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Talk:Backpropagation

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This article was the subject of a Wiki Education Foundation-supported course assignment, between 6 September 2020 and 7 December 2020. Further details are available on the course page. Student editor(s): Lipute17.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 15:12, 16 January 2022 (UTC)

Confusing notation
What does the notation y(x) mean when y is an R^n vector and x is an R^m vector? That notation is found in the loss function section, and I've been having a hard time inferring what it means. 2804:14C:8793:86F6:76D4:35FF:FE5B:6F91 (talk) 16:14, 20 February 2017 (UTC)

 * It refers to an output vector y corresponding to a training example vector x. The definition at the top of the section ($$ y, y' \in \R^n $$) has been implicitly altered to something more like $$ y : \R^m \to \R^n $$, a mapping from input vector to output vector. I agree it is confusing. Andars97 (talk) 01:46, 22 April 2017 (UTC)

Questions
Dear All,

Apologies if this is a very naïve question, but in section 6.1 shouldn't the reference be to all neurons directly affected by the neuron (ie L is the next layer), rather than all neurons (L is the total set of neurons lying between the input neuron and the output neurons).

Thx

NeilHyatt (talk) 11:08, 9 January 2017 (UTC)

Dear all, why doesn't this article mention that one needs to learn the biases of multilayer perceptrons? — Preceding unsigned comment added by 92.227.230.174 (talk) 15:10, 12 December 2014 (UTC) Using the neurons weights on it's incoming connections - What does this mean? - Zoe 06:22, 31 January 2003 (UTC)
 * Hopefully this has been clarified. - Eyrian 05:30, 22 Apr 2005 (UTC)

 * This is due to that in the structure of a Neural Network, the neuros are all connected. Each link that connects two neurons carries a weight. - BestDaNiu (talk) 13:37, 12 November 2014 (UTC)

Backpropagation usually allows quick convergence on local minima - What does this mean? - Zoe 06:22, 31 January 2003 (UTC)
 * I think that this is reasonable terminology for use in an article on optimization (though hopefully clarified somewhat). - Eyrian 05:30, 22 Apr 2005 (UTC)

 * In all optimization problems, the objective is to find the maximum or minimum value of a given function with or without constraints. Backprobagation can be viewed as an optimization problem, as it tries to minimize the cost function between the hypothesis outputs and the actual outputs. And as the objective function of backprobagation is non-convex, given a vector of initially random weights, it usually ends with a local minima. -BestDaNiu (talk) 13:37, 12 November 2014 (UTC)

Is $$t_{j}-o_{j}$$ in the 2nd to last equation in the "Finding the derivative of the error" supposed to be backward from (negative of) the y - t in $$\frac{\partial E}{\partial o_j} = \frac{\partial E}{\partial y} = \frac{\partial}{\partial y} \frac{1}{2}(t - y)^2 = y - t $$ ? Couldn't figure out why it would be. — Preceding unsigned comment added by 206.248.153.120 (talk) 03:18, 27 July 2014 (UTC)
 * The order doesn't matter because the difference between these two variables is being squared. The order was chosen for convenience. [Similarly, the 1/2 that appears in the error/loss expression is there for convenience to make the terms simpler after the derivatives are taken. The error expression needs to measures how far off the mark the training round was. I don't think the training's behavior is understood well enough to define a best form for the loss function in all scenarios.]Hozelda (talk) 08:11, 21 June 2019 (UTC)

Please translate from German to English
There seems to be much more information in the German version of this page. Please translate it to English. Thanks! --Jcarroll 23:19, 5 May 2006 (UTC)

 * Added the template to the article. Nicholas Léonard 02:05, 8 January 2013 (UTC) — Preceding unsigned comment added by Strife911 (talk • contribs)

History of the technique
I had heard at some point that a review of Gauss's work indicated that the technique we call backpropagation was actually developed by Gauss. Werbos would then be an independent re-discoverer of the technique. It may even have been Werbos who told me this; I wasn't making notes at the time (about 1990). But I'm not finding corroboration of this, so I thought I would at least broach the topic here. Until there is such corroboration, of course, there should be no change to the article. --Wesley R. Elsberry 11:58, 27 August 2006 (UTC)
 * I somehow remember that Yann LeCun is blamed for this technique. On his web page, I found an article "generalization using back-propagation" from 1987. (http://yann.lecun.com/exdb/publis/index.html)
 * The mathematical theory was there for a long time, so a historical rewiev is indeed interesting. —Preceding unsigned comment added by 83.216.234.177 (talk) 09:58, August 28, 2007 (UTC)

 * Any technique for function minimization (in this case, classification error minimization) that is not simple trial-and-error will predate to the works of Isaac Newton and/or Leibnitz. Perceptron and MLP training are not exceptions, most training algorithms will be variations of Gradient Descent or Newton-Raphson (like Levenberg-Marquadt). Historical review on this would be endless.

--Lucas Gallindo (talk) 19:45, 8 September 2009 (UTC)

Tautology?
"Backpropagation usually allows quick convergence on satisfactory local minima for error in the kind of networks to which it is suited." —The preceding unsigned comment was added by 129.170.31.11 (talk • contribs) 03:16, 16 January 2007 (UTC).
 * I don't think so. The sentence indicates that backpropagation works well on certain networks. --Eyrian 05:49, 16 January 2007 (UTC)

Alternatives
Actually i would like some links to alternative methods for teaching multi-layered networks. Maybe a see also-section —Preceding unsigned comment added by 80.164.105.90 (talk) 07:11, 8 September 2007 (UTC)

Algorithm
Citation: Material seems to be directly copied from http://www2.cs.uh.edu/~ceick/ai/nn.ppt (slide 6); if it is, a reference should be included.

Explanation: I'm not understanding how to compute the per-node error. How much blame should be subtracted from each connection's weight, and how much should be propagated back to the inputing nodes'? (I'm assuming that it backpropagates according to the proportion of error contributed by each earlier connection.) --Jesdisciple 03:54, 8 October 2007 (UTC)

 * I detail the error propagation algorithm in multilayer perceptron. Perhaps some of the math should be copied to here? SamuelRiv (talk) 13:04, 18 November 2007 (UTC)

The phase 1 description and pseudocode need to be more detailed. The key propagation step is briefly described in point 3 of phase 1 and line 7,8 of the pseudocode, but how exactly one does the propagation is not explicitly defined. I.e. you could not write C code from the given information as is. 202.112.90.192 (talk) 04:12, 28 November 2018 (UTC)

Connection to Biology
Someone added a section on backpropagation of action potential in biological neurons. I just backed this change out. The material is irrelevant in the context of this article. (In this article, backpropgation refers to reverse propagation of errors through the computation graph. As far as anyone knows, this has nothing to do with the potential jump of action potentials invading the proximal regions of the dendritic arbor) Barak (talk) 19:10, 17 November 2007 (UTC)
 * term "Backpropagation" is ambiguous

 * How about some tact here. I added 2000 bytes of information, so maybe there should be some discussion before wiping it. The idea of backpropagation as a biological model, as it has been applied by several research groups (IBNS for one) is useless without some justification. A computational model is effectively a neuroscience model, and any information added to this effect is useful. Anyway, if more context or a separate article is needed, then we can add that. But please don't just blank a good half-hour of factual and relevant information. SamuelRiv (talk) 21:14, 17 November 2007 (UTC)

 * I'm sorry if my change seemed abrupt. The material you added is both interesting and (I say this as someone knowledgeable in the field) entirely correct.  The reason I removed it is because it belongs in a different article.  Perhaps in an article about action potentials in neurons, or in one about Hebbian synaptic plasticity, or some place like that.  But unfortunately, it is not appropriate here: "back propagation" of potential from the soma into the dendritic arbor is a different sense of the term "backpropagation" than that being used here, which refers to a mathematical construction for an estimation problem.  Please do not take this personally though, and I am serious when I say that the text you wrote deserves a home.  It just doesn't fit here.  Barak (talk) 11:05, 18 November 2007 (UTC)

 * Thanks for the detailed response. I disagree, obviously, because from my perspective artificial and biological neural nets are inseparable concepts. The nonlinear activation function, for example, was partially inspired by biology, and in this case the success of backprop as an algorithm encouraged biologists to find evidence for it in biological systems. I don't think there is enough there for it to warrant a separate article (it still seems like a lot of speculation as to the algorithmic purpose of the retrograde signal). It belongs here because backpropagation is a feedforward algorithm, where as Hebbian learning, for example, has no such bias (it could work with a feedback loop to transmit errors, for instance). I don't know, personally I can't think of a more appropriate place for this information, especially as this article is pretty short already. I'll think about it more, though, and see if there might be a better fit somewhere. SamuelRiv (talk) 13:02, 18 November 2007 (UTC)

 * I'm sorry but what you're saying doesn't really support the idea that this particular material should be included in this particular article. You're summarizing a biology paper that happens to have the word "backpropagation" in its title.  But that paper is using that word in a completely irrelevant way.  Any other paper about some detailed electrophyiological measurement would be just as relevant.  This article is short, yes.  There are many relevant hunks of information that could be added.  Eg: a review of backprop-based work that has cast new light on a variety of biological phenomena, such as NETtalk and language acquisition, Qian et al's shape-from-shading model and the bar detector story.  Or some hooks into the literature of practical applications could be added: PAPnet is a billion-dollar thousands-of-lives success of backprop.  Credit card transaction validation.  Loan application testing.  ALVINN.  Face detection.  Facial gender discrimination.  Or hooks into the relevant theoretical literature: theory of generalization in such networks, VC dimension bounds, early stopping, optimal brain damage.  Convolutive networks and TDNNs enjoy wide application (leNet is the gold standard for handwritten digit recognition, for example.)  Pointers to implementations that are really useful, like "lush", so people can go out and build real systems.  But a summary of a bit of completely irrelevant biology data just doesn't belong here.  (You mention Leon Cooper's group at Brown as if it makes this relevant.  But that group doesn't work on backprop or related methods.) Barak (talk) 19:54, 18 November 2007 (UTC)

