How to Disentangle the Past and the Future

byroyf7y2nd Jan 201313 comments

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I'm on my way to an important meeting. Am I worried? I'm not worried. The presentation is on my laptop. I distinctly remember putting it there (in the past), so I can safely predict that it's going to be there when I get to the office (in the future) - this is how well my laptop carries information through space and time.

My partner has no memory of me copying the file to the laptop. For her, the past and the future have mutual information: if Omega assured her that I'd copied the presentation, she would be able to predict the future much better than she can now.

For me, the past and the future are much less statistically dependent. Whatever entanglement remains between them is due to my memory not being perfect. If my partner suddenly remembers that she saw me copying the file, I will be a little bit more sure that I remember correctly, and that we'll have it at the meeting. Or if somehow, despite my very clear mental image of copying the file, it's not there at the meeting, my first suspicion will nevertheless be that I hadn't.

These unlikely possibilities aside, my memory does serve me. My partner is much less certain of the future than me, and more to the point, her uncertainty would decrease much more than mine if we both suddenly became perfectly aware of the past.

But now she turns on my laptop and checks. The file is there, yes, I could have told her that. And now that we know the state of my laptop, the past and the future are completely disentangled: maybe I put the file there, maybe the elves did - it makes no difference for the meeting. And maybe by the time we get to the office a hacker will remotely delete the file - its absence at the meeting will not be evidence that I'd neglected to copy the file: it was right there! We saw it!

(By "entanglement" I don't mean anything quantum theoretic; here it refers to statistical dependence, and its strength is measured by mutual information.)

The past and the future have mutual information. This is a necessary condition for life, for intelligence: we use the past to predict and plan for the future, and we couldn't do it if it were useless.

On the other hand, the future is independent of the past given the present. That's not profound metaphysics, that's simply how we define the state of a system: it's everything one needs to know of the past of the system to compute its future. The past is gone, and any information that it had on the future - information we could use to predict and make a better future - is inherited by the present.

But as limited agents inside the system, we don't get to know its entire state. Most of it is hidden from us, behind walls and hills and inside skulls and in nanostructures. So for us, the past and the future are entangled, which means that by learning one we could reduce our uncertainty about the other.

 


 

In control theory, memoryless agents have an unchanging internal structure, unable to entangle with the past and carry information useful for the future. Instead they react to whatever last input they received, like a function. These degenerate agents have an internal memory state Mt that depends only on the most recent observation Ot:

 

Figure 1: Dynamics of a memoryless reinforcement learning agents

Wt is the state of the world outside the agent at time t, Ot is the observation the agent makes of the world, Mt is the resulting internal state of the agent, and At is the action the agent chooses to take.

When a LED observes voltage, it emits light, regardless of whether it did so a second earlier. When the LED's internal attributes entangle with the voltage, they lose all information of what came before.

When the q key on a keyboard is pressed and released, the keyboard sends a signal to that effect to the computer, and that signal is mostly independent of which keys were pressed before and in what order (with a few exceptions; a keyboard is not entirely memoryless). A keyboard gets entangled with vast amounts of information over the years, but streams it through and loses almost any trace of it within seconds.

For a memoryless agent, all of the information between past and future flows through the environment outside the agent - through Wt. The world sans agent retains all the power to disentangle the past and the future: you can check in the graphical model in Figure 1 that Wt-1 and Wt+1 are independent given Wt.

The internal state Mt of the memoryless agent, on the other hand, of course reveals nothing about the link between past and future. Looking at my keyboard, you can't tell if I copied the presentation to my laptop, and if it's going to be there in half an hour.

 


 

Intelligent agents need to have memory:


Figure 2: General dynamics of a reinforcement learning agent

Now control over the flow of information has shifted, to some extent, in favor of the agent. The agent has a much wider channel over which to receive information from the past, and it can use this information to recover some truths about the present which aren't currently observable.

The past and the future are no longer independent given Wt alone, you need Mt and Wt together to completely separate the past and the future. An agent with memory of how Wt came to be can partly assume both roles, thus making itself a better separator than its memoryless counterpart could.

 


 

So here's how to become a good separator of past and future: remember things that are relevant for the future.

Memory is necessary for intelligence, you already knew that. What's new here is a way to measure just how useful memory is. Memory is useful exactly to the extent to which it shifts the power to control the flow of information.

For the agent, memory disentangles the past and the future. If you maintain in yourself some of the information that the past has about the future, you overcome the limitations of your ability to observe the present. I know I put the presentation on my laptop, so I don't need to check it's there.

For other agents, at the same time, the agent's memory is yet another limitation to their observability. Think of a secret handshake, for example. It's useful precisely because it predicts (and controls) the future for the confidants, while keeping it entangled with the hidden past for everyone else.

Continue reading: How to Be Oversurprised 

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