87 | 卡尔·弗里斯顿：大脑、预测与自由能

有一种必然性，有一种对无序的驱动力，熵会增加。

There's an imperative, there's a drive for disorder, the entropy will increase.

但这是关于我们信念的熵。

But it's the entropy of our beliefs.

那这意味着什么？

Now what does that mean?

这基本上意味着，我试图为我的数据找到一个低能量的解释，同时保持多种可能性。

Well, it basically means I'm trying to find a low energy explanation for my data whilst at the same time keeping my options open.

这本质上就是奥卡姆剃刀原理。

So this is essentially Occam's razor.

它本质上是不倾向于一个非常精确的后验信念。

It's basically not committing to a very precise posterior belief.

我看到了这些数据，于是我相信是它导致了这些结果。

I've seen these data, then I believe this caused it.

所以你不想对一个非常精确的信念做出承诺。

So you don't want to commit to a very precise one.

所以你必须找到最简单、最能包容你数据的解释。

So you've got to find the simplest, the most accommodating explanation for your data.

因此，这里就出现了悖论——如果你愿意这么说的话——即你究竟是试图最大化还是最小化熵项。

So that's where the paradox, if you like, in terms of whether you're trying to maximise or minimise the entropy term comes in.

我认为更根本的是，我们目前所讨论的熵是关于某种信念的函数或标量函数。

I think more fundamentally makes the point that the entropy we're talking about at the moment is a functional or a scalar functional of a belief about something.

它并不是编码这些信念的实体本身。

It's not the thing that is encoding those beliefs.

它不是神经元放电、分子或原子。

It's not the neuronal firing on the molecules or the atoms.

这其中的转折，或者说有点悖论的地方在于，当你展望未来，并对某种行动的后果形成信念时，比如朝那边看一眼、在搜索引擎中输入某个关键词，或者去维基百科查找。

The twist, the the the sort of the the the slightly paradoxical aspect of this is when you move into the future and when you have the beliefs about the consequences of an action, say, looking over there or Googling at your certain entry or going to Wikipedia.

在你采取行动之前，你已经对你的自由能将如何变化有了信念。

Before you make that action, have beliefs about how your free energy is going to change.

到了这个时候，你的熵或相对熵实际上发生了逆转，因为结果现在变成了随机变量。

And at that point, your entropy or your relative entropies effectively switch around because the outcomes now become random variables.

你必须取一个期望值。

You have to take an expectation.

这有点技术性，是一段很精妙的技术内容，它本质上在将这一最小化熵和相对熵的指令应用于当前系统及其行为时，实现了反转。

This is a bit technical, it's a beautiful little bit of techie stuff, which basically flips this imperative to minimize these entropy and relative entropies when you're applying it to the system as it is now and as it is behaving.

当系统审视自身时，会想：为了在未来最小化我的自由能，我现在该如何行动？

When the system looks at itself saying, well, how would I have to now act in order to minimize my free energy in the future?

我现在将结果视为随机变量，并将它们纳入期望算子中。

I now include basically outcomes as random variables, and they get into the expectation operators.

于是，你突然开始服务于最小化自由能——因此，这里有一种阴阳平衡：当我正在处理当前数据时，我努力寻找那些能最大化我不确定性的解释，因为我并不想固守某种特定信念。

And suddenly, you're then in the service of minimizing the So so there's this sort of yin yang, which means that as I'm currently processing my data, I'm striving to find the explanations that maximize my uncertainty because I don't want to commit to a particular belief.

但与此同时，我又朝着完全相反的方向前进。

Yet at the same time, I'm going in the exactly opposite direction.

我试图采样那些能缩小我不确定性的数据。

I'm trying to sample those data that will shrink my uncertainty.

当我找到这种平衡时，我们就实现了这种主动的自我验证。

And then when I find that balance, then then then we have this sort active self evidencing.

让我试着用我自己的话来说一遍，你可以告诉我我有没有说对。

Let me let me try to put it in my words, you can tell me if I'm coming close here.

我的意思是，我们希望尽量减少感到惊讶的时刻。

I mean, you we want to minimize the times that we're surprised.

你可能会想，那就一直预测你认为最有可能为真的那个结果吧。

You might think, well, just predict the thing you think is most likely to be true all the time.

但如果你对某个结果赋予100%的概率，那么只要稍有偏差，你就会极度惊讶，而这并不好。

And but if you put a 100% probability on that, then anytime you're not exactly right, you're hugely surprised and that's bad.

没错。

Absolutely.

所以，你可能会说，那我们换另一种方式吧。

So, you might say, well, let's do the other thing.

我们对任何事情都不要有信念。

Let's have no beliefs about anything.

我们可以说任何事情都可能发生，但在某些情况下，尤其是当你进行数学推导时，你总会感到惊讶。

Let's say anything could happen, but then in some cases, especially when you go through the math, you're always surprised.

每一件事的发生都带有一点不太可能的性质，因为它本可以是其他任何情况，因此这里存在一种折中：你试图逼近你认为最可能发生的情况，但同时也为偏差留出了空间。

Everything that happens is a little bit unlikely because it could have been anything else and so there's this compromise where you sort of try to home in on something you think is most likely, but you do give allowance for the deviations.

完全正确。

Absolutely.

说得太好了。

Beautifully put.

我只是，是的。

I just yeah.

作为一名物理学家，你刚才所说的可以理解为：我们如何描述那些具有某种游走性，但仍将自身限制在状态空间或相空间有限区域内的系统。

As as a sort of a a physicist, what what what you could understand what you've just said as is basically how do we describe systems that have some itinerancy, but they still restrict themselves to a limited part of their face space or their state space.

所以它不是一个点。

So it's not one point.

我们不是小弹珠，也不是月球岩石，也不是气体。

We're not little marbles or moon rocks, nor are we gases.

但我们确实有边界，也有形状和形式，也就是说，我们能占据的状态空间部分，或者那些潮虫活动的区域。

But we are we certainly have boundaries and we have a shape and a form in the sense of, you know, those parts of the state space we could occupy or where the wood lice are running around.

你知道，那里存在着一种结构。

You know, there's a structure there.

所以，如果这种系统确实存在——比如你我，或者任何以非平凡方式存在的事物——那么所谓非平凡，我的意思是，它拥有一个吸引子，这个吸引子对应着一个单一的状态。

So that structure, if it is the case that these sorts of systems exist, things like you and me or anything actually exists in a nontrivial way, By nontrivial, I mean basically having an attracting set that is just one being in one state.

确定性的。

Deterministic.

当然。

Absolutely.

必须在它inerancy（游走性）与结构化探索相空间之间取得平衡，即虽然会访问许多区域，但某些区域被访问的频率高于其他区域。

There has to be this balance between this itinerancy, this sort of the exploration of a phased space in a structured way where many regions are visited but some regions are visited more often than other regions.

当你开始思考如何用数学语言来表达这一点时，就会逐渐得到所谓的随机吸引子，它们源自随机对角系统。

And when you start to think about, well, how would you articulate that mathematically, you start to get sort of random attractors that inherit from random diagonal systems.

你所说的，就是存在一个吸引子。

What you're saying is there's an attracting set out there.

它并不是它的概率分布。

It is not its probability distribution.

如果我在很长一段时间内测量自己在状态空间中任何一点出现的概率，那么这并不是物理学家在二十世纪所熟知、热爱并被教导的那种平衡稳态。

If I measure the probability of finding me at any point in my state space over a very long period of time, So it is not the kind of equilibrium steady states that physicists knew and love and know and love and were taught in the twentieth century.

这是理解开放系统中非平衡稳态的新挑战，这些系统恰好在成为点吸引子和完全扩散之间保持着这种微妙的平衡——如果这就是宇宙的终点的话。

This is the new challenge of understanding nonequilibrium steady state for in open systems that exactly have this delicate balance between being a point attractor and being completely diffused, the end of the universe if that's That's the the way Yeah.