 * You still have not addressed why it is irrelevant. Here we have an algorithm that essentially cannot function without some method of backward propagation of signals (simple feedback loops don't work by nature of the correction algorithm). This is used in neural networks, which are almost by definition the best existing model of a functional brain. So as soon as you have an algorithm, you have a brain model. The Brown group works on brain models from both a top-down and bottom-up perspective, so they address both algorithms (mostly RBNs - granted I haven't seen any papers specifically working with backprop) and biological models. So as a model of the brain, which the backpropagation algorithm is, we would naturally want some evidence for it. That's where this addition comes into play.
 * Now I'd rather have a discussion than an edit war, but I fail to see why, in a dispute, you'd rather default to having less information visible in the article than more. SamuelRiv (talk) 20:15, 18 November 2007 (UTC)
 * Addendum: I have tagged this page on Third opinion. Additionally, I want to clarify that IBNS has done work on backprop algorithms, but no paper deals specifically with them. Most use multilayer perceptrons in comparison to RBNs. SamuelRiv (talk) 20:43, 18 November 2007 (UTC)

 * Let me answer your actual question above, which I paraphrase: "Here we have an algorithm that cannot function without some method of backward propagation of signals ... why is evidence for backward (i.e., into the dendritic arbour) propagation of action potentials not relevant?" The reason is that what is being retrograde transmitted into the dendrites are action potentials, which is the activity of the neurons.  It is not the error, which is what would need to be transmitted to implement backprop.  It is backward something, but the wrong thing!  It is not backward propagation of errors.  Barak (talk) 21:00, 18 November 2007 (UTC)

 * Okay, new paragraph because I'm sick of typing colons. In response, your point about error is fair, in that error or its energy is not necessarily what is being backpropagated. But it can be. Imagine a 3-layer perceptron that wants to learn to match its output to a memorized binary pattern, say. So its output layer connects in a linear 1-1 fashion with the memory, producing a spike frequency in the memory layer that increases with the amount of error in the output, that is, if the output approaches "0" frequency, the memory wants frequency "1" and spikes at full frequency to signal that error. Once the signals match, the memory stops spiking. So each of these error spikes backpropagates, and then you get the full LTP/LTD effects (this last sentence has not yet been observed). I'll see if I can find a paper on this mechanism when I get to the office. SamuelRiv (talk) 15:15, 19 November 2007 (UTC)

 * Addendum - see if you can open it for a paper outlining a biological backprop mechanism. Does information from this at least deserve to be in the article? SamuelRiv (talk) 19:04, 19 November 2007 (UTC)

 * That's not a bad paper, although there are two other efforts I'd look at first. One is a paper by Paul Werbos on implementing backprop in neural hardware.  The other is the "Recirculation Neural network" architecture (G. E. Hinton and J. L. McClelland, J. L., "Learning representations by recirculation", in D. Z. Anderson (ed), "Neural Information Processing Systems," pages 358-366, AIP, ), which was the start of a line of research that, in a modern probabilistic context, developed into the Helmholtz Machine and the Restricted Boltzmann Machine architectures.

 * A wikipedia article on Biologically Plausible NN Learning Algorithms would be a useful place to have pointers to these various strands of research, and to put them all in perspective. Barak (talk) 10:51, 26 November 2007 (UTC)

 * Yikes, another thing on my "to do" list. I'll explore making that article (I have to look at the literature on biological SVMs and CMs first). Meanwhile, thanks for the papers, except I can't find the Werbos one - do you remember the title or keywords? SamuelRiv (talk) 16:28, 26 November 2007 (UTC)

Request for comments on biological evidence section
The question is whether or not a section which was alternately added and removed is pertinent, relevant, and suitable for inclusion in this article. — Athaenara ✉  03:16, 19 November 2007 (UTC)

 * Responding to RfC. This article is about a computer algorithm, while the section in question describes a biological process that works in the same way. I don't believe the section should be included, as it is of little relevanse to what I believe the article should be about (the algorithm and its properties). But the information presented in the section is interesting and seems to be notable, so I beleive it should be added to a seperate article and linked to from this article. Labongo (talk) 11:58, 19 November 2007 (UTC)

 * My main problem is that every neural network algorithm doubles as a biological model for the time being, because we simply don't know for sure what algorithms the brain uses. We have some evidence for several different algorithms, so where do we put all that information? SamuelRiv (talk) 15:17, 19 November 2007 (UTC)

 * The information should probably be in the other article or some related article, since how the brain works is clearly outside the scope of this article. Labongo (talk) 16:00, 20 November 2007 (UTC)

 * I created Neural backpropagation, as per the third opinion. However, I frankly think this is ridiculous, as the literature only refers to the phenomenon as "backpropagation" and there is enough overlap between these topics that they deserve separate articles. I'd also like to say that repeatedly deleting large-scale factual and arguably relevant contributions to an article seems to me to violate the spirit of Wikipedia, as stated in its revert policies. Someone will inevitably come along and suggest these articles be merged, if anyone ever reads them. SamuelRiv (talk) 23:58, 20 November 2007 (UTC)

 * I added otheruses templates to both algorithms, to ensure that there is no confusion with regard to the term. Since the issues seems to be resolved I have also removed to RfC tag from the talkpage. Labongo (talk) 15:32, 22 November 2007 (UTC)

Poor summary?
It's a very good idea to have a summary of an algorithm like this, but I don't find the summary as it currently stands, to be very good. Thomas Tvileren (talk) 10:01, 19 January 2009 (UTC)

Much better now! Thanks to Strife911. Thomas Tvileren (talk) 17:42, 23 February 2011 (UTC)

 * Because this is an encyclopedia, I was hoping for an introduction that would give a general idea of the topic to non-specialists. The first sentence refers to the "objective function", but it is not linked or defined, and non-specialists will have no idea what it is. It's my view that the first sentence in any article should come as close as possible to a general description, even if not perfectly precise, without resorting to opaque jargon, and with a minimal number of words and concepts that the general reader has to look up in order to understand that description. I'd like to invite someone who's knowledgeable about the subject take on the challenge of making the whole introductory section more accessible to non-specialists. - Do c  t  orW  23:36, 23 June 2012 (UTC)

 * This is not my area, but let me take a stab at what I have in mind, in order to illustrate:
 * Backpropagation, an abbreviation for "backward propagation of errors", is a common method of training artificial neural networks. From a desired output, the network learns from many inputs, similar to the way a child learns to identify a dog from examples of dogs. [Perhaps a more exact and more technical, but nevertheless brief, explanation could comprise the next sentence.]
 * The introduction could then go on to talk about the supervised learning method, and then the delta rule.
 * The second paragraph could introduce the seminal figures (Bryson & Ho, Werbos, Rumelhart, and Hinton & Williams). - Do c  t  orW  00:19, 24 June 2012 (UTC)

There was no response to my suggestion from 6 months ago, so I was bold and took a crack at it, even though this is not my area. Please feel free to correct any errors I may have made and continue to make at least the introduction more accessible to non-specialists. This is an encyclopedia, after all. - Do c  t  orW  09:47, 24 December 2012 (UTC)

Invented by
The article attributed the first description to "Paul Werbos in 1974". According to my source this is incorrect, I have updated the text to cite Bryson and Ho 1969. I am mentioning this in Talk since I am surprised to see a long-standing error of such importance. 78.105.234.140 (talk) 17:01, 15 October 2009 (UTC)

If one actually reads the relevant section of Bryson and Ho (1969) it plainly (a) cites an earlier journal paper describing the idea, and (b) mentions that this method is an application of Pontryagin's minimum principle. Barak (talk) 22:35, 16 October 2011 (UTC)

Observer's comment: 87.205.28.164 (talk) 21:35, 1 January 2013 (UTC) As an active researcher in Backpropagation and Pontryagin's maximum principle, I can assure you that backpropagation and pontryagain's principle are not connected. Barak, Can you give the page number of the source where you read this, and I'll check it out?

Relationship to Delta Rule?
The sentence enclosing the link to the Delta rule for this page states:

"It [Back-propagation] is a supervised learning method, and is an implementation of the Delta rule."

Implying that back-propagation is a subset of Delta Rule, but for the link to Back-propagation from the Delta Rule page it states:

"It [The Delta Rule] is a special case of the more general backpropagation algorithm."

Can this be? Or is the wording simply a bit confusing? —Preceding unsigned comment added by 72.221.98.197 (talk) 02:44, 20 December 2010 (UTC)

 * If you look in books, it appears that the delta rule only works at outputs where you have a target, and the back-prop is a generalization of it. So the first quoted sentence should have "implementation" changed to "generalization", I think.  Dicklyon (talk) 03:17, 20 December 2010 (UTC)

If you read the original article by Rumelhart, Hinton & Williams, they explicitly call it the "generalized delta rule." The original delta rule applies to linear single-layer networks, although it can be shown to be identical to the perceptron algorithm. The generalization is to nonlinear networks with a squashing function, and to multilayer networks (hence, "backpropagation", which is unnecessary in single layer networks). -gary cottrell —Preceding unsigned comment added by 75.80.97.109 (talk) 10:00, 25 January 2011 (UTC)

It doesn't explain how the delta rule is generalised. It just duplicates the derivation of the delta rule and then gives up on explaining what happens to hidden nodes. Ptolom (talk) 11:06, 19 January 2014 (UTC)

A new algorithm proposal
Could we change the layout of the algorithm? Why not make each instruction a link to additional information? But should this information be put in the same page, or a one relating to the 'next level of detail', for the algorithm? —Preceding unsigned comment added by 139.80.206.172 (talk) 08:57, 1 May 2011 (UTC)

Equations
The article is missing the equation(s) for back propagation learning algorithms. Malithyapa (talk) 23:21, 31 August 2011 (UTC)

Meaning of Weight
I was unfamiliar with the term "weight" used in this context- I think it ought to be more clearly explained early on. Also, it might be good for someone more knowledgeable to add a quick reference to the Weight disambiguation page. Brauden (talk) 03:20, 7 May 2012 (UTC)
 * I added a bit at the disambig page. Dicklyon (talk) 04:22, 7 May 2012 (UTC)

Stochastic versus online?
In adding cross-references to the Modes of Learning section, I found an apparent contradiction between this article and that for stochastic gradient descent (SGD), where the latter (specifically, in the  Iterative method section) equates SGD with  online learning while this article distinguishes between them. Come anyone wiser than me please advise if these should be equated here or the other article corrected?

