BTW as a concrete note, you may want to sub in 15 - ceil(log10(n))
instead of just “15”, which really only matters if you’re dealing with numbers above 10 (e.g. 1000 is represented as 0x408F400000000000, while the next float 0x408F400000000001 is 1000.000000000000114, which differs in the 13th decimal place).
faul_sname
That makes sense. I think I may have misjudged your post, as I expected that you would classify that kind of approach as a “duct tape” approach.
Checking a number’s precision correctly is quite trivial, and there were one-line fixes I could have applied that would make the function work properly on all numbers, not just some of them.
I’m really curious about what such fixes look like. In my experience, those edge cases tend to come about when there is some set of mutually incompatible desired properties of a system, the the mutual incompatibility isn’t obvious. For example
We want to use standard IEEE754 floating point numbers to store our data
If two numbers are not equal to each other, they should not have the same string representation.
The sum of two numbers should have a precision no higher than the operand with the highest precision. For example, adding
0.1 + 0.2
should yield0.3
, not0.30000000000000004
.
It turns out those are mutually incompatible requirements!
You could say “we should drop requirement 1 and use a fixed point or fraction datatype” but that’s emphatically not a one line change, and has its own places where you’ll run into mutually incompatible requirements.
Or you could add a “duct tape” solution like “use
printf("%.2f", result)
in the case where we actually ran into this problem, in which we know both operands have a 2 decimal precision, and revisit if this bug comes up again in a different context”.
AGIs derived from the same model are likely to collaborate more effectively than humans because their weights are identical. Any fine-tune can be applied to all members, and text produced by one can be understood by all members.
I think this only holds if fine tunes are composable, which as far as I can tell they aren’t (fine tuning on one task subtly degrades performance on a bunch of other tasks, which isn’t a big deal if you fine tune a little for performance on a few tasks but does mean you probably can’t take a million independently-fine-tuned models and merge them into a single super model of the same size with the same performance on all million tasks).
Also there are sometimes mornings where I can’t understand code I wrote the previous night when I had all of the necessary context fresh to me, despite being the same person. I expect that LLMs will exhibit the same behavior of some things being hard to understand when examined out of the context which generated them.
That’s not to say a worldin which there are a billion copies of GPT-5 running concurrently will have no major changes, but I don’t think a single coherent ASI falls out of that world.
If you use ublock (or adblock, or adguard, or anything else that uses EasyList syntax), you can add a custom rule
lesswrong.com##.NamesAttachedReactionsCommentBottom-footerReactionsRow lesswrong.com##.InlineReactHoverableHighlight-highlight:remove-class(InlineReactHoverableHighlight-highlight)
which will remove the reaction section underneath comments and the highlights corresponding to those reactions.
The former of these you can also do through the element picker.
It strikes me that there’s a rather strong selection effect going on here. If someone has a contrarian position, and they happen to be both articulate and correct, they will convince others and the position will become less surprising over time.
The view that psychology and sociology research has major systematic issues at a level where you should just ignore most low-powered studies is no longer considered a contrarian view.
@the gears to ascension I see you reacted “10%” to the phrase “while (overwhelmingly likely) being non-scheming” in the context of the GPT-4V-based MAIA.
Does that mean you think there’s a 90% chance that MAIA, as implemented, today is actually scheming? If so that seems like a very bold prediction, and I’d be very interested to know why you predict that. Or am I misunderstanding what you mean by that react?
Do you want me to spoil it for you, do you want me to drop a hint, or do you want to puzzle it out yourself? It’s a beautiful little puzzle and very satisfying to solve. Also note that the solution I found only works if you are given a graph with the structure above (i.e. every node is part of the lattice, and the lattice is fairly small in each dimension, and the lattice has edges rather than wrapping around).
Can you give a concrete example of a situation where you’d expect this sort of agreed-upon-by-multiple-parties code to be run, and what that code would be responsible for doing? I’m imagining something along the lines of “given a geographic boundary, determine which jurisdictions that boundary intersects for the purposes of various types of tax (sales, property, etc)”. But I don’t know if that’s wildly off from what you’re imagining.