它正在走向的地方。

Where it's where it's going.

顺便说一句，我不久前请过安东尼奥·迪马乔做客播客，他最喜欢的一个词就是‘稳态’，对吧？

Just parenthetically, I did have Antonio Di Macio on the podcast a little while and his favorite word in the universe is homeostasis, right?

尽可能将自己维持在这个极小的范围内，但也要保留一定的灵活性。

The idea of keeping within this tiny little range as much as we can, but some flexibility there.

是的。

Yeah.

而且

And

如果我理解得没错的话，你其实是想说，最小化自由能和意外感是理解大脑运作机制的关键，对吧？

you want to do if correct me if I'm wrong again, but you really want to say that this minimization of free energy and surprise is sort of the key to unlocking what the brain does, right?

这是几乎所有事物的基础。

It's the underlying thing for most everything.

是的，确实如此。

Yeah, it is.

当然。

Absolutely.

我的小组会议上有个笑话，任何问题的答案都是模型证据。

I mean, there's a joke in my group meetings that the answer to any question is model evidence.

是的。

Yeah.

所以我通常会回答它

So I I usually answer It

再差也差不到哪去。

could do worse.

是的。

Yeah.

是的。

Yeah.

你知道，当你谈论同事和研究伙伴时，每当他们提出一个问题，比如‘如果这种情况发生会怎样？’

You know, and certainly when you're talking about colleagues and research fellows and, you know, whenever they ask a question, well, what happens if this is like that?

那就去获取这个假设的证据，然后你就可以量化你对它是这样、还是像那样破裂、或者这种差异是否在起作用的信念。

Well, get the evidence for that hypothesis and and then, you know, and then you can quantify your beliefs about whether it was like that or whether it broke like that or whether there's that difference is in play.

所以我能不能再插一句，因为我觉得这很好地承接了安东尼奥·达马西奥对稳态的关注？

So can I come back with another parenthesis because I think it nicely follows on from Antonio Damasio's focus on homeostasis?

当然，许多自组织和非平衡稳态的根源，都源自罗斯·阿什比等人的工作。

Of course, the roots of much of self organization to nonequilibrium steady state inherit from the work of people like Ross Ashby Mhmm.

他通过稳态器清晰地展示了这些观点。

Who made apparent his ideas through the homeostat.

哦。

Oh.

所以这正是同样的内容，或者说是‘最佳调节器定理’。

So it's exactly the same or the good regulator theorem.

我认为这只是我个人的看法。

I think that this is a this is just my personal opinion.

我认为物理学还有很多工作要做，沿着这些方向还有很多发现等待我们去实现。

I think that physics has, a lot of work to do and there's a lot of discoveries to be made along exactly these lines.

你知道，非平衡统计力学是一个蓬勃发展的领域，我试图让我的同事们对它产生兴趣，但他们已经习惯了做自己的事情。

Know, where non equilibrium statistical mechanics is a booming growth field that I need, try to get my colleagues excited about it but, it's a, you know, they're they're used to doing their things.

这是一个比较棘手的前范式领域，我们还不太清楚。

It's a tricky kind of pre paradigmatic area where we don't exactly know.

这么说真是个不错的表达方式。

Is it, that's a nice way to phrase it.

我不确定，因为你知道，我后来成了精神科医生，把物理学放下了，但在网上浏览时，这种前范式的东西确实非常令人兴奋，不是吗？

I I don't know because, you know, as as a you know, I I became a psychiatrist and left the physics behind, but but certainly surfing the web, that preparadigmatic thing, that's very exciting, isn't it?

因为那将是下一步。

Because that's the next thing.

是的。

Yes.

没错。

Exactly.

二十一世纪的物理学。

Twenty first century physics.

当你像在粒子物理或宇宙学中那样，从小就清楚问题是什么、什么才算洞见时，会舒服得多。

It's much more comfortable when you know, like in particle physics or cosmology where I was raised, you know what the questions are, you know what would qualify as an insight.

而在复杂系统、耗散系统中，伊利亚·普里高津也是早期的先驱者，对吧？

Whereas in complex systems, dissipative systems, Ilya Prigogine was a was an early pioneer here also, right?

自组织，但我们根本不知道该用什么词来描述。

Self organization, and we just don't know what words to use.

我们不知道该用什么方程，但我觉得，和你一样，我推崇用这种统计力学的视角来看待这些问题。

We don't know what what equations to use, but it I think like you, I'm a fan of these sort of statistical mechanical, lenses at which to view these things.

是的。

Yes.

我相信这确实是唯一真正的方法——对我而言，这是唯一能写下这些想法的方式，因为归根结底，你必须有一个能生成预测的代码模型，来分析大脑数据。

Well, I I'm sure that's the only way really to well, for me, it is the only way to write these things down because at the end of the day, you actually have to have a model in code that generates predictions to analyze the brain data.

没错。

That's right.

除非你是哲学家或者写书的人，否则你真的没有其他办法，你必须要有

There is no other you don't really have the unless you're a philosopher or you write books, You you know, there's no there is no You need

能够把它交给计算机，问它你做得怎么样。

to be able to give it to a computer and ask it how how well you're doing.

是的。

Yeah.

但让我们就这个视角来做个现实检验。

But let let's just do sort of the reality check for this, perspective here.

我当然明白，如果我开车在路上，我希望越少感到意外越好。

I I certainly get that if I'm driving down the street, I would like to be surprised as little as possible.

但难道不是说，非正式地，我们有时也会主动寻求新体验吗？

But isn't it true that also informally, do sometimes seek out new experiences, right?

这该怎么解释呢？

How does that fit in?

这正是我们从技术角度所探讨的悖论：即在当前这一刻，我通过最大化我对当前状况的解释或信念的熵（不确定性）来最小化我的自由能，并选择那些在未来能最小化我预期自由能的行为。

Well, it's exactly that sort of paradox that we were addressing technically in terms of the difference between me at this point in time, this moment, minimizing my free energy via a maximization of the entropy uncertainty of my explanations or beliefs about what's going on now, and choosing those actions that will in the future minimize my expected free energy.

因此，当你谈论基于特定行动（比如开车时往那边看）的预期自由能时，你就有了这种相反的驱动力。

So that basically means that when you talk about the expected free energy conditioned upon a particular action move, you know, looking over there when driving the car, you have this opposite imperative.

于是，你开始追求信息，成为好奇的生物，成为寻求感官刺激的个体。

So now you become information seeking, now you become a curious creature, now you become sensation seeking.

但这是一种特定类型的感官刺激寻求。

But it's a particular kind of sensation seeking.

它是指那些能够解决‘如果我那样做会发生什么’这一不确定性所带来的感觉。

It's those sensations that would resolve uncertainty about what would happen if I did that.

当然，我刚才描述的许多方式背后，都隐含着一种‘我作为能动者’的意识。

Of course, behind a lot of the ways I've just described that is a sense of me as an agent.

因此，一旦你将有感知系统的非平衡物理规律推广开来，写出它们作用于世界、体现其能动性的基本驱动力，并假设或试图证明这别无他法——即它们必然以最小化未来长期平均自由能为目标行动，那么这种好奇心就会被写入信息论之中。

So once you generalise the non equilibrium physics of sentient systems, to write down what might be the imperative for the way that they act upon the world, that they evidence their agency, and you make the assumption that or you try to prove it can be no other way, that they will act in the service of minimizing the long term average of free energy in the future, then you get this curiosity written into the information theory.

要解决不确定性，就意味着你会成为寻求感官刺激的个体。

To resolve uncertainty means you're going to be sensation seeking.

无论是这种平庸的寻求感官刺激，比如盯着交通灯或街灯看是绿灯还是红灯，还是去迪斯科舞厅或玩蹦极，都属于这种类型。

Now whether that's the sensation seeking of a banal sort that you're looking at the traffic lights or the street lamps to see whether it's go or stop or whether it's going to a disco or doing bungee jumping.