Also, the statement that "Stochastic goes through the data set in a random order in order to reduce its chances of getting stuck in local minima" seems quite far from the method and purpose described in the SGD article. Perhaps the Modes of Learning section would be better simply cross-referencing the others rather than trying to summarise them. Or have I entirely missed a point?

Many thanks. p.r.newman (talk) 13:33, 4 April 2013 (UTC)

Threshold? Derivative? Other activation functions?
1. What happens with the threshold? It is mentioned in othe articles, here is no word of it. In the German version, they say they replace the threshold with an "on-neuron", but even they do not venture to describe it.

2. How do you get the derivative? - I think this is very nicely explained here:

https://en.wikipedia.org/wiki/Delta_rule

3. It should be explained what happens with other activation functions. In particular, that the derivative may actually be 1 in case of a linear activation. It is elsewhere mentioned that you can use tanh as activation, too.

- Nino — Preceding unsigned comment added by 188.23.245.69 (talk) 05:38, 26 February 2014 (UTC)

misleading statements
It wasn't said or implied in the article that input layer isn't affected by error estimate. Corrected algorithm description. Rest of article still misleading. 2001:470:600D:DEAD:E94B:92C8:B4E1:F8C5 (talk) 11:57, 28 August 2014 (UTC)

Outdated
This article, or at least parts of it, are quite outdated. They follow the old definition of backpropagation, where this name refers to the entire gradient descent algorithm for squared-error feed-forward networks. The lede, by contrast, uses the more modern meaning, where backprop is the generic gradient computation algorithm based on the chain rule, which can be combined with any gradient-based optimizer (conjugate gradient, L-BFGS) and any differentiable loss (log-loss, squared-error).

I'm planning a rewrite of this entire article to bring it in line with Bishop's (2006) Pattern Recognition and Machine Learning instead of Rojas's (1996) Neural Networks, which (judging by the notation) is the main source for the current text. Q VVERTYVS (hm?) 20:34, 4 November 2014 (UTC)

Modes of learning
Statement "Yet batch learning will yield a much more stable descent to a local minimum since each update is performed based on all patterns." can be misleading. Batch learning requires one to go through all of the test cases, while online learning can cope with a adding a single one, or a few. But if you pass through all of the test cases with on-line learning, you shouldn't end up further away from solution than with a batch learning which should actually get completely abandoned, as it is nonesense. Refer to http://axon.cs.byu.edu/papers/Wilson.nn03.batch.pdf for explanation why Wiki should abandon any talks of batch learning entirely, due to it not being useful in any sort of way. --213.174.16.2 (talk) 14:38, 21 January 2015 (UTC)

 * Usefulness is not the criterion for covering something on WP. Also, while batch learning may not be optimal or even better for gradient descent, it also allows using algorithms like L-BFGS or conjugate gradient (see Bishop, Pattern Recognition and Machine Learning, p. 240). These are not easily recast as online or minibatch algorithms. Q VVERTYVS (hm?) 16:57, 21 January 2015 (UTC)

global convergence?
"However, convergence to the global minimum is said to be guaranteed using the adaptive stopping criterion.[3]" is an extraordinary claim. As such, it requires extraordinary proof. The referenced article provides only the claim. Mborg (talk) 15:25, 16 September 2015 (UTC)
 * It's not really an extraordinary claim. The quotation is not a claim; the quotation reports that "it is said". If you feel that's too strong, you could change it to "articles report..., but there is no proof for it".--Gciriani (talk) 15:52, 16 September 2015 (UTC)
 * "It is said" is certainly not a strong claim; it's far too vague a claim for a technical article. I've removed the claim and the reference because a poorly-cited article by some unknown researchers in an off-track journal that presents a ridiculous algorithm without proof of effectiveness or even an intuitive justification as to why its crazy formulas should work is not the kind of material on which to base an encyclopedic article. Q VVERTYVS (hm?) 20:09, 16 September 2015 (UTC)

Error in algorithm?
In its current form the algorithm has two nested loops initialize network weights (often small random values) do forEach training example ex        prediction = neural-net-output (network, ex)  // forward pass actual = teacher-output (ex) compute error (prediction - actual) at the output units compute $\Delta w_h$ for all weights from hidden layer to output layer // backward pass compute $\Delta w_i$ for all weights from input layer to hidden layer  // backward pass continued update network weights // input layer not modified by error estimate until all examples classified correctly or another stopping criterion satisfied return the network

The way I learned the algorithm, the network weights aren't updated for every training example, but rather once for each iteration of the outer loop. That is the inner loop is used to calculate the gradient and then, after the inner loop, the gradient is used to update the weights. So I suggest initialize network weights (often small random values) do forEach training example ex        prediction = neural-net-output (network, ex)  // forward pass actual = teacher-output (ex) compute error (prediction - actual) at the output units compute $\Delta w_h$ for all weights from hidden layer to output layer // backward pass compute $\Delta w_i$ for all weights from input layer to hidden layer  // backward pass continued end forEach update network weights // input layer not modified by error estimate until all examples classified correctly or another stopping criterion satisfied return the network

— Preceding unsigned comment added by 142.166.157.21 (talk • contribs)

 * It's explained (inadequately) below the pseudocode:

"Technically speaking, backpropagation calculates the gradient of the error of the network regarding the network's modifiable weights. This gradient is almost always used in a simple stochastic gradient descent algorithm to find weights that minimize the error."

 * The pseudocode is actually that of stochastic gradient descent, not backprop; backprop is the part labeled "backward pass" and practically glanced over. What you're suggesting is batch gradient descent. Q VVERTYVS (hm?) 15:24, 18 October 2015 (UTC)

Wrong Error Function Visualization and Description under the "Intuition" Heading
I believe that under the "Intuition" heading, given the current example of (x1,x2,t) = (1,1,0), the correct error function is NOT a parabolic bowl as written, but instead what Wolfram Alpha refers to as a parabolic cylinder. I believe the correct graphic should be of E= 0 - (x1*w1 + x2*w2)^2, and not the current graphic which models E= 0 - [(x1w1)^2 + (x2w2)^2].

I concur - this is a very confusing picture. If w1=-w2 then the error is zero. Henk.muller (talk) 10:37, 6 June 2016 (UTC)

Sources on the history of backpropagation
According to various sources, basics of continuous backpropagation were derived in the context of control theory by Henry J. Kelley in 1960 and by Arthur E. Bryson in 1961, using principles of dynamic programming. In 1962, Stuart Dreyfus published a simpler derivation based only on the chain rule.

In 1970, Seppo Linnainmaa finally published the general method for automatic differentiation (AD) of discrete connected networks of nested differentiable functions. This corresponds to the modern version of backpropagation which is efficient even when the networks are sparse.

In 1973, Stuart Dreyfus used backpropagation to adapt parameters of controllers in proportion to error gradients. In 1974, Paul Werbos mentioned the possibility of applying this principle to artificial neural networks, and in 1982, he applied Linnainmaa's AD method to neural networks in the way that is widely used today.

In 1986, David E. Rumelhart, Geoffrey E. Hinton and Ronald J. Williams showed through computer experiments that this method can generate useful internal representations of incoming data in hidden layers of neural networks. In 1993, Eric A. Wan was the first to win an international pattern recognition contest through backpropagation.

One should insert the missing references in the article. Mathpriest (talk) 15:56, 28 March 2016 (UTC)

Remake of the algorithm section
I have written a candidate for a better description of the algorithm here: User:Esraiak/sandbox, and I am considering replacing the current Algorithm (and/or Summary) section with that one.

I will do the replacement in a few days unless someone objects.

Esraiak (talk) 14:25, 28 September 2016 (UTC)

Added content from Spanish/German articles. Improved for non-technical readers.
I added some sections from the German article (mostly the Extension section) and from the Spanish article (introduction).

I also tried to make the introduction and a few other sections better for non-technical readers. AlgorithmEdits (talk) 02:02, 12 December 2016 (UTC)

Buzzwords
Some buzzwords in the algorithm description: input thought, output activations, weight-synapse.

With a bit of critical thinking it's possible to infer what they refer to, but they are not defined here and inappropriate (subjective interpretations) for a purely technical description. — Preceding unsigned comment added by 88.177.31.169 (talk) 15:38, 26 December 2016 (UTC)

Core concepts in first sentences
I am unhappy with the first sentences in this article. I don't mean that they are wrong, only that they do not explain well what it is all about. Here is a better explanation that I found in Deep Learning by Goodfellow, Bengio and Courville, 2016. I think this is now the dominating course book on Deep Learning. It says on page 198: "The term back-propagation is often misunderstood as meaning the whole learning algorithm for multi layer neural networks. Actually back-propagation refers only to the method for computing the gradient, while another algorithm, such as stochastic gradient descent, is used to perform the learning." That is, when tuning an ANN to perform well on a set of data, the weights in the network are changed so that a cost calculated from the difference between the network output for the data and the known correct output is minimized. This minimization algorithm calculates the gradient of the cost as a function of the weights. Back-propagation is a method to calculate that gradient. Therefore, in my view, backprop is a method to calculate a gradient that is needed in the calculation of the weights to be used in an artificial neural network. --Ettrig (talk) 08:50, 5 February 2018 (UTC)

Confusing discussion of gradient descent
Why is gradient descent mentioned in this wiki article? Backpropagation is an algorithm to find the gradients, then what you do with those gradients is an entirely different issue. Reading the wiki one may think that backpropagation also concerns itself with SGD or similar; see discussion about choosing an adaptive learning rate, etc.