Fun side note: in this particular example, it doesn’t actually matter how you pick your direction. “Choose the axis closest to the target direction” performs exactly as well as “choose any edge which does not make the target node unreachable when traversed at random, and then traverse that edge” or “choose the first edge where traversing that edge does not make the target node unreachable, and traverse that edge”.
Edit: at least assuming that the graph is directed
So I keep seeing takes about how to tell if LLMs are “really exhibiting goal-directed behavior” like a human or whether they are instead “just predicting the next token”. And, to me at least, this feels like a confused sort of question that misunderstands what humans are doing when they exhibit goal-directed behavior.
Concrete example. Let’s say we notice that Jim has just pushed the turn signal lever on the side of his steering wheel. Why did Jim do this?
The goal-directed-behavior story is as follows:
Jim pushed the turn signal lever because he wanted to alert surrounding drivers that he was moving right by one lane
Jim wanted to alert drivers that he was moving one lane right because he wanted to move his car one lane to the right.
Jim wanted to move his car one lane to the right in order to accomplish the goal of taking the next freeway offramp
Jim wanted to take the next freeway offramp because that was part of the most efficient route from his home to his workplace
Jim wanted to go to his workplace because his workplace pays him money
Jim wants money because money can be exchanged for goods and services
Jim wants goods and services because they get him things he terminally values like mates and food
But there’s an alternative story:
When in the context of “I am a middle-class adult”, the thing to do is “have a job”. Years ago, this context triggered Bob to perform the action “get a job”, and now he’s in the context of “having a job”.
When in the context of “having a job”, “showing up for work” is the expected behavior.
Earlier this morning, Bob had the context “it is a workday” and “I have a job”, which triggered Bob to begin the sequence of actions associated with the behavior “commuting to work”
Bob is currently approaching the exit for his work—with the context of “commuting to work”, this means the expected behavior is “get in the exit lane”, and now he’s in the context “switching one lane to the right”
In the context of “switching one lane to the right”, one of the early actions is “turn on the right turn signal by pushing the turn signal lever”. And that is what Bob is doing right now.
I think this latter framework captures some parts of human behavior that the goal-directed-behavior framework misses out on. For example, let’s say the following happens
Jim is going to see his good friend Bob on a Saturday morning
Jim gets on the freeway—the same freeway, in fact, that he takes to work every weekday morning
Jim gets into the exit lane for his work, even though Bob’s house is still many exits away
Jim finds himself pulling onto the street his workplace is on
Jim mutters “whoops, autopilot” under his breath, pulls a u turn at the next light, and gets back on the freeway towards Bob’s house
This sequence of actions is pretty nonsensical from a goal-directed-behavior perspective, but is perfectly sensible if Jim’s behavior here is driven by contextual heuristics like “when it’s morning and I’m next to my work’s freeway offramp, I get off the freeway”.
Note that I’m not saying “humans never exhibit goal-directed behavior”.
Instead, I’m saying that “take a goal, and come up with a plan to achieve that goal, and execute that plan” is, itself, just one of the many contextually-activated behaviors humans exhibit.
I see no particular reason that an LLM couldn’t learn to figure out when it’s in a context like “the current context appears to be in the execute-the-next-step-of-the-plan stage of such-and-such goal-directed-behavior task”, and produce the appropriate output token for that context.
Easier question: Let’s say you have a single node in this graph of nodes. You want to figure out where that single node should be embedded in your 100-dimensional space, but you only care about its embedding location relative to a few specific other nodes.