但这是不同的，是的。

It's it's it's a different yeah.

但其背后的基本动因是一样的。

But it's the same imperative underneath.

但这正是对那种俏皮话的回应：如果我们只是想最小化意外，那我们干脆坐在黑屋子里什么也不做好了。

But this is the response to sort of the wisecrack that if we just want to minimize surprise, we would sit in a dark room and not do anything.

对吧？

Right?

但问题是，从最小化意外转向最小化我未来所有意外的期望值，这种转变究竟有多单纯？

Because but is it how innocent is that move to go from minimizing surprise to minimizing the expectation value of all my future surprises?

这似乎是一种略有不同的最小化方式。

That that that seems like a little bit of a different minimization.

这么说公平吗？

Is that fair?

我们到底是在做哪一个呢？

Which one is it that we're doing?

从最简化的角度来说，你其实两者都在做。

Well, in a minimal sense, you're you're doing both.

但你实际上触及了通常在对话末尾才会出现的问题。

But but you you're you're sort of touching on the sort of the issues that normally come to the end of the conversation.

你和病毒之间的区别是什么？

Is the difference between you and the virus?

所以在重新探讨未来最小化预期自由能的基本原理之前，或许某些系统、某些生物体，本质上已经获得了在生成模型中植入一种先验信念的能力——即它们是最小化自由能的生物。

So to cut to that distinction before revisiting the fundaments of minimizing expected free energy in the future, It may be the case that certain systems, certain biotic systems, creatures basically, have acquired the capacity to include and install in their generative models the prior belief that they are free energy minimizing creatures.

如果它们能做到这一点，那么它们就会拥有这样的先验信念：我的行为方式将是最小化我的自由能。

And if they can do that, then they will have the prior belief that the way that I will act will be to minimize my free energy.

这正是物理学家可能会这样表述的方式。

That was how you might write it down as a physicist.

我明白你的意思了。

I see where this is going.

是的。

Yes.

很好。

Good.

如果你是个心理学家，你只是在说，我有规划的能力。

If you were a psychologist, all you're saying is, I have the capacity to plan.

对吗？

Yeah?

所以你只是在说这个。

So that's all you're saying.

或者想象。

Or to imagine.

没错。

Exactly.

是的。

Yeah.

所以你某种程度上确实如此，完美。

So you have sort of so yeah, perfect.

因此，你的遗传模型现在具备了想象反事实或虚构未来的能力，能够设想未来，并推演行为的可能后果。

So that's the your genetic model is now equipped with the capacity to imagine a counterfactual or fictive future, to imagine the future, to roll out possible consequences of actions.

当然，这些行为在当前观察中的后果是随机变量，因为它们尚未发生。

And of course, the consequences of those actions in terms of the observations now are random variables because they haven't happened yet.

这就是为什么你会出现这种逆转。

And that's why you get this reversal.

突然间，你变成了一种追求感官刺激的生物，确切地说是寻求感觉的生物。

Suddenly you become a creature that seeks out sensations, literally sensation seeking.

这能消除不确定性。

That resolves uncertainty.

你会变得好奇，去参加迪斯科舞会，在某个年龄段玩蹦极。

You become curious, and you go to your discos, you do your bungee jumping at a certain age.

因此，我认为这在非常简单的吸引子之间是一个重要的区别。

So that's, I think, an important distinction between very simple attracting sets.

让我们回到月球岩石的问题上。

Let's go right back to the moon rock.

好的。

Okay.

因此，对这种非平衡稳态的恰当描述实际上是一种平衡稳态，这是因为其具有一个点吸引子。

So an appropriate description of that nonequilibrium steady state is in fact an equilibrium steady state, and that's because it's got a point attractor.

它也可能具有准周期吸引子，比如行星的轨道运动。

It could have a quasi periodic attractor, so the orbiting of the planets.

但这些是非常简单的、非游走性的吸引子集合，会趋向于平衡稳态。

But these are very simple non itinerant attracting sets that would approach an equilibrium steady state.

然后我们向上推进到系统，从岩石一直到——嗯，我甚至可以说，虽然不包括昆虫，但肯定包括病毒。

Then we move up to systems right from sort of rocks through to yeah, I would pretty may even go as far as some not insects, but certainly say viruses.

所以那些不会规划的事物。

So things that don't plan.

但它们确实活着。

But they live.

它们在占据我们的宇宙方面非常有效。

They're very effective at occupying our universe.

但某种意义上，它们活在当下。

But they live in the moment in some sense.

绝对如此。

Absolutely.

是的。

Yeah.

根据杰里·埃德尔曼的说法，不存在被记住的当下。

In Jerry Edelman's word, there is no remembered present.

没有想象。

There is no imagination.

没有规划。

There's no planning.

它们具备恒温器所有的机械精巧性。

They have all the mechanical finesse of a thermostat.

但他们非常擅长自己所做的事情。

But they're very good at what they do.

所以，你知道的。

So, you know.

内稳态。

Meostasis.

是的。

Yeah.

他们实现了这一点。

They achieve it.

对。

Yeah.

嗯，这真是一个很好的例子。

Well, mean, that's a nice beautiful example.

所以，即使在我们自己的身体里，可能高达99%的生理活动——也就是内稳态——都只是这种即时的、反射性的自我维持过程

So even in our own bodies, possibly 99% of all that actually goes on in terms of the physiology, which is herostasis, is just this reflexive in the moment, keeping yourself

调节你自己。

Regulating even yourself.

调节你自己。

Regulating yourself.

我认为，这类系统与你我这样开始规划并具备相应能力的系统是不同的。

So those kinds of systems are distinct, I think, from systems like you and me that start to plan and have the ability to them.

它们的生成模型确实涵盖了未来，进而也涵盖了过去。

Their generative models do actually span the future and by implication the past.

隐含地，它们的轨迹在其生成模型中会延伸到相当远的未来。

Implicitly have a dynamic where the trajectories actually go quite a long way in their generative model go quite a long way into the future.

因此，这将是一个非常有趣的方式，来推进这个论点或回应你的问题。

So that would be a really interesting sort of way to take forward the argument or a response to your question.

但你的问题稍微回到原点：究竟是最小化自由能，还是最小化基于特定行动的条件自由能？

But your question is slightly just to return to, well, is it minimizing free energy or is it minimizing the free energy conditioned upon a particular action?

它

It

两者都是。

is both.

你主动最小化不确定性的程度，实际上取决于我们所讨论的吸引子——即吸引集合的形状。

The degree to which you actively minimise your uncertainty depends really upon the shape of the attractor that we're talking about, the attracting set that we're talking about.

对于游荡系统而言，有可能写出密度动力学，并计算出未来行动轨迹的概率分布。

So with itinerant systems, it is possible to write down the density dynamics and work out the probability distribution of trajectories of action into the future.

因此，行动本身只是另一种状态，你可以应用波动定理或病态形式体系，来计算出未来状态中行动轨迹的分布，抱歉，我表达得不够准确。

So this just action is another state and you can apply fluctuation theorems or pathological formalisms to work out a distribution over trajectories of action into the state, into the future, my apologies.

这意味着，从技术上讲，你现在可以基于概率分布来描述一个给定系统在未来的行动路径或策略，即在某种模型下，特定行动对我的感官输入会产生什么影响。当你写下这一点时，有一种方法可以证明，这本质上是对那些以最小化预期自由能（即最小化距离，实际上是它们自认为所处位置的概率分布与其吸引集合之间的KL散度）为特征的系统的描述。

Which means that technically what you can do now is characterise a given system in terms of probability distributions over courses of action, policies into the future, trajectories or paths of action under a model of what would the implications of that particular action have for my When sensory input, for you write that down, there is a way of showing that that is essentially a description of systems that do minimise their expected free energy in the sense of just minimizing distance, in fact, the KL divergence between where they think they are, probabilistically, and their attracting set.

这就是预期自由能的一个方面。

So that's one part of expected free energy.