What do you think? Should we delete those discussions? User:Daniel.Cardenas

 * Good point! For orientation, gradient descent should be mentioned as the most common application and the context in which it was developed. Currently gradient descent occurs 12 times. That is far too much. The subject is difficult as it is. We should not add to the confusion by adding off-topic material.--Ettrig (talk) 06:42, 28 November 2018 (UTC)
 * There are whole sections of such off-topic material. Should this be just removed, or dumped on articles where it belongs? --Ettrig (talk) 07:20, 28 November 2018 (UTC)
 * I moved it to artificial neural network. That is at least a small step in the right direction. But a lot of restructuring of ANN material is neede. --Ettrig (talk) 14:16, 28 November 2018 (UTC)
 * 10K bytes moved, out of 38K. Now, there is a lot to clean up in ANN, but at least it is in the right place. There is a lot of mathematical notation, which is cumbersome to produce. So it would be unfortunate to just lose it. I think it is mostly correct. --Ettrig (talk) 16:43, 28 November 2018 (UTC)

History section added
I added a history section. I consider it a poor attempt, but figured something was better than nothing. Please improve. Thanks! Daniel.Cardenas (talk) 16:14, 30 September 2018 (UTC)
 * There was a history at the bottom of the article. I merged yours with that one.--Ettrig (talk) 14:17, 28 November 2018 (UTC)

Confusing notation #2
Using $$o_k$$ for both the input and output of a neural network layer in the Derivation section is super confusing. Could this be changed (at least add some accent to distinguish the two)? Attila I Szabo (talk) 09:49, 11 April 2019 (UTC)
 * Looks like several people have cleaned up most of that Hozelda (talk) 13:10, 16 June 2019 (UTC)

"total derivative" just before eqn 5 is not correct explanation
There is a mention of "total derivative" presumably to justify a summation formula that follows, "taking the total derivative with respect to $$o_j$$, a recursive expression for the derivative is obtained: $$\frac{\partial E}{\partial o_j} = \sum_{\ell \in L} \left(\frac{\partial E}{\partial \text{net}_\ell}\frac{\partial \text{net}_\ell}{\partial o_j}\right) = \sum_{\ell \in L} \left(\frac{\partial E}{\partial o_\ell}\frac{\partial o_\ell}{\partial \text{net}_\ell}\frac{\partial \text{net}_\ell}{\partial o_j}\right) = \sum_{\ell \in L} \left(\frac{\partial E}{\partial o_\ell}\frac{\partial o_\ell}{\partial \text{net}_\ell}w_{j \ell}\right)$$ (eqn 5)."

That appeal seems incorrect. The total derivative comes into play if you wanted to know the approximate change in the error based on all the small $$\Delta w_{i,j}$$. As far as calculating any individual $$w_{i,j}$$ (the purpose of the section) the total derivative has nothing to do with it.

I am not presenting a proof of eqn 5, but I think it could be true because of at least 2 things: the error function is a sum of terms (one for each output neuron), and the inputs to every neuron are combined in a summation (before applying the logistic function). These summations of inputs make it so that the partial derivatives, after the chain rule applications, separate into summed components since the derivative of a sum is the sum of derivatives.

I am not sure what changes should be made, but suggesting the "total derivative" is why eqn 5 is true is not true imo. — Preceding unsigned comment added by Hozelda (talk • contribs) 08:26, 21 June 2019 (UTC)
 * I'm back 6 months later and just did a particular case on paper (not the generalized case) and got an answer consistent with $$\delta_j$$ as per this page, but the reason for the summation in the $$\delta_j$$ formula has nothing to do with "total derivative" as stated on the page. It is a result of working the partial of that loss function* all the way to the end for the relevant $$w_{ij}$$ that gives that form for $$\delta_j$$. If the loss function was something else then the result could be different for $$\delta_j$$. Similarly if the definition of the perceptron was other than the dot product of the inputs with their weights then $$\delta_j$$ could have a different form that might not even recurse in a compact way. Also, you guys should look up the meaning of total derivative. It doesn't even make sense how it is being used here. In summary, it is a coincidence that the correct answer for $$\delta_j$$ looks somewhat like a total derivative (summation of partial derivative factors). This happens for the typical loss functions and the definition of perceptron (which have linear aspects to them). [*] square error or any similar error function that separates each output perceptron contribution into a distinct "term". Hozelda (talk) 05:04, 4 January 2020 (UTC)
 * OK I am reinterpreting the meaning of total derivative so that instead of having several independent variables with respect to which we derive the various parts under the summation, that those don't have to be independent variables. In that case, the explanation more or less makes sense. Hozelda (talk) 11:44, 4 January 2020 (UTC)

 * Hi
 * Thanks for the analysis! Yes, the fundamental confusion is that backpropagation computes the gradient, not the total derivative. These are frequently conflated, because they have the same components, but are distinct: the gradient is computed backwards from the end, while the total derivative is computed forwards from the start (see the gradient page for more). The $$\delta_j$$ is the gradient at a specific level, interpreted as "(backwards) propagation of error", which is why computing it in terms of total derivatives is confusing: it's backwards.
 * I've rewritten the lead and written a "Overview" section in terms of gradient, notably in, but haven't rewritten other sections.
 * Are these new "Overview" and "Matrix multiplication" sections clearer?
 * —Nils von Barth (nbarth) (talk) 03:06, 5 January 2020 (UTC)

Incoherent introduction
It has already been mentioned several times in this page, but there is still a confusion in the introduction between “error backpropagation” the algorithm from Rumelhart et al. and LeCun to train a NN and “gradient computation by backpropagation” the more modern understanding of the term that comes from the fact that people have now decoupled the gradient computation and SGD parts of the original algorithm (and don't always use SGD anymore). As is, the first paragraph seem to use the first one and the second paragraph the second one, which is confusing. It would be better to explicit that there are several meanings to the term and explain why. I nobody is against it, I will try to rework it in the next days --Evpok (talk) 08:42, 18 September 2019 (UTC)
 * Sounds like a good move.  We might have a chicken-and-the egg situation here because the leads should be a summary of what is in the article.   But it sounds like a good step. North8000 (talk) 18:08, 18 September 2019 (UTC)
 * As a non-expert, I've gone through the first para and made a few changes to the wording. Please check. In my view, the language could be more precise in a few places. For example: "The term backpropagation strictly refers only to the algorithm for computing the gradient, but is often used loosely to refer to the entire learning algorithm, including how the gradient is used, such as by stochastic gradient descent." It's a winding, complex sentence, so could be kinder to less-informed readers like me. But critically, by this start to the second para, I'm still unsure whether "the algorithm" is a single identifiable algorithm for universal use, or a class of algorithms that are developed for particular contexts. I should not be unsure by that stage. Tony (talk)  23:46, 4 January 2020 (UTC)
 * Thanks, your perspective is very useful, and your tweaks and comments are appreciated!
 * I've tweaked a bit more, so it's hopefully more useful. The efficiency is the key point, but I realize now that it was mentioned only in passing, so I've elaborated and emphasized briefly.
 * —Nils von Barth (nbarth) (talk) 03:23, 5 January 2020 (UTC)
 * —Nils von Barth (nbarth) (talk) 03:23, 5 January 2020 (UTC)

I'm not expert enough to judge, but it looks good and thank you to both of you. This is the kind of work needed on these articles. North8000 (talk) 13:48, 7 January 2020 (UTC)

Sigmoid function?

 * Added title. —Nils von Barth (nbarth) (talk) 23:53, 8 March 2020 (UTC)

The lead makes no mention of the sigmoid function; but isn't that critical to understanding "e.g. 0.1, 0.7, 0.2", which occurs soon after the lead? Tony (talk)  02:47, 5 March 2020 (UTC)
 * Probably not critical. It used to be common to use the logistic sigmoid to get outputs between 0 and 1 for class probabilities, but nowadays the use of a "softmax" layer is more commom for that.  The sigmoid would be great for definiteness, but it's certainly not required or unique. Dicklyon (talk) 07:01, 5 March 2020 (UTC)
 * Thx. Tony (talk)  07:03, 5 March 2020 (UTC)

Imprecise language at the end of the section Finding the Derivative of the Error.
The text reads:

The new $$\Delta w_{ij}$$ is added to the old weight, and the product of the learning rate and the gradient, multiplied by $$-1$$ guarantees that $$w_{ij}$$ changes in a way that always decreases $$E$$.

This is false for any reasonable definition of "guarantees". E.g. consider if the present value of $$w_{ij}$$ is a local minimum. At such a location any change to $$w_{ij}$$ will result in an increase in error, while the gradient at that value will be zero.

The text further says:

In other words, in the equation immediately below, $$- \eta \frac{\partial E}{\partial w_{ij}}$$ always changes $$w_{ij}$$ in such a way that $$E$$ is decreased:

This is also incorrect for any definition of "always" since, with large values of $$\eta$$, it is possible to overshoot a local minimum an increase the error.

Let's tighten up this language.

