Questions tagged [computational-complexity]

The amount of resources required to run a given algorithm in relation to a given task.

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Why is the time complexity of the Triplet Loss $O(N^3)$

The triplet loss function uses an anchor, positive, and negative examples. If $N$ are the number of examples in the training set with $C$ classes, then I think that the time complexity should be $O(...
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Is there a literature on the time complexity of Neural Networks?

There exist various blog posts describing the time complexity of Fully Connected Neural Networks (1, 2, 3, 4); Convolutional Neural Networks (CNN) (5) and of Long Short-Term Memory (LSTM) networks (6)....
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What consequence would a polynomial time algorithm for SAT have on AGI?

$P$ vs $NP$ is a famous problem. We generally believe $P\neq NP$. However suppose there is a polynomial time algorithm of order say $O((n+m)^2)$ or $O((n+m)^3)$ (a low degree polynomial complexity ...
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Recursive Memory Optimized Gradient Graph Explained?

I'm reading the paper Training Deep Nets with Sublinear Memory Cost by Tianqi Chen, et. al. The paper is known for the $O(\sqrt n)$ memory cost to train a $n$-layer neural network. My problem is ...
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Why do off-policy algorithms suffer from worse computational or time efficiency compared to on-policy algorithms?

When I run Soft-Actor-Critic (off-policy) in my Environment, the calculation of gradient updates takes almost twice the time compared to using PPO (on-policy). I also saw that ACER has a higher time ...
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What is the time complexity of Deep VGG-16 Net?

I would like to compute the time complexity (in Big O notation) of Deep Vgg16 Net by feeding forward 1000 images with size 224x224x3 and retrieving features from the second fully connected layer 'fc7' ...
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How is the training comlexity of NNLM word2vec calculated?

I was reading this paper on word2vec, and came around the following description of a feedforward NNLM: It consists of input, projection, hidden and output layers. At the input layer, N previous words ...
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If Least-Squares TD is computationally more expensive, then why is it more data efficient than semi-gradient TD(0)?

In Sutton-Barto (Section: 9.8 Least-Squares TD, page 228): Authors say that Least-Squares TD is the most "data efficient" form of linear TD(0). Later, in this section, they say the ...
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What is the time complexity for testing a stacked LSTM model?

In the data preparation phase, we have to divide the dataset into two parts: the training dataset and the test dataset. I have seen this post regarding the time complexity for training a model. ...
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Why does research on faster Transformers focus on the query-key product?

A lot of recent research on Transformers has been devoted to reducing the cost of the self-attention mechanism: $$\text{softmax}\left(\frac{Q K^T}{\sqrt{d}} \right)V,$$ As I understand it, the runtime,...
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Given an input of shape $(3, 32, 32)$, which is convolved with a $(3 \times 3)$ kernel, how do I calculate the FLOPS?

I have an input tensor of shape $\mathbf{(3, 32, 32)}$ consisting of 3 channels, 16 rows, and 16 columns. I want to convolve the input tensor using $\mathbf{(3 \times 3)}$ kernel/filter. How can I ...
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Do we need as much information to know if we can can answer a question as we need to actually answer the question?

I am reading The Book of Why: The New Science of Cause and Effect by Judea Pearl, and in page 12 I see the following diagram. The box on the right side of box 5 "Can the query be answered?" ...
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How to know if a real-time classifier is achivable in a low-power emdedded system?

Say I have an Machine/Deep learning algorithm I developed on a desktop pc to achieve a real-time classification of time series events from a sensor. Once the algorithm is trained and performs good, I ...
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Why multiplayer, imperfect information, trick-taking card games are hard for AI?

AI reached a super-human level in many complex games such as Chess, Go ,Texas hold’em Poker, Dota2 and StarCarft2. However it still did not reach this level in trick-taking card games. Why there is no ...
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What is the space complexity for training a neural network using back-propagation?

Suppose that a simple feedforward neural network (FFNN) contains $n$ hidden layers, $m$ training examples, $x$ features, and $n_l$ nodes in each layer. What is the space complexity to train this FFNN ...
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What is the computational complexity in terms of Big-O notation of a Gated Recurrent Unit Neural network?

I have been digging up of articles across the internet in context of computational complexity of GRU. Interestingly, I came across this article, http://cse.iitkgp.ac.in/~psraja/FNNs%20,RNNs%20,LSTM%...
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What is the efficiency of trained neural networks?

Training neural networks takes a while. My question is, how efficient is a neural network that is completely trained (assuming it's not a model that is constantly learning)? I understand that this is ...
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What is the time complexity of the upsampling stage of the U-net?

I am trying to determine the complexity of the neural network we use. The neural network is a U-net generator with an input shape of NxN (not an image but image-like data) and output of the same shape....
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What is the computational complexity of the forward pass of a convolutional neural network?

How do I determine the computational complexity (big-O notation) of the forward pass of a convolutional neural network? Let's assume for simplicity that we use zero-padding such that the input size ...
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What is symbol-to-number differentiation?

I recently came across symbol-to-symbol and symbol-to-number differentiation, out of which symbol to symbol seemed fairly straightforward - the computational graph is extended to include gradient ...
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How much time does it take to train DQN on Atari environment?

I am trying to build a DQN model for the Atari Pong game, but I am not sure whether the model is learning at all. I am using the architecture described in the paper Playing Atari with Deep ...
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Why is the space-complexity of greedy best-first search is $\mathcal{O}(b^m)$?

I am reading through Artificial Intelligence: Modern Approach and it states that the space complexity of the GBFS (tree version) is $\mathcal{O}(b^m)$. While I am reading, at some points, I found ...
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Given an input $x \in R^{1\times d}$ and a network with $s$ hidden layers, is the time complexity of the forward pass $O(d^{2}s)$? [duplicate]

I have a neural network that takes as an input a vector of $x \in R^{1\times d}$ with $s$ hidden layers and each layer has $d$ neurons (including the output layer). If I understand correctly the ...
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What are examples of promising AI/ML techniques that are computationally intractable?

To produce tangible results in the field of AI/ML, one must take theoretical results under the lens of computational complexity. Indeed, minimax effectively solves any two-person "board game"...
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How to estimate the cost and time to complete an AI Project [closed]

If you are a freelancer, when a client asks to create a website we can easily measure how much the total cost is needed based on the requirements of the client. (the backend, UI/UX design, features, ...
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When using hashing in tile coding, why are memory requirements reduced and there is only a little loss of performance?

In the book "Reinforcement Learning: An Introduction" (2018) Sutton and Barto explain, on page 221, a form of tile coding using hashing, to reduce memory consumption. I have two questions ...
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Is time/space estimation of possible actions required for creating an AGI?

Given infinite resources/time, one could create AGIs by writing code to simulate infinite worlds. By doing that, in some of the worlds, AGIs would be created. Detecting them would be another issue. ...
6 votes
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What does "hard for AI" look like?

In theoretical computer science, there is a massive categorization of the difficulty of various computational problems in terms of their asymptotic worst-time computational complexity. There doesn't ...
2 votes
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Why is exact inference in a Bayesian network both NP-hard and P-hard?

I should show that exact inference in a Bayesian network (BN) is NP-hard and P-hard by using a 3-SAT problem. So, I did formulate a 3-SAT problem by defining 3-CNF: $$(x_1 \lor x_2) \land (\neg x_3 \...
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Would it take 1700 years to run AlphaGo Zero in commodity hardware?

From this link, AlphaGo would take millennia to run in regular hardware. They generated 29 million games for the final result, which means it's going to take me about 1700 years to replicate this. ...