还有另一个方面，是关于减少模糊性的，当你们和我由于存在本身而展现出这种概率分布的特定约束时，这一方面就会发挥作用。

There's another part which is all about ambiguity reducing, which kicks in when there are particular constraints on the shape of this probability distribution that you and I evince just by existing.

而这实际上取决于游荡性，你可以通过不同状态分区之间的互信息或相对熵来衡量它。

And that depends really upon the itinerancy which you can measure in terms of mutual information or relative entropies between different partitions of the states.

这里可能有一些细节。

Would There's probably some details here.

这里有一个小细节。

Here comes one little detail.

这一切都建立在马尔可夫划分和马尔可夫毯的基础上。

All of this rests upon a Markovian partition into a Markov blanket.

这一切都依赖于将宇宙划分为：你内部的内部状态、宇宙其余部分，以及关键的毯层状态——这些毯层状态明确地将你与宇宙其他部分分隔开来，使你能被识别，此外还要将毯层状态进一步划分为行动状态和感知状态。

All rests upon carving the universe into internal states that are inside you that constitute your internal states, the rest of the universe, and then crucially blanket states that separate specifically you from the rest of the universe that enable you to be identified, and a further bipartition on those blanket states into active and sensory states.

一旦你进行了分隔。

Once you've Compartmentalizing.

将描述一个存在物所必需的不同类型的状态进行分隔后，我。

Compartmentalizing the different kinds of states that would be necessary to describe a universe in which something exists, I.

以一种能与非我区分开的方式来理解，你就可以开始构建模型，超越二十世纪物理学中仅针对理想化气体或封闭系统熵的讨论。

You, in a way that is separable from not you, then you can start to write down you can go beyond just the, you know, sort of twentieth century physics in terms of entropies of distributions of, say, an idealized gas or some sort of closed system.

现在你必须处理分区的熵，以及进一步的相对熵。

Now you have to deal with the entropies of a partition And then furthermore, you've the relative entropies now.

所以你突然进入了一个纯粹物理学的游戏。

So suddenly you're in a game of which is pure physics.

现在你必须考虑相对熵了。

It's just now you've got to think about the relative entropies.

你不能再仅仅谈论这个集合的熵，或者与这个波函数或这个解相关的熵。

You can't just talk about the entropy of this ensemble or this the entropy of associated with this wave function or this solution.

你现在必须将其划分开来，讨论相对熵，正是在这里，信息论的所有信息丰富性和所有不确定性开始发挥作用。

You now have to carve it up talk about the relative entropies, which is where the information theoretic and all the information richness and all the uncertainty, that's where it all starts to kick in.

当然，在这样做的同时，你实际上已经承诺接受一种开放系统的力学，因为马克ov毯的整个意义就在于它使得内部与外部之间能够双向互动。

And of course, in so doing, you've actually now committed yourself to a mechanics of open systems because the whole point of having the Markov blanket is that it it enables a two way traffic between the inside and the outside.

因此，根据定义，你现在处于撰写开放系统统计力学的游戏中，这些系统由于具有吸引集而处于某种非平衡稳态。

So now by definition, you're in the game of writing down the statistical mechanics of open systems that have some non equilibrium steady state in virtue of having an attracting set.

所以现在的问题变成了：究竟可能存在哪些不同类型的吸引集？

So now the game becomes, well, what different kinds of attracting set could be?

如果它们存在，从互信息、相对熵或不确定性消除压力的角度来看，它们会呈现出什么样子？这些压力是描述吸引集存在的某种方式。

And if they are, what would it look as if they are doing in terms of these mutual information or relative entropies or uncertainty resolving pressures that, you know, are one way of describing the very existence of this attracting set.

我确实想更深入地探讨马尔可夫毯，但我不想完全放弃从活在当下转向活在预期未来这一转变。

I do want to get more into the Markov blankets, but I don't want to quite let go of this transition from living in the moment to living in the expected future, guess.

这似乎在我没有刻意规划的情况下，反复出现在播客中。

We this seems to be without me planning something that appears on the podcast over and over again.

最近在与哲学家贾内恩·伊斯梅尔的对话中，当我们讨论自由意志及其含义时，这个问题出现了。

Recently in a conversation with the philosopher, Janane Ismail, when in when we were talking about free will and what that means that came up.

更早之前，我和机械工程师兼神经科学家马尔科姆·麦克伊弗交谈过，他提出一个理论：在通向意识的道路上，其中一个关键步骤是我们鱼类爬上陆地，开始能够规划未来，因为在陆地上，生命的时间尺度要慢得多。

And earlier with Malcolm McIvor, who is a mechanical engineer and neuroscientist, who has a theory that, one of the steps on the road to consciousness was when we fish climbed up onto land and could begin planning in the future because the the life the the time scales are much slower on land.

所以你拥有了规划的能力。

So you have the, ability to plan.

但因此，我想知道，在这个框架下，是否有可能在进化过程中精确地指出一个转折点，让我们从活在当下转变为更善于规划的生物？

So but so I I wonder, is it possible in this framework to sort of pinpoint a place in the evolutionary scheme where we flip over from living in the moment to being more planning animals?

我个人的理论是，这个转折点发生在猫身上。

My personal theory is that it's with cats.

嗯。

Uh-huh.

好的。

Okay.

这说法不错。

That's a good one.

因为我养了两只猫。

Because I have two cats.

我的听众都很熟悉，它们叫Ariel和Caliban，我发誓其中一只，Caliban，完全活在当下。

My my listeners are well aware, Ariel and Caliban, and I swear that one of them, Caliban, just lives in the moment.

比如，他的需求得到了满足，或者没有，就只有这两种状态。

Like, he he his needs are being met or they're not, and that those are the only two states he has.

而Ariel，你能看出她正在试图推测，如果她做了某件事，会发生什么，她的猫脑正在尽全力思考。

Whereas Ariel, you could see that she's trying to figure something out about what would happen subjunctively if she did something, and, like, her little kitty brain is trying its best.

所以我很确定说猫是过度夸张了，但这种能力是否直到哺乳动物阶段才变得重要，还是你觉得应该追溯得更早？

So I I'm sure the cats is an exaggeration, but is is it as late as mammals where this becomes important, or do you wanna attribute it much earlier than that?

我不知道，但我被你提出的这个问题深深吸引了。

I don't know, but I I I'm I'm compelled by your question of saying.

这看起来非常清楚，我想。

It seems very clear, guess.

但你知道，你从其他角度——尤其是哲学角度——所说的一切，对我来说都完全合理。

But, you know, everything you've said in terms of these other perspectives, you know, particularly from philosophy makes entire sense to me.

规划的能力意味着你现在拥有了未来的一系列可能轨迹和行动路径。

The ability to plan suddenly means you have now a space of trajectories, courses of actions in the future.

这意味着你必须做出选择，因为你只能实现一个确定性的行动，因为行动实际上是宇宙的一种物理状态，它本身并不是一种信念。

And it means that you have to because you can only realize one deterministic action, because action is actually a physical state of the universe, it's not, you know, The action in and of itself is not a belief.

我们对行动有信念，但行动是被实现的。

We have beliefs about action, but the action is realised.

因此，这种实现意味着你必须从众多可能性中选择其一。

So that realisation means that you have to commit to one of a multitude.

所以这里存在一个选择过程，这在某种意义上与自由意志有关。

So there's a selection process in play which must in some sense speak to the free will.

或者至少，如果你对自由意志持某种特定立场，那么它所表明的是：如果存在一个选择过程，从某种概率分布或对当前行为的信念中选择行动，那么这只能适用于那些真正拥有对未来后验信念的系统。

Or at least if it doesn't, depending upon your committed attitudes to free will, what it does say is if there is a selection process in play in terms of selecting action from some probability distribution or beliefs about the way that I am currently acting, then it must be the case that that only applies to systems that actually have posterior beliefs about the future.