Skremer (talk) 17:48, 18 May 2020 (UTC)

Problem with equation before equation 5
Hi All,

I think there is a problem with the equation $$ \frac{\partial E}{\partial w_{ij}} = o_i \delta_j$$ because the index $$i$$ and $$j$$ are interchaged. The correct expression could be $$ \frac{\partial E}{\partial w_{ij}} = o_j \delta_i$$

The source of the problem may be in Eq.1 $$\frac{\partial E}{\partial w_{ij}} = \frac{\partial E}{\partial o_{j}} \frac{\partial o_{j}}{\partial w_{ij}} = \frac{\partial E}{\partial o_j} \frac{\partial o_j}{\partial\text{net}_j} \frac{\partial \text{net}_j}{\partial w_{ij}}$$

And the correct expression could be $$\frac{\partial E}{\partial w_{ij}} = \frac{\partial E}{\partial o_{i}} \frac{\partial o_{i}}{\partial w_{ij}} = \frac{\partial E}{\partial o_i} \frac{\partial o_i}{\partial\text{net}_i} \frac{\partial \text{net}_i}{\partial w_{ij}}$$

Please, look at the book Bishop, C. M. (2006). Pattern recognition and machine learning (1st ed.). Springer-Verlag New York, p. 243 at the equation 5.53 --Memo26167 (talk) 02:08, 9 August 2021 (UTC)

Introduction is way, way, way too complicated
Wikipedia has this habit of writing introductions to mathematical topics as if the reader is a Math graduating student.

Why can't the introduction just start saying that backpropagation at its core uses iteractive methods like inverse gradient method:

Xk+1 = Xk - ε .ᐁf(Xk)

to atune the parameters X={x1, x2, ..., xn} of a neural neural network, so that it minimizes an error function f(X), and that the basis of it is rather simple, but implementation can be complicated due to troubles of calculating ᐁf(Xk)? Instead one gets right out of the bat: "stockastic gradient method" "g(X) = lenghty formula". These things are very confusing and discouraging to those like me that don't want to be mathematicians.

I read the article in Wikipedia first, understood nothing of it, then went to https://codesachin.wordpress.com/2015/12/06/backpropagation-for-dummies/, and it was completely clear to me, I wrote my first neural network the same day. That was almost 10 years ago. As time passes Wikipedia is becoming less and less of an asset to the public and more and more an obscure "mathematician's pub (and physicist's pub too, btw)". I write this with the greatest love, as I love Wikipedia and I think it is (and should increasingly be) an asset to the general population. 136.54.50.251 (talk) 04:49, 30 April 2024 (UTC)

title: Talk:Backpropagation


text:
Immortality

Immortality is the concept of eternal life. Some species possess 'biological immortality' due to an apparent lack of the Hayflick limit.

Some scientists, futurists and philosophers have theorized about the immortality of the human body, with some suggesting that human immortality may be achievable in the first few decades of the 21st century with the help of certain technologies such as mind uploading (digital immortality). Other advocates believe that life extension is a more achievable goal in the short term, with immortality awaiting further research breakthroughs. The absence of aging would provide humans with biological immortality, but not invulnerability to death by disease or injury. Whether the process of internal immortality is delivered within the upcoming years depends chiefly on research (and in neuron research in the case of internal immortality through an immortalized cell line) in the former view and perhaps is an awaited goal in the latter case.

From at least the time of the ancient Mesopotamians, there has been a conviction that gods may be physically immortal, and that this is also a state that the gods at times offer humans. In Christianity, the conviction that God may offer physical immortality with the resurrection of the flesh at the end of time has traditionally been at the center of its beliefs. What form an unending human life would take, or whether an immaterial soul exists and possesses immortality, has been a major point of focus of religion, as well as the subject of speculation and debate. In religious contexts, immortality is often stated to be one of the promises of divinities to human beings who perform virtue or follow divine law.

Scientific
Life extension technologies claim to be developing a path to complete rejuvenation. Cryonics holds out the hope that the dead can be revived in the future, following sufficient medical advancements. While, as shown with creatures such as hydra and Planarian worms, it is indeed possible for a creature to be biologically immortal, these are animals which are physiologically very different from humans, and it is not known if something comparable will ever be possible for humans.

Religious
Immortality in religion refers usually to either the belief in physical immortality or a more spiritual afterlife. In traditions such as ancient Egyptian beliefs, Mesopotamian beliefs and ancient Greek beliefs, the immortal gods consequently were considered to have physical bodies. In Mesopotamian and Greek religion, the gods also made certain men and women physically immortal, whereas in Christianity, many believe that all true believers will be resurrected to physical immortality. Similar beliefs that physical immortality is possible are held by Rastafarians or Rebirthers.

Physical immortality
Physical immortality is a state of life that allows a person to avoid death and maintain conscious thought. It can mean the unending existence of a person from a physical source other than organic life, such as a computer.

Pursuit of physical immortality before the advent of modern science included alchemists, who sought to create the Philosopher's Stone, and various cultures' legends such as the Fountain of Youth or the Peaches of Immortality inspiring attempts at discovering an elixir of life.

Modern scientific trends, such as cryonics, digital immortality, breakthroughs in rejuvenation, or predictions of an impending technological singularity, to achieve genuine human physical immortality, must still overcome all causes of death to succeed.

Causes of death
There are three main causes of death: natural aging, disease, and injury. Such issues can be resolved with the solutions provided in research to any end providing such alternate theories at present that require unification.

Aging
Aubrey de Grey, a leading researcher in the field, defines aging as "a collection of cumulative changes to the molecular and cellular structure of an adult organism, which result in essential metabolic processes, but which also, once they progress far enough, increasingly disrupt metabolism, resulting in pathology and death." The current causes of aging in humans are cell loss (without replacement), DNA damage, oncogenic nuclear mutations and epimutations, cell senescence, mitochondrial mutations, lysosomal aggregates, extracellular aggregates, random extracellular cross-linking, immune system decline, and endocrine changes. Eliminating aging would require finding a solution to each of these causes, a program de Grey calls engineered negligible senescence. There is also a huge body of knowledge indicating that change is characterized by the loss of molecular fidelity.

Disease
Disease is theoretically surmountable by technology. In short, it is an abnormal condition affecting the body of an organism, something the body should not typically have to deal with its natural make up. Human understanding of genetics is leading to cures and treatments for a myriad of previously incurable diseases. The mechanisms by which other diseases do damage are becoming better understood. Sophisticated methods of detecting diseases early are being developed. Preventative medicine is becoming better understood. Neurodegenerative diseases like Parkinson's and Alzheimer's may soon be curable with the use of stem cells. Breakthroughs in cell biology and telomere research are leading to treatments for cancer. Vaccines are being researched for AIDS and tuberculosis. Genes associated with type 1 diabetes and certain types of cancer have been discovered, allowing for new therapies to be developed. Artificial devices attached directly to the nervous system may restore sight to the blind. Drugs are being developed to treat a myriad of other diseases and ailments.

Trauma
Physical trauma would remain as a threat to perpetual physical life, as an otherwise immortal person would still be subject to unforeseen accidents or catastrophes. The speed and quality of paramedic response remains a determining factor in surviving severe trauma. A body that could automatically repair itself from severe trauma, such as speculated uses for nanotechnology, would mitigate this factor. The brain cannot be risked to trauma if a continuous physical life is to be maintained. This aversion to trauma risk to the brain would naturally result in significant behavioral changes that would render physical immortality undesirable for some people.

Environmental change
Organisms otherwise unaffected by these causes of death would still face the problem of obtaining sustenance (whether from currently available agricultural processes or from hypothetical future technological processes) in the face of changing availability of suitable resources as environmental conditions change. After avoiding aging, disease, and trauma, death through resource limitation is still possible, such as hypoxia or starvation.

If there is no limitation on the degree of gradual mitigation of risk then it is possible that the cumulative probability of death over an infinite horizon is less than certainty, even when the risk of fatal trauma in any finite period is greater than zero. Mathematically, this is an aspect of achieving 'actuarial escape velocity'.

Biological immortality

Biological immortality is an absence of aging. Specifically it is the absence of a sustained increase in rate of mortality as a function of chronological age. A cell or organism that does not experience aging, or ceases to age at some point, is biologically immortal.

Biologists have chosen the word "immortal" to designate cells that are not limited by the Hayflick limit, where cells no longer divide because of DNA damage or shortened telomeres. The first and still most widely used immortal cell line is HeLa, developed from cells taken from the malignant cervical tumor of Henrietta Lacks without her consent in 1951. Prior to the 1961 work of Leonard Hayflick, there was the erroneous belief fostered by Alexis Carrel that all normal somatic cells are immortal. By preventing cells from reaching senescence one can achieve biological immortality; telomeres, a "cap" at the end of DNA, are thought to be the cause of cell aging. Every time a cell divides the telomere becomes a bit shorter; when it is finally worn down, the cell is unable to split and dies. Telomerase is an enzyme which rebuilds the telomeres in stem cells and cancer cells, allowing them to replicate an infinite number of times. No definitive work has yet demonstrated that telomerase can be used in human somatic cells to prevent healthy tissues from aging. On the other hand, scientists hope to be able to grow organs with the help of stem cells, allowing organ transplants without the risk of rejection, another step in extending human life expectancy. These technologies are the subject of ongoing research, and are not yet realized.

Biologically immortal species
Life defined as biologically immortal is still susceptible to causes of death besides aging, including disease and trauma, as defined above. Notable immortal species include:
 * Bacteria – Bacteria reproduce through binary fission. A parent bacterium splits itself into two identical daughter cells which eventually then split themselves in half. This process repeats, thus making the bacterium essentially immortal. A 2005 PLoS Biology paper suggests that after each division the daughter cells can be identified as the older and the younger, and the older is slightly smaller, weaker, and more likely to die than the younger.
 * Turritopsis dohrnii, a jellyfish (phylum Cnidaria, class Hydrozoa, order Anthoathecata), after becoming a sexually mature adult, can transform itself back into a polyp using the cell conversion process of transdifferentiation. Turritopsis dohrnii repeats this cycle, meaning that it may have an indefinite lifespan. Its immortal adaptation has allowed it to spread from its original habitat in the Caribbean to "all over the world".
 * Hydra is a genus belonging to the phylum Cnidaria, the class Hydrozoa and the order Anthomedusae. They are simple fresh-water predatory animals possessing radial symmetry.

