# set the remainder of the customers to the testing set
testIds <- setdiff(userIds,trainIds)

# filter information. 
# notice S.Okay.: renamed to train_data for consistency with 
# variable naming used on this publish
train_data <- filteredObservations %>% 
  filter(userId %in% trainIds)

# notice S.Okay.: renamed to test_data for consistency with 
# variable naming used on this publish
test_data <- filteredObservations %>% 
  filter(userId %in% testIds)

# notice S.Okay.: renamed to pad_size for consistency with 
# variable naming used on this publish
pad_size <- trainData$information %>% 
  map_int(nrow) %>% 
  quantile(p = 0.98) %>% 
  ceiling()

# notice S.Okay.: renamed to one_hot_classes for consistency with 
# variable naming used on this publish
one_hot_classes <- . %>% 
  {. - 7} %>%        # convey integers all the way down to 0-6 from 7-12
  to_categorical()   # One-hot encode
Reyes-Ortiz, Jorge-L., Luca Oneto, Albert Samà, Xavier Parra, and Davide Anguita. 2016. “Transition-Conscious Human Exercise Recognition Utilizing Smartphones.” Neurocomput. 171 (C): 754–67. https://doi.org/10.1016/j.neucom.2015.07.085.

Previous articleElevating Knowledge Intelligence: Key Insights from Business Leaders on Knowledge and AI
Next articleLG In search of Compensation From Apple Over Canceled MicroLED Apple Watch Mission
Adminhttps://dwipanks.xyz

Related Articles

LEAVE A REPLY

Please enter your comment!
Please enter your name here

Latest Articles

Load more

ABOUT US

Dwipanks is your Technology, Nanotechnology, Telecom, Cloud Computing, Artificial Intelligence, Mobile, Robotics, Drone, Big Data and 3D Printing related news website. We provide you with the latest breaking news and videos straight from the Tech industry. For more latest updates keep visiting us, Thankyou.

Copyright © 2024 - dwipanks.xyz. All rights reserved.