这不可能，我认为恒温器不可能被误认为具有自由意志的东西。

It cannot So a thermostat could not, I think, be confused with something that might express free will.

而你现在的问题是，我们在哪种情况下会拥有具有这种精妙稳态机制的生物恒温器，它们进而具备想象、规划、思考的能力，正如你所暗示的，甚至可能具备某种最原始形式的意识，或甚至在意识之前就已具备自我。

Whereas your question now is, at what point do we have biological thermostats that have this beautiful homeostasis that become equipped with the capacity to imagine, to plan, to think, and as you intimated, possibly even have some minimal form of consciousness or even self, perhaps selfhood before consciousness.

因此，我通常诉诸于哲学中关于模糊概念的观点。

And so I normally recourse to the philosophical notion of a vague concept here.

你知道，我最近才了解到这一点。

So, you know, I only recently learned about this.

这就是我喜欢交谈的原因。

This is why I like talking

整个模糊性哲学。

whole philosophy of vagueness.

确实如此。

It's true.

我们还没在播客中讨论过这个话题，但这是一个有趣的话题。

We haven't talked about that on the podcast, but that's an interesting topic.

是的。

Yeah.

所以，对于那些像我一样，几个月前还不了解的人，一堆沙子在什么时候才算是一堆呢？

So, you know, for those people who don't, you know, like me, who don't know and like I was a a few months ago, so at what point is a pile of sand a pile?

你知道的。

You know?

是一个、两个、三个、四个还是五个沙粒？

Is it one, two, three, four, five grains?

我很喜欢这种说法，它不回避问题，而是问：你在哪个点上设定你的阈值？

So I quite like that as a way of without moving, getting out of the question, at what point would you you put your cap threshold?

对。

Right.

我认为这是有数学依据的，因为即使是恒温器和病毒，它们也被称为预测编码。

And I think it's warranted or licensed mathematically because even things like thermostats and viruses, they say predictive coding.

说预测编码，但并不具备这种规划能力。

Say predictive coding does not have this planning.

它没有这种感觉。

It doesn't have this sense.

也许你可以为观众定义一下预测编码。

Maybe define for the audience predictive coding.

预测编码最初是在20世纪50年代被发明出来，用于压缩音频文件。

Well, predictive coding is just, well, originally devised in the 1950s as a way of compressing sound files.

因此，这是一种非常高效的方式，遵循奥卡姆剃刀原则，在最简单的编码中保留最多的信息，这也是另一种说法。

So it's a very efficient way of complying with Occam's principle by providing the most retaining the most information but in the simplest coding that you can, which is another way of

某种程度上就是算法可压缩性。

Sort of algorithmic compressibility.

是的。

Yeah.

这实际上也是费里原则，只不过用算法复杂性和最短消息长度来表达。

That is in fact the Fieri principle as well, but just written in terms of algorithmic complexity and minimum message rather.

数学上完全相同，只是从事件空间的角度来看。

It's exactly the same maths but sort of event spaces.

因此，目前应用于大脑的预测编码，只是指我们正在最小化预测误差。

So predictive coding as currently applied to things like the brain is just the notion that we're minimizing our prediction error.

它并不涉及行动。

So it doesn't talk about action.

它讨论的是我们的大脑可能如何响应，我们的解码器可能如何应对新的数据。

What it does talk about is how our brains might respond, how our sort of decoders might respond to some new data.

它们通过重新组织信念更新或状态估计来实现这一点，以最小化预测误差。

And they do it by sort of reorganizing belief updating or state estimation in a way that minimises the prediction error.

因此，如果你能完全基于你之前所见的内容，准确预测当前呈现的内容，那么你必然对生成该信号、音轨或听觉流的源头拥有一个完美的模型。

So if you can predict what is currently being presented currently exactly on the basis of what you have previously seen, then you must have a perfect model of what is generating that signal or that soundtrack or the auditory stream.

因此，你已经最小化了你的自由能或变分自由能，或者从纯粹感官、感知的角度来看，你已经最大化了你的证据下界。

And therefore you have minimized your free energy or variation free energy or you've maximized your evidence lower bound in terms of the pure sensory, the sentient aspects of it.

请注意，我们尚未——这一点很重要——讨论我们将要做什么，或者我如何

Notice that we haven't which is the important thing, we haven't talked about what we're going to do or how I'm

正在谈论这一点，是的。

talking about that, yes.

是的，没错。

Yeah, right.

所以，这种预测编码并不涉及主动推理，也不涉及主动学习。

So this you know, the procedure coding doesn't address active inference, It doesn't, or active learning.

它只是讨论如何理解数据。

It just talks about sort of how to make sense of data.

因此，这可以很好地说明病毒或恒温器的感知部分。

So that would be a nice example of, you know, the sensory part of a virus or a thermostatic.

它可以被完全描述为最小化差异。

It can be completely described as just minimizing the discrepancy.

以恒温器为例，现在我们把行动重新纳入考虑。

Take a thermostat, for example, let's now put action back into the mix.

你可以将恒温器描述为只是在最小化其预测误差。

So you can describe a thermostat as just minimizing its prediction error.

预测误差是相对于什么而言的？

Prediction error between what?

嗯，是在它感知的温度和其吸引的固定点之间。

Well, between the temperature it's sensing and its attracting fixed point.

所以它属于这类固定点生物。

So it's one of these fixed point creatures.

它拥有一个吸引集合，即它对温度会保持在某个水平的先验信念。

And it's got its attracting set, it has its prior belief that temperature will be like this.

我只需要最小化我的预测误差，最小化我的自由能。

And all I need to do is to minimize my prediction error, minimize my free energy.

我不清楚我是怎么做到的，但我确实看到它在转向

And I don't know how I'm doing it, but I do see Turning to

加热器或空调上，

on the heater or the air conditioning,

我想是这样。

I guess.

它并不知道自己在做什么，但它具备了能够使其达到固定点的行为。

It don't doesn't know what it's about, but it is equipped with action that will enable it to get to its fixed point.

那么，这在什么意义上算是规划呢？

So in what sense is that planning?

如果你还记得，我正试图在这里强调一种模糊性，这样我就不用回答你的问题。

If you remember, I'm trying to argue for a vagueness here so I don't have to answer your question.

当你用卡尔曼滤波或贝叶斯滤波来表述这种预测编码时——也就是技术专家或统计学家描述预测编码方案的方式——你总是在处理导数。

Well, when you formulate that kind of predictive coding in terms of Kalman filtering or Bayesian filtering, which would be the technical or the statistician's way of describing a predictive coding scheme, you're always working with derivatives.

因此，你总是在一个动态环境中工作，不仅处理预测误差，还处理预测误差随时间的变化率。

So you're always working in a dynamical setting with not just the prediction errors, but the rate of change of prediction errors with time.

所以，从最基础的意义上讲，你通过线性一阶近似获得了一种对未来的概念。

So in a minimal sense, you've got a notion of the future through a linear first order approximation.

无论如何，下一次事件。

The next incident anyway.

绝对如此。

Absolutely.

是的。

Yeah.

好的。

Okay.

所以，这就是我所说的最小意义上的观点：每个生成模型都因其具有轨迹或动态的概念而具备对未来的理解。

So that's what I meant with in a minimal sense that everything has, every generative model has a notion of the future just in virtue of having a notion of trajectories or dynamics.

是的。

Yeah.

好的。

Okay.

但这和你的第二个猫并不完全一样。

But it's not quite the same as your second cat.

是的。

Yeah.

它并不是在思考，如果我那样说，那是对的。

It's not thinking well, if I That's right.

我来解释一下。

I'll explain

是的。

the yeah.

你可以看到，这仅仅关乎她的能力水平。

You can see it's just at the level of her capacities.

但你提到了行动，我认为这是一个很自然的切入点，因为你还想说，自由能原理有助于我们理解我们的行为方式。

But but you mentioned action and I think this is a natural place to go there because you also want to say that free energy helps us understand how we behave.