Evolution of aging
As the existence of biologically immortal species demonstrates, there is no thermodynamic necessity for senescence: a defining feature of life is that it takes in free energy from the environment and unloads its entropy as waste. Living systems can even build themselves up from seed, and routinely repair themselves. Aging is therefore presumed to be a byproduct of evolution, but why mortality should be selected for remains a subject of research and debate. Programmed cell death and the telomere "end replication problem" are found even in the earliest and simplest of organisms. This may be a tradeoff between selecting for cancer and selecting for aging.

Modern theories on the evolution of aging include the following:
 * Mutation accumulation is a theory formulated by Peter Medawar in 1952 to explain how evolution would select for aging. Essentially, aging is never selected against, as organisms have offspring before the mortal mutations surface in an individual.
 * Antagonistic pleiotropy is a theory proposed as an alternative by George C. Williams, a critic of Medawar, in 1957. In antagonistic pleiotropy, genes carry effects that are both beneficial and detrimental. In essence this refers to genes that offer benefits early in life, but exact a cost later on, i.e. decline and death.
 * The disposable soma theory was proposed in 1977 by Thomas Kirkwood, which states that an individual body must allocate energy for metabolism, reproduction, and maintenance, and must compromise when there is food scarcity. Compromise in allocating energy to the repair function is what causes the body gradually to deteriorate with age, according to Kirkwood.

Immortality of the germline
Individual organisms ordinarily age and die, while the germlines which connect successive generations are potentially immortal. The basis for this difference is a fundamental problem in biology. The Russian biologist and historian Zhores A. Medvedev considered that the accuracy of genome replicative and other synthetic systems alone cannot explain the immortality of germlines. Rather Medvedev thought that known features of the biochemistry and genetics of sexual reproduction indicate the presence of unique information maintenance and restoration processes at the different stages of gametogenesis. In particular, Medvedev considered that the most important opportunities for information maintenance of germ cells are created by recombination during meiosis and DNA repair; he saw these as processes within the germ cells that were capable of restoring the integrity of DNA and chromosomes from the types of damage that cause irreversible aging in somatic cells.

Life-extending substances
Some scientists believe that boosting the amount or proportion of telomerase in the body, a naturally forming enzyme that helps maintain the protective caps at the ends of chromosomes, could prevent cells from dying and so may ultimately lead to extended, healthier lifespans. A team of researchers at the Spanish National Cancer Centre (Madrid) tested the hypothesis on mice. It was found that those mice which were "genetically engineered to produce 10 times the normal levels of telomerase lived 50% longer than normal mice".

In normal circumstances, without the presence of telomerase, if a cell divides repeatedly, at some point all the progeny will reach their Hayflick limit. With the presence of telomerase, each dividing cell can replace the lost bit of DNA, and any single cell can then divide unbounded. While this unbounded growth property has excited many researchers, caution is warranted in exploiting this property, as exactly this same unbounded growth is a crucial step in enabling cancerous growth. If an organism can replicate its body cells faster, then it would theoretically stop aging.

Embryonic stem cells express telomerase, which allows them to divide repeatedly and form the individual. In adults, telomerase is highly expressed in cells that need to divide regularly (e.g., in the immune system), whereas most somatic cells express it only at very low levels in a cell-cycle dependent manner.

Technological immortality, biological machines, and "swallowing the doctor"
Technological immortality is the prospect for much longer life spans made possible by scientific advances in a variety of fields: nanotechnology, emergency room procedures, genetics, biological engineering, regenerative medicine, microbiology, and others. Contemporary life spans in the advanced industrial societies are already markedly longer than those of the past because of better nutrition, availability of health care, standard of living and bio-medical scientific advances. Technological immortality predicts further progress for the same reasons over the near term. An important aspect of current scientific thinking about immortality is that some combination of human cloning, cryonics or nanotechnology will play an essential role in extreme life extension. Robert Freitas, a nanorobotics theorist, suggests tiny medical nanorobots could be created to go through human bloodstreams, find dangerous things like cancer cells and bacteria, and destroy them. Freitas anticipates that gene-therapies and nanotechnology will eventually make the human body effectively self-sustainable and capable of living indefinitely in empty space, short of severe brain trauma. This supports the theory that we will be able to continually create biological or synthetic replacement parts to replace damaged or dying ones. Future advances in nanomedicine could give rise to life extension through the repair of many processes thought to be responsible for aging. K. Eric Drexler, one of the founders of nanotechnology, postulated cell repair devices, including ones operating within cells and using as yet hypothetical biological machines, in his 1986 book Engines of Creation. Raymond Kurzweil, a futurist and transhumanist, stated in his book The Singularity Is Near that he believes that advanced medical nanorobotics could completely remedy the effects of aging by 2030. According to Richard Feynman, it was his former graduate student and collaborator Albert Hibbs who originally suggested to him (circa 1959) the idea of a medical use for Feynman's theoretical micromachines (see biological machine). Hibbs suggested that certain repair machines might one day be reduced in size to the point that it would, in theory, be possible to (as Feynman put it) "swallow the doctor". The idea was incorporated into Feynman's 1959 essay There's Plenty of Room at the Bottom.

Cryonics
Cryonics, the practice of preserving organisms (either intact specimens or only their brains) for possible future revival by storing them at cryogenic temperatures where metabolism and decay are almost completely stopped, can be used to 'pause' for those who believe that life extension technologies will not develop sufficiently within their lifetime. Ideally, cryonics would allow clinically dead people to be brought back in the future after cures to the patients' diseases have been discovered and aging is reversible. Modern cryonics procedures use a process called vitrification which creates a glass-like state rather than freezing as the body is brought to low temperatures. This process reduces the risk of ice crystals damaging the cell-structure, which would be especially detrimental to cell structures in the brain, as their minute adjustment evokes the individual's mind.

Mind-to-computer uploading
One idea that has been advanced involves uploading an individual's habits and memories via direct mind-computer interface. The individual's memory may be loaded to a computer or to a new organic body. Extropian futurists like Moravec and Kurzweil have proposed that, thanks to exponentially growing computing power, it will someday be possible to upload human consciousness onto a computer system, and exist indefinitely in a virtual environment.

This could be accomplished via advanced cybernetics, where computer hardware would initially be installed in the brain to help sort memory or accelerate thought processes. Components would be added gradually until the person's entire brain functions were handled by artificial devices, avoiding sharp transitions that would lead to issues of identity, thus running the risk of the person to be declared dead and thus not be a legitimate owner of his or her property. After this point, the human body could be treated as an optional accessory and the program implementing the person could be transferred to any sufficiently powerful computer.

Another possible mechanism for mind upload is to perform a detailed scan of an individual's original, organic brain and simulate the entire structure in a computer. What level of detail such scans and simulations would need to achieve to emulate awareness, and whether the scanning process would destroy the brain, is still to be determined.

It is suggested that achieving immortality through this mechanism would require specific consideration to be given to the role of consciousness in the functions of the mind. An uploaded mind would only be a copy of the original mind, and not the conscious mind of the living entity associated in such a transfer. Without a simultaneous upload of consciousness, the original living entity remains mortal, thus not achieving true immortality. Research on neural correlates of consciousness is yet inconclusive on this issue. Whatever the route to mind upload, persons in this state could then be considered essentially immortal, short of loss or traumatic destruction of the machines that maintained them.

Cybernetics
Transforming a human into a cyborg can include brain implants or extracting a human processing unit and placing it in a robotic life-support system. Even replacing biological organs with robotic ones could increase life span (e.g. pace makers) and depending on the definition, many technological upgrades to the body, like genetic modifications or the addition of nanobots would qualify an individual as a cyborg. Some people believe that such modifications would make one impervious to aging and disease and theoretically immortal unless killed or destroyed.

Religious views
As late as 1952, the editorial staff of the Syntopicon found in their compilation of the Great Books of the Western World, that "The philosophical issue concerning immortality cannot be separated from issues concerning the existence and nature of man's soul." Thus, the vast majority of speculation on immortality before the 21st century was regarding the nature of the afterlife.

Abrahamic religion
The viewpoints of Christianity, Islam, and Judaism regarding the concept of immortality diverge as each faith system encapsulates unique theological interpretations and doctrines on the enduring human nature soul or spirit.

Christianity

Christian theology holds that Adam and Eve lost physical immortality for themselves and all their descendants through the Fall, although this initial "imperishability of the bodily frame of man" was "a preternatural condition".

Christians who profess the Nicene Creed believe that every dead person (whether they believed in Christ or not) will be resurrected from the dead at the Second Coming; this belief is known as universal resurrection. Paul the Apostle, in following his past life as a Pharisee (a Jewish social movement that held to a future physical resurrection ), proclaims an amalgamated view of resurrected believers where both the physical and the spiritual are rebuilt in the likeness of post-resurrection Christ, who "will transform our lowly body to be like his glorious body" (ESV). This thought mirrors Paul's depiction of believers having been "buried therefore with him [that is, Christ] by baptism into death" (ESV).

N.T. Wright, a theologian and former Bishop of Durham, has said many people forget the physical aspect of what Jesus promised. He told Time: "Jesus' resurrection marks the beginning of a restoration that he will complete upon his return. Part of this will be the resurrection of all the dead, who will 'awake', be embodied and participate in the renewal. Wright says John Polkinghorne, a physicist and a priest, has put it this way: 'God will download our software onto his hardware until the time he gives us new hardware to run the software again for ourselves.' That gets to two things nicely: that the period after death (the Intermediate state) is a period when we are in God's presence but not active in our own bodies, and also that the more important transformation will be when we are again embodied and administering Christ's kingdom." This kingdom will consist of Heaven and Earth "joined together in a new creation", he said.