You have the following affordances:
List the edges that originate at a node. The edges will always be returned in the same order for the same node, but the order is not necessarily the same for different nodes (i.e. the first edge may point along the 57th axis for one node and in the 22nd axis for a different node)
Given an edge, retrieve the node at the far end of that edge
Compare two nodes to see if they are the same node as each other
That is to say, if you have the following problem definition
import random class Node: key = None edges = None def __init__(self): self.edges = [] class Edge: _src = None _get_dst = None _dst = None def __init__(self, src, get_dst): self._src = src self._get_dst = get_dst def get_dst(self): if self._dst is None: self._dst = self._get_dst() return self._dst class Graph: def __init__(self, axis_length, n_dims): self.axis_length = axis_length self.n_dims = n_dims self._nodes = {} self._next_node_id = 1 def get_node_at(self, coords): axis_order = list(range(self.n_dims)) random.shuffle(axis_order) if coords not in self._nodes: node = Node() node.key = self._next_node_id self._next_node_id += 1 for axis in axis_order: if coords[axis] == 0: continue dst_coords = list(coords) dst_coords[axis] -= 1 dst_coords = tuple(dst_coords) def make_edge(dst_coords): def get_dst(): return self.get_node_at(list(coords)) return Edge(node, lambda: self.get_node_at(dst_coords)) edge = make_edge(dst_coords) node.edges.append(edge) self._nodes[coords] = node return self._nodes[coords] def get_random_node(self): return self.get_node_at(tuple([random.randint(0, self.axis_length-1) for _ in range(self.n_dims)]))
and you want a function which will take an arbitrary node and give you the coordinates of that node in a consistent basis in finite time with arbitrarily high probability of correctness
class ComputedBasis: def __init__(self): self.node_positions_by_key = {} def get_coords(node): # Given a node, give the coordinates of that node in some # consistent basis pass
I claim that this is indeed possible to do, and the steps to do it look nothing like “compute things”.
Edit: To be explicit about the motivation, once we define this function, we can find a path from our position to the sandwich using something like
def path_to_sandwich(my_node, sandwich_node): basis = ComputedBasis() my_coords = basis.get_coords(my_node) sandwich_coords = basis.get_coords(sandwich_node) for axis, (my_pos, sandwich_pos) in zip(my_coords, sandwich_coords): if my_pos < sandwich_pos: raise(f""" Can't get to sandwich from here! I can only travel towards the origin on each axis. axis: {axis} my_pos: {my_pos} sandwich_pos: {sandwich_pos} """) return get_path(basis, my_node, sandwich_node) def get_path(basis, start_node, goal_node): curr_node = start_node path = [curr_node] goal_coords = basis.get_coords(goal_node) while curr_node != goal_node: curr_coords = basis.get_coords(curr_node) # Find the first axis where we need to move towards the goal along that axis. for axis, (curr_pos, goal_pos) in zip(cur_coords, goal_coords): if curr_pos > goal_pos: step_coords = [p for p in curr_pos] step_coords[axis] -= 1 step_coords = tuple(step_coords) break for edge in curr_node.edges: dst_node = edge.get_dst() dst_coords = basis.get_coords(dst_node) if dst_coords == step_coords: step_node = dst_node break curr = step_node path.append(curr) return path
Note that my framing of the problem is slightly different, in that
(0, 0, 0, ..., 0, 0, 0)
is the point from which there are no outbound edges, rather than(10, 10, 10, ..., 10, 10, 10)
in your version. Doesn’t really make a difference logically, just makes the code more readable.
In that post, you say that you have a graph of vertices with a particular structure. In that scenario, where is that structured graph of vertices coming from? Presumably there’s some way you know the graph looks like this
rather than looking like this
If you know that your graph is a nice sparse graph that has lots of symmetries, you can take advantage of those properties to skip redundant parts of the computation (and when each of your nodes has at most 100 inbound edges and 100 outbound edges, then you only have on the order of a trillion distinct nodes (if we consider e.g.
(0, 0, 0, ..., 0, 0, 1)
to be identical to(0, 0, 0, ..., 0, 1, 0, ..., 0, 0, 0)
).It’s probably worth looking at the process which is generating this graph, and figuring out if we can translate the output of that process directly to a coordinate in our 100-dimensional space without going through the “translate the output to a graph, and then embed that graph” intermediate step.
I think the probability of getting the exact continuation “a a a a a …” is genuinely higher than the probability of getting the exact continuation “little girl who was born with a very special gift...”, though getting a continuation in the class of “a a a a a...” is much lower-probability than getting a continuation in the class of “little girl who was born with a very special gift..”, because the latter class has a much larger possibility space than the former. So there might be 1e4 different low-entropy length-32 completions with an average probability of 1e-10 each, and 9.999999e15 different high-entropy length-32 completions with an average probability of 1e-16. This adds up to normality in that if you were to randomly sample this distribution, you’d get a weird low-entropy output one time in a million, and a normal high-entropy output the other 999999 times in a million. But if you try to do something along the lines of “take the best K outputs and train the model on those”, you’ll end up with almost entirely weird low-entropy outputs.