这样说安全吗？

Is that safe to say?

事实上，让我复述一下我读到的内容，然后你再帮我纠正。

In fact so let me let me sort of repeat the thing that I read and then, you know, again, you'll fix it.

一种理解我移动手的方式是，我的大脑故意对我的手的位置产生错误判断。

One way of thinking about what happens when I move my hand is that my brain sort of intentionally gets it wrong about where my hand is.

于是，我的手实际位置与大脑认为的位置之间出现了不一致。

And then there seems to be a mismatch between where my hand actually is and where my brain thinks it is.

而我没有去修正大脑的判断，而是移动了我的手，使其到达大脑所认为的位置。

And rather than fix my brain, I move my hand to bring it to where it is.

是这样吗

Is that

这太美了。

That's beautiful.

是的。

Yeah.

好的。

Okay.

对。

Yeah.

事实上，那里根本不需要修正。

I I don't need to fix anything there.

事实上，我们应该为此感到欣喜，因为你刚才描述的正是现代版的意动理论，这一理论在十九世纪非常流行，即

In fact, we should celebrate that because what you've just described is a modern day recount of ideomotor theory, which prevalent in the nineteenth century, which

赫尔姆霍兹。

Helmholtz.

是的。

Yes.

嗯，没错。

Well, yeah.

他什么都做了。

He did everything.

我可以对他表示同意。

I could say yes to him.

他是一个高熵思维者。

He's a high entropy thinker.

是的。

Yeah.

当时还有一些德国神经学家和自然科学家，他们特别专注于这一领域。

There were other sort of German neurologists and natural scientists, you know, sort of focused specifically on that.

威廉·詹姆斯在欧洲游历期间注意到了这一点。

That was picked up by William James, you know, for on his European tours.

但眼睛恰恰就是你刚才说的那样。

But the eye the eye is exactly what you just said.

我只是需要在脑海中想象那个动作的结果，然后让我的反射机制实现这个想象出来的结果，这在维多利亚时代被用来解释催眠术中的现象——你的手臂变得越来越轻、越来越轻、越来越轻。

It's just to move, I have to, in my mind, imagine the outcome of that movement and then just let my reflexes realize that imagined outcome, which basically was in the Victorian era, posited as an explanation for stage hypnotism that your arm is getting lighter and lighter and lighter and lighter.

当然，如果你相信自己的手臂正在变得越来越轻、越来越轻、越来越轻，并且正在漂浮，那么你对自身本体感觉输入的预测——即如果手真的在漂浮时会感受到什么——就可以在无意识层面通过反射机制得到满足，于是你的手真的会抬起来。

And of course, if you believe your arm is getting lighter and lighter and lighter and lighter and it's floating, then your predictions about the proprioceptive input that you would get if your hand was in fact floating can now be fulfilled at a sort of pre awareness level simply by reflexes, and your hand will indeed just rise.

所以，你知道，这几乎就是自由能原理的全部内容，尤其是当它被应用于主动推理这类概念时。

So, you know, this is as much as nearly all the free energy principle, actually, particularly sort of incarnations when applied to things like active inference.

这些都是非常古老的想法。

These are very old ideas.

你实际上可以追溯到柏拉图的学生，但它们是通过康德和赫尔姆霍兹传承下来的。

And you can actually probably trace them back to the students of Plato, but they come through Kant and Helmholtz.

好的。

Okay.

确实如此。

Very much so.

是的

Yeah.

与此相伴的，是这种将感知视为推断的观点，同时也涉及行动的推断。

And alongside that that sort of perception as inference was this sort of actions inference, basically.

行动，以及我对自身应有状态的信念。

Actions, beliefs about the way I should be.

哦，对的。

Oh, yes.

现在我就这样了。

Now I am like that.

当然，如果你确实注意到证据表明你的手并没有漂浮，那么它就不会动，这就引出了一个有趣的场景：你必须在某种程度上削弱

And if, of course, you actually tend to the evidence that, in fact, your hand is not floating, then, of course, it won't move, which sort of takes us into the interesting scenario that you must, in some sense, attenuate

这些证据。

the evidence.

阻止自己接收到这些信息。

Prevent yourself from getting that.

没错。

Exactly.

是的。

Yeah.

好的。

Okay.

我想，我们所拥有的、而柏拉图、赫尔姆霍兹或威廉·詹姆斯所没有的是能够深入大脑内部、观察其内部活动的能力。

Is this is this I guess, what we'd have that Plato or Helmholtz or William James did not have is the ability to poke inside a brain and see what's going on there.

这种观点——即行为是由模型与感官输入之间的差异所驱动的——能在大脑中得到验证和检验吗？

Is this is this idea that action is driven by a mismatch between model and sensory input verified, testable, in the brain?

是的。

Yeah.

是的。

Yeah.

是的。

Yeah.

当然。

Absolutely.

多个层面。

A number of levels.

但再说一遍，回到这种观点，即从自由能原理的机械处理中得出的大部分内容早已为人所知；我们所描述的实际上是一百年前就已知晓的经典反射。

But, again, just coming back to this sort of notion that most of what emerges from a sort of mechanical treatment of the free energy principle was well known So a century what we are describing are classical reflexes.

因此，大脑会向脊髓中的α运动神经元发送信号，这些信号本质上是预期信号、来自肌肉和运动系统的感官信号与实际接收到的信号之间的不匹配。

So the brain sends down messages to alpha motor neurons in the spinal cord that effectively are a mismatch between the intended signals, sensory signals from the muscles, the motor plant, and what it's actually receiving.

然后这些细胞生成信号传递给肌肉，使其收缩，直到信号达成一致。

And then those cells elaborate signals to the muscles to cause them to contract until the signals match.

因此，我们运动的方式，事实上我们自主功能的分泌方式、心脏的工作方式，乃至所有稳态机制的运作方式，都是通过向周围系统的伺服系统、稳态系统或反射机制提供正确的设定点来实现的。

So the way that we move, and in fact the way that we secrete our autonomic function works, way that our heart works, in fact all of our homeostasis works, generalized homeostasis works, is by supplying the right set points to servos or homeostatic or reflex mechanisms in the periphery.

这些设定点是什么？

What are those set points?

它们只是我对自身状态的预期。

They're just predictions of the way I want to be.

那么，自由能在这里是否扮演了某种优化问题或低效机制的角色？

And is the role of does free energy have a role here in kind of an optimization problem or inefficiency maybe mechanism?

比如，你可以想象大脑或神经系统有多种方式来实现预期与现实之间的匹配，但是否有一种更简便的方法，利用自由能来计算如何做到这一点？

Like, there's different ways you could imagine the brain or the the nervous system bringing this match between expectation and reality, but is there just a sort of there are easier ways to calculate how to do that using free energy?

利用

Using

我的意思是，自由能形式体系可以说是所有这些具体表现的祖师爷。

Well, I mean, you know, the free energy formalism is is is, if you like, the grandfathers all of these particular manifestations.

是的。

Yes.

我想你问的是，如果我现在想描述生物学、神经连接或时间常数，你就得写出生成模型。

I guess what you're asking is if I wanted to now describe the biology or the wiring or the time constants, what you'd have to do is to write down the generative model.

如果你还记得，自由能是信念的一个泛函，而信念是相对于生成模型来定义的。

If you remember, the free energy is a functional of a belief and the belief is defined in relation to a generative model.

所以，如果你能写出生成模型，就能进一步写出关于感觉和主动内部状态的微分方程。

So if you can write down the generative model you can then write down the differential equations of the sort of sensory and active internal states.

内部状态可以与神经活动相关联。

Internal states you can associate with neural activity.

主动状态可以是分泌物，也可以是手臂的物理运动。

Active states can be either secretions or it could be physical movements of an arm.

然后你就能模拟这类现象。

And then you will be able to simulate these kinds of phenomena.