Christian apocrypha include immortal human figures such as Cartaphilus who were cursed with physical immortality for various transgressions against Christ during the Passion. The medieval Waldensians believed in the immortality of the soul. Leaders of sects such as John Asgill and John Wroe taught followers that physical immortality was possible.

Many Patristic writers have connected the immortal rational soul to the image of God found in Genesis 1:26. Among them is Athanasius of Alexandria and Clement of Alexandria, who say that the immortal rational soul itself is the image of God. Even Early Christian Liturgies exhibit this connection between the immortal rational soul and the creation of humanity in the image of God.

Islam
Islamic beliefs bears the concept of spiritual immortality within it; following the death of a certain individual, it will be arbitrated consistent with its beliefs as well as actions and will embark on the ever-lasting place where they will abate. The Muslim who holds the five pillars of Islam will make an entrance into the Jannah, where they will inhabit eternally.

Al-Baqarah (2:25): "But give glad tidings to those who believe and work righteousness, that their portion is gardens, beneath which rivers flow. Every time they are fed with fruits therefrom, they say, 'Why, this is what we were fed with before,' for they are given things in similitude; and they have therein companions pure (and holy); and they abide therein forever."

In contrast, the kafir hold the contradictory notion that they abide in Jahannam perpetually.

Angels in Islam are reckoned as immortals from the perspective of Islam but most people believe is that the angels will die and that the Angel of Death will die, but there is no clear text concerning this. Rather there are texts which may indicate this, and there is the well known hadeeth (narration) about the "trumpet", which is a munkar hadeeth (rejected report). alternatively, Jinn have a long lifespan between 1000 and 1500. In some Muslim Sufi mystics, Khidr is given a long life but not immortality or there is more than a little argument stated about the demise of khidr; however, it is the matter of debate, and there is a fabrication point that goes around the Khidr drank from the fountain of Life, which is thoroughly invalid. Jesus in Islam was summoned to the sky by Allah's sanction to preserve him from the cross and endow him with long life until the advent of the Dajjal. Dajjal is, additionally, given a long life. Jesus Christ dispatches the Dajjal as he stays after 40 days, one like a year, one like a month, one like a week, and the rest of his days like normal days. The Qur'an states that it is the ultimate fate of all life, including humans, to die eventually. ""

Judaism
The traditional concept of an immaterial and immortal soul distinct from the body was not found in Judaism before the Babylonian exile, but developed as a result of interaction with Persian and Hellenistic philosophies. Accordingly, the Hebrew word nephesh, although translated as "soul" in some older English-language Bibles, actually has a meaning closer to "living being". Nephesh was rendered in the Septuagint as $ψυχή$ (psūchê), the Greek word for 'soul'.

The only Hebrew word traditionally translated "soul" (nephesh) in English language Bibles refers to a living, breathing conscious body, rather than to an immortal soul. In the New Testament, the Greek word traditionally translated "soul" (ψυχή) has substantially the same meaning as the Hebrew, without reference to an immortal soul. "Soul" may refer either to the whole person, the self, as in "three thousand souls" were converted in (see ).

The Hebrew Bible speaks about Sheol (שאול), originally a synonym of the grave – the repository of the dead or the cessation of existence, until the resurrection of the dead. This doctrine of resurrection is mentioned explicitly only in although it may be implied in several other texts. New theories arose concerning Sheol during the intertestamental period.

The views about immortality in Judaism is perhaps best exemplified by the various references to this in Second Temple period. The concept of resurrection of the physical body is found in 2 Maccabees, according to which it will happen through recreation of the flesh. Resurrection of the dead is specified in detail in the extra-canonical books of Enoch, and in Apocalypse of Baruch. According to the British scholar in ancient Judaism P.R. Davies, there is "little or no clear reference ... either to immortality or to resurrection from the dead" in the Dead Sea scrolls texts. Both Josephus and the New Testament record that the Sadducees did not believe in an afterlife, but the sources vary on the beliefs of the Pharisees. The New Testament claims that the Pharisees believed in the resurrection, but does not specify whether this included the flesh or not. According to Josephus, who himself was a Pharisee, the Pharisees held that only the soul was immortal and the souls of good people will be reincarnated and "pass into other bodies", while "the souls of the wicked will suffer eternal punishment." The Book of Jubilees seems to refer to the resurrection of the soul only, or to a more general idea of an immortal soul.

Rabbinic Judaism claims that the righteous dead will be resurrected in the Messianic Age, with the coming of the messiah. They will then be granted immortality in a perfect world. The wicked dead, on the other hand, will not be resurrected at all. This is not the only Jewish belief about the afterlife. The Tanakh is not specific about the afterlife, so there are wide differences in views and explanations among believers.

Indian religions
The perspectives on immortality within Hinduism and Buddhism exhibit nuanced differences, with each spiritual tradition offering distinctive theological interpretations and doctrines concerning the eternal essence of the human soul or consciousness.

Hinduism

Hindus believe in an immortal soul which is reincarnated after death. According to Hinduism, people repeat a process of life, death, and rebirth in a cycle called samsara. If they live their life well, their karma improves and their station in the next life will be higher, and conversely lower if they live their life poorly. After many life times of perfecting its karma, the soul is freed from the cycle and lives in perpetual bliss. There is no place of eternal torment in Hinduism, although if a soul consistently lives very evil lives, it could work its way down to the very bottom of the cycle.

There are explicit renderings in the Upanishads alluding to a physically immortal state brought about by purification, and sublimation of the 5 elements that make up the body. For example, in the Shvetashvatara Upanishad (Chapter 2, Verse 12), it is stated "When earth, water, fire, air and sky arise, that is to say, when the five attributes of the elements, mentioned in the books on yoga, become manifest then the yogi's body becomes purified by the fire of yoga and he is free from illness, old age and death."

Another view of immortality is traced to the Vedic tradition by the interpretation of Maharishi Mahesh Yogi: That man indeed whom these (contacts) do not disturb, who is even-minded in pleasure and pain, steadfast, he is fit for immortality, O best of men.

To Maharishi Mahesh Yogi, the verse means, "Once a man has become established in the understanding of the permanent reality of life, his mind rises above the influence of pleasure and pain. Such an unshakable man passes beyond the influence of death and in the permanent phase of life: he attains eternal life ... A man established in the understanding of the unlimited abundance of absolute existence is naturally free from existence of the relative order. This is what gives him the status of immortal life."

An Indian Tamil saint known as Vallalar claimed to have achieved immortality before disappearing forever from a locked room in 1874.

Buddhism
One of the three marks of existence in Buddhism is anattā, "non-self". This teaching states that the body does not have an eternal soul but is composed of five skandhas or aggregates. Additionally, another mark of existence is impermanence, also called anicca, which runs directly counter to concepts of immortality or permanence. According to one Tibetan Buddhist teaching, Dzogchen, individuals can transform the physical body into an immortal body of light called the rainbow body.

Ancient Greek religion
Immortality in ancient Greek religion originally always included an eternal union of body and soul as can be seen in Homer, Hesiod, and various other ancient texts. The soul was considered to have an eternal existence in Hades, but without the body the soul was considered dead. Although almost everybody had nothing to look forward to but an eternal existence as a disembodied dead soul, a number of men and women were considered to have gained physical immortality and been brought to live forever in either Elysium, the Islands of the Blessed, heaven, the ocean or literally right under the ground. Among those humans made immortal were Amphiaraus, Ganymede, Ino, Iphigenia, Menelaus, Peleus, and a great number of those who fought in the Trojan and Theban wars. Asclepius was killed by Zeus, and by Apollo's request, was subsequently immortalized as a star.

In ancient Greek religion a number of men and women have been interpreted as being resurrected and made immortal. Achilles, after being killed, was snatched from his funeral pyre by his divine mother Thetis and brought to an immortal existence in either Leuce, the Elysian plains or the Islands of the Blessed. Memnon, who was killed by Achilles, seems to have received a similar fate. Alcmene, Castor, Heracles, and Melicertes, are also among the figures interpreted to have been resurrected to physical immortality. According to Herodotus's Histories, the seventh century BC sage Aristeas of Proconnesus was first found dead, after which his body disappeared from a locked room. He would reappear alive years later. However, Greek attitudes towards resurrection were generally negative, and the idea of resurrection was considered neither desirable nor possible. For example, Asclepius was killed by Zeus for using herbs to resurrect the dead, but by his father Apollo's request, was subsequently immortalized as a star.

Writing his Lives of Illustrious Men (Parallel Lives) in the first century, the Middle Platonic philosopher Plutarch in his chapter on Romulus gave an account of the king's mysterious disappearance and subsequent deification, comparing it to Greek tales such as the physical immortalization of Alcmene and Aristeas the Proconnesian, "for they say Aristeas died in a fuller's work-shop, and his friends coming to look for him, found his body vanished; and that some presently after, coming from abroad, said they met him traveling towards Croton". Plutarch openly scorned such beliefs held in ancient Greek religion, writing, "many such improbabilities do your fabulous writers relate, deifying creatures naturally mortal." Likewise, he writes that while something within humans comes from the gods and returns to them after death, this happens "only when it is most completely separated and set free from the body, and becomes altogether pure, fleshless, and undefiled."

The parallel between these traditional beliefs and the later resurrection of Jesus was not lost on early Christians, as Justin Martyr argued:
 * "when we say ... Jesus Christ, our teacher, was crucified and died, and rose again, and ascended into heaven, we propose nothing different from what you believe regarding those whom you consider sons of Zeus."

The philosophical idea of an immortal soul was a belief first appearing with either Pherecydes or the Orphics, and most importantly advocated by Plato and his followers. This, however, never became the general norm in Hellenistic thought. As may be witnessed even into the Christian era, not least by the complaints of various philosophers over popular beliefs, many or perhaps most traditional Greeks maintained the conviction that certain individuals were resurrected from the dead and made physically immortal and that others could only look forward to an existence as disembodied and dead, though everlasting, souls.