But yeah, I think I misunderstood your proposal as something along the lines of “take the k most probable n-token outputs” rather than “take the k% most probable n-token outputs” or “randomly sample a bunch of n-token outputs”.
And I think one way to create a 2-token reasoner is to generate all plausible completions of 2 tokens, and then propagate the joint loss of the log-probs of those two tokens.
I think this just doesn’t work very well, because it incentivizes the model to output a token which makes subsequent tokens easier to predict, as long as the benefit in predictability of the subsequent token(s) outweighs the cost of the first token. Concretely, let’s say you have the input “Once upon a time, there was a” and you want 32 tokens. Right now,
davinci-002
will spit out something like[" little"," girl"," who"," was"," born"," with"," a"," very"," special"," gift","."," She"," could"," see"," things"," that"," others"," could"," not","."," She"," could"," see"," the"," future",","," and"," she"," could"," see"," the"," past"]
, with logprobs of[-2.44, -0.96, -0.90, ..., -0.28, -0.66, 0.26]
, summing to −35.3. But if instead, it returned[" a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"," a"]
, it would have logprobs like[-9.32, -7.77, -1.51, ..., -0.06, -0.05, -0.05]
, summing to −23.5. And indeed, if you could somehow ask a couple quadrillion people “please write a story starting withOnce upon a time, there was a
”, I suspect that at least 1 in a million people would answer with low-entropy completions along the lines ofa a a a ...
(and there just aren’t that many low-entropy completions). But “Once upon a time there was a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a” is not a very good completion, despite being a much higher-probability completion.
You could use a more sophisticated loss function that “sum of individual-token logprob”, but I think that road leads towards PPO (nothing says that your criterion has to be “helpful/harmful/honest as judged by a human rater” though).
Do you need to store information about each object? If so, do you need to do so before or after the operation.
If you need to store information about each object before processing (let’s say 1 bit per object, for simplicity), the Landauer limit says you need of mass to store that information (at the current cosmic microwave background temperature of 2.7ºK). That’s about a factor of more than the mass of the observable universe, so the current universe could not even store bits of information for you to perform your operation on in the first place.
I think if you’re willing to use all the mass in the universe and wait a trillion billion years or so for the universe to cool off, you might be able store one bit of output per operation for operations, assuming you can do some sort of clever reversible computing thing to make the operations themselves approximately free.
Is there some specific computation you are thinking of that is useful if you can do it times but not useful if you can only do it times?
Ideally one would want to be able to compute the logical correlation without having to run the program.
I think this isn’t possible in the general case. Consider two programs, one of which is “compute the sha256 digest of all 30 byte sequences and halt if the result is
9a56f6b41455314ff1973c72046b0821a56ca879e9d95628d390f8b560a4d803
” and the other of which is “compute the md5 digest of all 30 byte sequences and halt if the result is055a787f2fb4d00c9faf4dd34a233320
”.Any method that was able to compute the logical correlation between those would also be a program which at a minimum reverses all cryptograhic hash functions.
Your POS system exports data that your inventory software imports and uses. But I strongly suspect that this is often not possible in practice.
This sounds like exactly the sort of problem that a business might pay for a solution to, particularly if there is one particular pair of POS system / inventory software that is widely used in the industry in question, where those pieces of software don’t natively play well together.
The other baseline would be to compare one L1-trained SAE against another L1-trained SAE—if you see a similar approximate “1/10 have cossim > 0.9, 1⁄3 have cossim > 0.8, 1⁄2 have cossim > 0.7” pattern, that’s not definitive proof that both approaches find “the same kind of features” but it would strongly suggest that, at least to me.
Or to point to a situation where LLMs exhibit unsafe behavior in a realistic usage scenario. We don’t say