你可以获取实证数据，然后调整生成模型的参数，直到你对手臂运动或神经对知觉合成的模拟结果与观察到的脑信号相匹配。

What you can then do is take empirical data and then change the parameters of the generative model until your simulation of an arm movement for example or a neuronal response to perceptual synthesis matches what you observe in terms of brain signals.

从某种意义上说，这正是我们已经做的事情的另一种描述。

So that, in a sense, that's another description of what we already do.

这就是神经科学家所思考的：大脑如何建模其世界，如何做出这些预测，如何生成例如运动？

That's what neuroscientists We think about the functional anatomy in terms of how does the brain model its world, how does it make these predictions, How does it generate, for example, movement?

它是如何生成这些运动指令的？

How does it generate these motor commands?

但这些并不是运动指令。

But they're not motor commands.

它们只是对如果我实际处于这个姿势、行走或说话时应该感受到什么的预测。

They're just predictions of what I should feel if I was actually in this position or walking or talking.

事实上，这不仅涉及解释反射弧和运动系统的整个理论体系，即所谓的平衡点假说，还引发了大量关于该理论实际实现方式的争论，以及这是否是看待问题的正确方式。

And in fact, that that was the whole industry of not only theories of interpreting reflex arcs and the motor system under that kind of perspective called the equilibrium point hypothesis, but there's also massive debates about, you know, the actual implementation of that and, you know, whether that's the right way to look at things.

我想我有一种印象，你可能会认为大脑试图做的只是使用贝叶斯定理。

I guess I had this impression that, you might imagine that what the brain is trying to do is just use Bayes' theorem.

它拥有一些信念。

It has some beliefs.

它获取更多数据，并更新其信念，但这在计算上很困难，计算量很大，而计算自由能是一种捷径。

It gets in more data, it updates its beliefs, but that is calc calculationally difficult, computationally intensive, and calculating free energy is a sort of shortcut.

你知道，最小化自由能比直接条件化概率要更容易计算。

You know, minimizing free energy is calculation easier than simply conditionalizing probabilities.

我明白了。

I see.

是的。

Yeah.

是的。

So yes.

你已经让我们关注到一个非常重要的观察。

You you you've you've moved us into a, you know, a very important observation.

所以，我的意思是，我们一直在讨论关于我们应该处于什么状态的信念，以及先验信念和对未来信念的思考。

So so, I mean, we've been talking about sort of beliefs about where we should be and prior beliefs and beliefs about the future.

当然，先验信念隐含地基于贝叶斯区分：即在观察任何感觉状态或感觉数据之前的先验信念，和在观察这些数据后通过信念更新所产生的后验信念。

And of course prior beliefs implicitly rests upon a Bayesian distinction between prior beliefs prior to seeing any sensory states or sensory data and posterior beliefs the product of belief updating having observed those data.

因此，这就是最小化自由能变化的过程，例如。

So that is the process of minimizing variation free energy for example.

还是说并非如此？

Or is it?

并不完全如此。

Not quite.

如果这种信念更新过程与物理学联系起来，我们所说的是一种梯度流在起作用，它支撑着一个随机吸引子，而这个吸引子集合定义了我们所是之物，并且存在一个马尔可夫毯或分区在发挥作用。

If that process of belief updating and this just connected back to physics, so what we are saying is that there is a gradient flow that is in place, that underwrites a random attractor and that attracting set defines the kind of thing that we are and there's this Markov blanket or partition in play.

因此，我们将这种梯度流与信念更新联系起来，前提是某些状态编码了概率分布或代表信念的参数。

So that gradient flow we're going to now associate with belief updating on the assumption that some states encode probability distributions or stand in for the parameters of beliefs.

一旦我们做出这一假设，我们就可以用信念更新来表述梯度流，也就是说，我们将一个随机动力系统——比如朗之万系统——的动态解释为信念更新。

And once we've made that move then we can actually write down the gradient flows in terms of belief updating, which is literally we're taking a random dynamical system, I'll say a Langevin system, you know, interpreting the dynamics as belief updating.

而这种信念更新是从先验到后验的过程。

And the belief updating is from priors to posteriors.

所以，所以

So that So

在这种情况下，梯度流就是一种说法，表示我们从当前状态略微向目标状态靠近。

gradient flow in this case is a is a way of saying moving from where we are a little bit closer to where we wanna be.

是的。

Yes.

对。

Yeah.

绝对如此。

Absolutely.

嗯，我的意思是，这正是自由能实际上所衡量的内容。

Well, I I mean, that that that's exactly what the free energy actually scores.

是的。

Yeah.

所以我们在这里讨论了各种精彩的问题。

So we're covering all sorts of wonderful issues here.

我只是说，我们还没谈到生命的起源，但我们也一定会说到。

I I just well We haven't gotten to the origin of life yet, but we're going to get there too.

所以，没错，这正是贝叶斯与近似贝叶斯推断之间的区别。

So yeah, no, it was difference between Bayes and approximate Bayesian inference.

这就是我们目前所处的位置，但我觉得你实际上触及到了我们之前讨论过的一个观点，即关于变分自由能的另一种视角。

That's where we're But I think actually you're touching on something which we'd rehearsed previously, which is another perspective on variational free energy.

为了让你感兴趣，一旦你放弃平衡态物理——二十世纪的物理——而只生活在非平衡稳态的世界中，这意味着存在某个吸引子，你必须解释它的机制，那么自由能，即变分自由能，就开始呈现出与物理学家的热力学自由能非常相似的特征。

Just for your interest, once you abandon equilibrium physics, twentieth century physics, and you just live in a world of nonequilibrium steady state, which implies that there is some attracting set there and you have to explain it, you know, its mechanics, then the the free energy, the variational free energy now starts to have the look and feel of something which is much closer to a physicist's thermodynamic free energy.

实际上，它衡量的是系统当前状态与它在吸引子上的概率分布之间的差异。

And effectively, it scores the divergence between the current state of the system and the probability distribution it would have on its attracting set.

就在吸引集上，是的。

Exactly on the attracting set, yeah.

所以本质上，这是我和我的吸引集或非平衡稳态概率分布之间的距离。

So it's basically how far away am I from my attracting set or my sort of non equilibrium steady state probability distribution.

因此，在这种意义上，它看起来非常像可用于做功的能量总量。

So in that sense, now it looks very much like the amount of energy available to do work.

所以我看看自己，我扰动自己，把我置于一种非常不寻常、令人恐惧、引发焦虑的新情境中，无论是从稳态还是概念上来说。

So I look at me, I perturb me, I put me in a highly unusual frightening, angst inducing situation I've never been in before, know, homeostatically or conceptually.

然后我会努力回到我的舒适区。

And I will work towards getting back to my comfort zone.

是的。

Yes.

我的快乐之地。

My happy place.

我的快乐之地，我适宜的温度。

My happy place, my right temperature.

通过这样做，我会最小化我的能量，并且实际上是在与环境互动。

And in so doing, will minimize my energy and I'll be working literally on the environment.

因此，在我看来，变分自由能（用于描述非平衡稳态及其吸引集的动力学或力学）与热力学自由能之间的区别几乎变得不可见。

So now, to my mind, becomes an almost invisible distinction between the variational free energy in the context of writing down the dynamics or the mechanics of non equilibrium steady states with attracting sets and thermodynamic free energy.

而且

And

事实上，

in fact,

你只需要乘上一个玻尔兹曼常数，它们就是同一回事。

you can just put a Boltzmann constant on and they are the same thing.

有趣的是，从纯粹的信息论视角来看，玻尔兹曼常数现在只是为随机波动的幅度赋予了单位。

And interesting, the Boltzmann constant is in the purely information theoretic perspective, it now becomes just equips the amplitude of random fluctuations with units.

现在你可以开始从物理量的角度来解释它。

And now you can start to interpret it in terms of, you know Physical measures.

当然。

Absolutely.

没错。

That's right.

对。

Yeah.

物理量度。

Physical measures.