Zoroastrianism
Zoroastrians believe that on the fourth day after death, the human soul leaves the body and the body remains as an empty shell. Souls would go to either heaven or hell; these concepts of the afterlife in Zoroastrianism may have influenced Abrahamic religions. The Persian word for "immortal" is associated with the month "Amurdad", meaning "deathless" in Persian, in the Iranian calendar (near the end of July). The month of Amurdad or Ameretat is celebrated in Persian culture as ancient Persians believed the "Angel of Immortality" won over the "Angel of Death" in this month.

Philosophical religions
Within the realm of philosophical religious paradigms, engage in a profound exploration of the concept of immortality. Simultaneously, expand the breadth and depth of this intellectual inquiry to afford a more intricate examination of the subject matter.

Taoism
It is repeatedly stated in the Lüshi Chunqiu that death is unavoidable. Henri Maspero noted that many scholarly works frame Taoism as a school of thought focused on the quest for immortality. Isabelle Robinet asserts that Taoism is better understood as a way of life than as a religion, and that its adherents do not approach or view Taoism the way non-Taoist historians have done. In the Tractate of Actions and their Retributions, a traditional teaching, spiritual immortality can be rewarded to people who do a certain amount of good deeds and live a simple, pure life. A list of good deeds and sins are tallied to determine whether or not a mortal is worthy. Spiritual immortality in this definition allows the soul to leave the earthly realms of afterlife and go to pure realms in the Taoist cosmology.

Alcmaeon of Croton
Alcmaeon of Croton argued that the soul is continuously and ceaselessly in motion. The exact form of his argument is unclear, but it appears to have influenced Plato, Aristotle, and other later writers.

Plato
Plato's Phaedo advances four arguments for the soul's immortality:
 * The Cyclical Argument, or Opposites Argument explains that Forms are eternal and unchanging, and as the soul always brings life, then it must not die, and is necessarily "imperishable". As the body is mortal and is subject to physical death, the soul must be its indestructible opposite. Plato then suggests the analogy of fire and cold. If the form of cold is imperishable, and fire, its opposite, was within close proximity, it would have to withdraw intact as does the soul during death. This could be likened to the idea of the opposite charges of magnets.
 * The Theory of Recollection explains that we possess some non-empirical knowledge (e.g. The Form of Equality) at birth, implying the soul existed before birth to carry that knowledge. Another account of the theory is found in Plato's Meno, although in that case Socrates implies anamnesis (previous knowledge of everything) whereas he is not so bold in Phaedo.
 * The Affinity Argument, explains that invisible, immortal, and incorporeal things are different from visible, mortal, and corporeal things. Our soul is of the former, while our body is of the latter, so when our bodies die and decay, our soul will continue to live.
 * The Argument from Form of Life or The Final Argument explains that the Forms, incorporeal and static entities, are the cause of all things in the world, and all things participate in Forms. For example, beautiful things participate in the Form of Beauty; the number four participates in the Form of the Even, etc. The soul, by its very nature, participates in the Form of Life, which means the soul can never die.

Plotinus
Plotinus offers a version of the argument that Kant calls "The Achilles of Rationalist Psychology". Plotinus first argues that the soul is simple, then notes that a simple being cannot decompose. Many subsequent philosophers have argued both that the soul is simple and that it must be immortal. The tradition arguably culminates with Moses Mendelssohn's Phaedon.

Metochites
Theodore Metochites argues that part of the soul's nature is to move itself, but that a given movement will cease only if what causes the movement is separated from the thing moved – an impossibility if they are one and the same.

Avicenna
Avicenna argued for the distinctness of the soul and the body, and the incorruptibility of the former.

Aquinas
The full argument for the immortality of the soul and Thomas Aquinas' elaboration of Aristotelian theory is found in Question 75 of the First Part of the Summa Theologica.

Descartes
René Descartes endorses the claim that the soul is simple, and also that this entails that it cannot decompose. Descartes does not address the possibility that the soul might suddenly disappear.

Leibniz
In early work, Gottfried Wilhelm Leibniz endorses a version of the argument from the simplicity of the soul to its immortality, but like his predecessors, he does not address the possibility that the soul might suddenly disappear. In his monadology he advances a sophisticated novel argument for the immortality of monads.

Moses Mendelssohn
Moses Mendelssohn's Phaedon is a defense of the simplicity and immortality of the soul. It is a series of three dialogues, revisiting the Platonic dialogue Phaedo, in which Socrates argues for the immortality of the soul, in preparation for his own death. Many philosophers, including Plotinus, Descartes, and Leibniz, argue that the soul is simple, and that because simples cannot decompose they must be immortal. In the Phaedon, Mendelssohn addresses gaps in earlier versions of this argument (an argument that Kant calls the Achilles of Rationalist Psychology). The Phaedon contains an original argument for the simplicity of the soul, and also an original argument that simples cannot suddenly disappear. It contains further original arguments that the soul must retain its rational capacities as long as it exists.

Ethics
The possibility of clinical immortality raises a host of medical, philosophical, and religious issues and ethical questions. These include persistent vegetative states, the nature of personality over time, technology to mimic or copy the mind or its processes, social and economic disparities created by longevity, and survival of the heat death of the universe.

Undesirability
Physical immortality has also been imagined as a form of eternal torment, as in the myth of Tithonus, or in Mary Shelley's short story The Mortal Immortal, where the protagonist lives to witness everyone he cares about die around him. For additional examples in fiction, see Immortality in fiction.

Kagan (2012) argues that any form of human immortality would be undesirable. Kagan's argument takes the form of a dilemma. Either our characters remain essentially the same in an immortal afterlife, or they do not: Either way, Kagan argues, immortality is unattractive. The best outcome, Kagan argues, would be for humans to live as long as they desired and then to accept death gratefully as rescuing us from the unbearable tedium of immortality.
 * If our characters remain basically the same – that is, if we retain more or less the desires, interests, and goals that we have now – then eventually, over an infinite stretch of time, we will get bored and find eternal life unbearably tedious.
 * If, on the other hand, our characters are radically changed – e.g., by God periodically erasing our memories or giving us rat-like brains that never tire of certain simple pleasures – then such a person would be too different from our current self for us to care much what happens to them.

Sociology
If human beings were to achieve immortality, there would most likely be a change in the world's social structures. Sociologists argue that human beings' awareness of their own mortality shapes their behavior. With the advancements in medical technology in extending human life, there may need to be serious considerations made about future social structures. The world is already experiencing a global demographic shift of increasingly ageing populations with lower replacement rates. The social changes that are made to accommodate this new population shift may be able to offer insight on the possibility of an immortal society.

Sociology has a growing body of literature on the sociology of immortality, which details the different attempts at reaching immortality (whether actual or symbolic) and their prominence in the 21st century. These attempts include renewed attention to the dead in the West, practices of online memorialization, and biomedical attempts to increase longevity. These attempts at reaching immortality and their effects in societal structures have led some to argue that we are becoming a "Postmortal Society". Foreseen changes to societies derived from the pursuit of immortality would encompass societal paradigms and worldviews, as well as the institutional landscape. Similarly, different forms of reaching immortality might entail a significant reconfiguration of societies, from becoming more technologically oriented to becoming more aligned with nature.

Immortality would increase population growth, bringing with it many consequences as for example the impact of population growth on the environment and planetary boundaries.

Politics
Although some scientists state that radical life extension, delaying and stopping aging are achievable, there are no international or national programs focused on stopping aging or on radical life extension. In 2012 in Russia, and then in the United States, Israel and the Netherlands, pro-immortality political parties were launched. They aimed to provide political support to anti-aging and radical life extension research and technologies and at the same time transition to the next step, radical life extension, life without aging, and finally, immortality and aim to make possible access to such technologies to most currently living people.

Some scholars critique the increasing support for immortality projects. Panagiotis Pentaris speculates that defeating ageing as the cause of death comes with a cost: "heightened stratification of humans in society and a wider gap between social classes". Others suggest that other immortality projects like transhumanist digital immortality, radical life extension and cryonics are part of the capitalist fabric of exploitation and control, which aims to extend privileged lives of the economic elite. In this sense, immortality could become a political-economic battleground for the twenty-first century between the haves and have-nots.

Symbols

There are numerous symbols representing immortality. The ankh is an Egyptian symbol of life that holds connotations of immortality when depicted in the hands of the gods and pharaohs, who were seen as having control over the journey of life. The Möbius strip in the shape of a trefoil knot is another symbol of immortality. Most symbolic representations of infinity or the life cycle are often used to represent immortality depending on the context they are placed in. Other examples include the Ouroboros, the Chinese fungus of longevity, the ten kanji, the phoenix, the peacock in Christianity, and the colors amaranth (in Western culture) and peach (in Chinese culture).

Religious and spiritual prospects for immortality

 * "Death and Immortality" Dictionary of the History of Ideas, etext at the University of Virginia Library
 * "Immortality" Immortality – What Will Eternal Life Be Like?
 * The Immortality of the Soul and the Resurrection of the Body Lecture by Heinrich J. Vogel
 * An Essay on the Scriptural Doctrine of Immortality by James Challis
 * Eternity: Christ's Return, Chiliasm, Resurrection of the Dead, Judgment, Hell, Luther on Eternity, Heaven J.P. Meyer, The Northwestern Lutheran, 22 August 1954, Vol. 41, # 17 to 14 April 1957, Vol. 44, No. 8
 * "How you Can Have Eternal Life" Jack Graham, PowerPoint Ministries, Crosswalk.com
 * Immortality Taoist essay, personaltao.com
 * The Trial to Conquer Death Ancient Scientific Yoga – The First Atom's Final Attempt
 * Search A review by Dr. Peter Fenwick of the book Human Immortality by Mohammad Samir Hossain

In literature

 * Mary Shelley's The Mortal Immortal

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title: Immortality