总之，我刚才有点自我放纵了，因为我知道你在问。

Anyway, that was that was me indulging myself because I I know you're asking.

不。

No.

不。

No.

是的。

Yeah.

谢谢，就像那种东西。

Thank like that sort of thing.

但回到你所说的，为什么不用贝叶斯推断呢？

But back to the, you know, why not just Bayesian inference?

最小化自由能和贝叶斯推断之间有什么区别？

And what's the difference between minimizing free energy and Bayesian inference?

很好的问题。

Great question.

如果贝叶斯模型证据仅仅是状态的边缘似然，那么人们可以简单地认为，只要优化我处于这种状态的似然性，这本质上就是我所做的，因为这就是我存在的方式，我就可以 trivially 地把自己描述为在进行贝叶斯推断，因为我只需将我的非平衡密度的负对数称为模型证据。

So if Bayesian model evidence is just simply the marginal likelihood of states of being, then one could trivially say just by optimizing the likelihood that I am in this state, which by definition is the thing that I do because that's how I exist, I could describe myself as performing Bayesian inference trivially so because I can just call the negative log of my nonequilibrium, so let's say, density model evidence.

因此，我所做的一切都是为了最大化模型证据。

And therefore, I do is in the service of maximizing model evidence.

我是决策的完美基础。

I'm the perfect basis of decision.

这并不能真正带你前进，但说起来挺不错的。

It doesn't get you anywhere, but it's a nice a nice thing to say.

变分自由能是从哪里来的？

Where does the variational free energy comes in?

变分自由能之所以重要，是因为它操作性地定义了所谓的近似贝叶斯推断。

Well, variational free energy comes in because it's operationally defines what's called approximate Bayesian inference.

那么，符合贝叶斯公式的贝叶斯推断与近似贝叶斯推断、变分贝叶斯，有时也称为集成学习，但变分方法可能是最技术准确的术语，它们之间的区别是什么？

So what's the difference between Bayesian inference that would conform to Bayes' rule and approximate Bayesian inference or variational Bayes or sometimes called ensemble learning, but probably variational basis is the most technically correct term.

区别在于你并没有最大化模型证据。

Well the difference is that you're not maximizing model evidence.

你是在最大化模型证据的一个下界，这意味着你可以测量的东西——即这种自由能变分或机器学习中的负值——在机器学习中总是低于你真正想最大化的目标，也就是你的模型证据。

You are maximizing a lower bound on model evidence, which means that the thing that you can measure, which is this variation of free energy or the negative in machine learning, now always a in machine learning, it's always below the actual thing you want to maximize, which is your model evidence.

如果我把这个式子反过来，回到物理学和自由能原理。

If I just flip this side and bring us back to physics and the free energy principle.

因此，模型证据的负对数——本质上是我们的自信息、我们的惊讶——可以始终通过最小化一个始终被证明更大的量来最小化，就像你是一个完美的贝叶斯统计学家一样。

So the negative logarithm of model evidence, which is essentially our self information, our surprise, can always be minimized as if you were a perfect Bayesian statistician by minimizing something that's always provably larger than that.

这就是KL散度或边界近似。

And that's the KL divergence or bound approximation.

因此，变分自由能是一个证据的上界。

So the variation of free energy is an upper evidence bound.

如果你最小化它，你就实现了近似的贝叶斯推断。

And if you minimize that, then you become an approximate Bayesian inference.

为什么是近似的？

Why approximate?

因为这个界限不一定为零。

Well, because the bound is not necessarily zero.

它没有达到饱和。

It's not saturated.

是的。

Yeah.

对。

Right.

但这样处理可能更容易。

But that might be easier to work that way.

这就是唯一的原因。

That's the only rationale for it.

是的。

Yeah.

因此，对实际证据的评估——如果你是物理学家，就是配分函数——在高维系统中变得无法处理。

So it's just that the evaluation of the actual evidence, a partition function if you're a physicist, becomes intractable in high dimensional systems.

那么，当你面对确实似乎能够实现这种过程的真实物理系统时，如何规避这种不可处理性呢？

So how do you elude that intractability when you've actually got real physical systems that would seem to be able to do this kind of thing?

嗯，你只需构建一个可处理的界限。

Well, you just create a tractable bound.

那是谁做的呢？

And who did that?

理查德·费曼。

Well, Richard Feynman.

这正是它的来源。

That's where it came from.

关于这一传统的某种解读中，还有一种俄罗斯式的解读，我们不会那样表述

On one reading of the legacy there's another Russian reading We wouldn't put it that

这么说，但没错。

way, but yes.

从物理学遗产的一种解读来看，这适用于自由能原理，当然也适用于机器学习。

On one reading of the legacy of physics for things like the free energy principle, and certainly machine learning.

这就是费曼的路径积分表述，它引入了变分界限的概念。

That's, you know, was Feynman's Pathological Formulation, which introduced the notion of a variational bound.

这种使用变分法的界限被证明始终大于你想要优化的目标值。

A bound that was using variational calculus was provably always greater than the thing you wanted to optimize.

所以你只需优化这个界限即可。

So you just optimize the bound instead.

你还会在经济学中遇到关于有界理性的精彩论述。

And you get into some nice rhetoric about bounded rationality in economics.

哦，明白了。

Oh, Okay.

是的，我听说过你对这个想法的思考。

Yeah, heard you thought of that.

但我认为这说得通。

But I guess it makes sense.

所以它并不是完全理性的。

So it's not perfectly rational.

它也不是精确的贝叶斯推断。

It's not exact Bayesian inference.

但它是可以实现的。

But it's doable.

它是物理上可实现的。

It's physically realizable.

这才是关键区别。

That's the key difference.

我们都不是拉普拉斯妖。

None of us is Laplace's demon.

当然。

Absolutely.

是的

Yeah.

这场对话的大部分内容——我认为这是有充分理由的——都是围绕代理或大脑展开的，偶尔也会提到恒温器。

So much of this conversation, and I think for good reason, has been in the context of agents or brains, occasionally thermostats.

但你是否希望更有雄心一点，讨论一下非平衡系统最小化自由能的普遍组织原则呢？

But you do want to be even a little bit more ambitious, right and talk about sort of a general organizing principle of non equilibrium systems to minimize their free energy.

这或许不仅与细胞和生物体的本质有关，还与它们的起源有关。

And maybe this has something to do not just with the nature of cells and organisms, but with their origin.

这么说安全吗？

Is that safe to say?

把这种雄心归于你，是否公平？

Is that a fair ambition to attribute to you?

最小化自由能有助于解释生命为何最初会诞生吗？

That minimizing free energy helps explain why life came into existence in the first place?

哦，是的。

Oh, Yeah.

你现在把我带出舒适区了。

You're taking me out out of my comfort zone now.

我在哪里说过这句话吗？

I say that somewhere?

它

It

可能是我。

could be me.

可能是我的镜片，因为我就是想这么做。

It could be my lenses because I want to do that.

啊，史蒂夫，你应该谈谈这个。

Ah, Steve, you should talk about that.

是的。

Yeah.

是的。

Yeah.

嗯，你知道的，好吧。

Well, you know, okay.

我们这么来说吧。

Let's put it this way.

你提到了马尔可夫毯。

You mentioned Markov blankets.

对吧？

Right?

这个想法是，事实上，宇宙中存在许多系统，它们与外界之间有着清晰的边界。

The idea of the you know, in fact, we have a bunch of systems in the universe that have a pretty clear boundary between themselves and the rest of the world.

对吧？

Right?

而这个边界调节着它们与外界的互动。

And this boundary mediates their interactions with the world.

细胞壁的出现显然是生命起源中最关键的步骤之一，而真正的细胞壁在精神上确实与内部和外部之间的概念性马尔可夫毯相似，尽管并不完全相同。

The appearance of cell walls is clearly one of the most important steps in the origin of life, and and a literal cell wall is is certainly similar in spirit, if not exactly identical to the conceptual Markov blanket between the inside and the outside.