Intelligence

Cognitive Algorithm

2012-01-17T01:30:00.000-05:00

I define intelligence as an ability to predict & plan (self-predict) by discovering & projecting patterns. In other words, it’s a capacity for cognition, formalized as a hierarchical pattern discovery process. The algorithm implementing this process should start by cross-comparing quantized sensory input flow within a fixed range. Comparisons discover initial patterns, which are selectively forwarded to the next level for expanded search. Recursive comparison & selective elevation of input patterns on successive levels of search will discover increasingly general patterns or concepts. Higher levels generate downward feedback, ultimately a motor action, to focus on sources expected to be additively predictive for a target level.

Hierarchical approaches are pretty common, & many use some sort of pattern recognition. But none that I know of attempts to implement a strictly incremental growth in scope & complexity of discoverable patterns. This is critical for efficient scalability because it allows for input selection at each increment. Without such selection, by theoretically derived criteria, a combinatorial explosion in potential search space is inevitable.

Most people find my writing on the subject “obtuse”, - that‘s not for the lack of effort. For a more gentle & contextual introduction see “On Intelligence” by Jeff Hawkins, but… it’s also more shallow & confused. I am actually pretty good at explaining normal things, but formalized intelligence must be a generalization of our entire experience. This requires an extreme “generalist mindset“: encyclopedic theoretical curiosity from the young age, followed by a full-time sustained effort at intuitive introspection, combined with progressive rigorous deduction from the results. It can’t be done as a hobby: many people, otherwise quite accomplished in superficially related fields, are reduced to piecemeal trial & error by the vast scope of this problem.

Contents:

1. Cognition vs. evolution: algorithmic perspective
2. Comparison: quantifying match & miss per input
3. Search: incremental range & derivation of comparisons
4. Patterns: syntactic expansion & re-integration
5. Feedback: selection by higher-level aggregate representations
6. Hierarchical short-cuts: selection by downward expectations
7. Notes on a working mindset & a prize for ideas

1. Cognition vs. evolution: algorithmic perspective.

We know one mechanism that produced a human-level intelligence: biological evolution.
Initially algorithmically very simple, the evolution alters heritable traits at random & selects those with above-average reproductive fitness. But, evolution is horribly　inefficient because selection is extremely coarse: on the level of a whole genome rather than individual traits, & also because intelligence is only one of many factors for reproductive fitness. And obviously, there’s nothing intelligent about random variation.
Unlike any evolutionary algorithm, I think cognitive process should be altered solely by the data: environmental stimuli, incrementally generalized into patterns, & then into algorithms. These categories differ only in the degree of discovered recurrence (generality).

If intelligence is an ability to predict, then cognitive fitness function is predictive correspondence of recorded inputs: their cumulative match to future inputs. We have no direct knowledge of the future, so predictive correspondence must be estimated by criteria that are found to be correlated with it.
To maintain efficiency of search, input selection should start at the highest level of resolution: single-variable inputs, such as pixels in case of vision. On this most basic level, predictive correspondence can only be estimated by past matches of these variables. I’ll try to show how more complex & refined criteria can be discovered on higher levels of search, & applied as a feedback to the lower levels.
Such “recursively self-improved” input selection should allow for scalable search expansion, where newly discovered predictive correspondence grows in proportion with the quantity of searched inputs.

A popular attitude in AI is that intelligence can be recognized but not defined. That seems absurd to me: recognition *is* a match between an input & a definition. Some researchers agree with my definition, but all neglect to apply it as a criterion for bottom-up development. I believe this lack of theoretical integrity is a main reason for the failure to scale, even in principle, in all AI/ AGI attempts to date.
Hence a dire scarcity of references in this blog. Everything ever written is somehow related to my subject. But, generalization is a reduction. And cognitive algorithm is a meta-generalization, which demands an utterly ruthless reduction. Unfortunately, I am yet to come across any approach sufficiently consistent with the principles outlined here to be a non-obvious foundation for mine.

My presentation here is self-contained: strictly & formally bottom-up, thus can be understood without references. But that would require relinquishing assumptions from any higher-level approach. I will try to address two of the closest: Algorithmic information theory & Bayesian inference, which use the same criteria as mine: compression & inductive prediction (future compression). A good introduction is Philosophical Treatise of Universal Induction by S. Rathmanner & M. Hutter.

While a progress compared to static “frequentist” probability, both BI & AIT still assume a “prior”, which doesn’t belong in a fully inductive approach. The attempt to introduce “universal prior” led to Solomonoff’s infinite “class of all models”: he hits combinatorial explosion even *before* receiving any inputs. That’s a “solution” only a mathematician may find interesting. I don’t think there is a hard distinction between experience & prior models / hypotheses. The “models” are simply past inputs, as well as correlations discovered by comparing them via inverse arithmetic operations. A distinct environmentally specific (non-AIT) class of priors could be a short-cut vs. unimaginably long learning process necessary for an autonomous cognitive algorithm. Yet, independent learning is the very essence of general intelligence, & “imagining” execution of the process is superfluous for its design.

Also perverse is binary resolution of initial inputs in BI & AIT: confirmation / disconfirmation events. In reality, expectations are rarely matched or missed precisely, so the degree of confirmation must be quantified for individual events. Quantifying partial match would add a micro-grayscale to the binary value of events in Bayesian prediction, just like the latter added macro-grayscale (partial probability) to binary (true| false) predictions of classical logic.
Besides, the events are assumed to be high-level concepts, the kind that occupy our conscious minds. But a scalable search algorithm must start from sensory data processing that’s subconscious for us, rather than depend on human preprocessing. So, this definition of initial inputs in BI & AIT already shows a total lack of discipline in incrementing complexity: a fatal fault for any attempt at scalability.
There’re plenty of other loosely & sloppily incremental approaches to AGI, but the “incremental” part always seems to be an afterthought. Coarse & arbitrary increments in the scope of search miss the opportunity for intermediate selection, which leads to unproductive comparisons. This inefficiency is multiplied at each increment, of which a general intelligence must have an indefinite number. Even a very minor inefficiency per step will result in predominantly “junk” searches after a million iterations.

I propose a strictly incremental inductive approach: search must start with minimal-complexity inputs & proceed with minimal-complexity increments in scope & syntax for selected inputs. There is always *one* best next step: an additive complexity cost that brings the greatest additive predictive value:

2. Comparison: quantifying match & miss per input.

It seems obvious to me that all our non-combinatorial knowledge is ultimately derived from senses. The "symbolic" data is implicitly encoded by the “neural algorithm” that derived it, & understanding this algorithm should be exponentially easier than automating further generalization without decoding the source. Thus, initial inputs for generally intelligent algorithm should be context-free: un-encoded or analog, such as those received by senses. Basically, if we can’t do it there, we can’t do it anywhere.

“Cognitive” purpose of processing inputs is to predict future inputs, where prediction is quantified as a match of an input to the expectations. In a non-random environment, the most basic expectations are simply older inputs, & their estimated predictive value is past average match among adjacent inputs. Subsequent individual matches refine expectations of future matches for a given input. I define match per comparison as a reduction (compression) of recorded magnitude by replacing a larger comparand with its derivative (miss) relative to a smaller comparand. Magnitude is a main criterion here because it represents physical values that we want to predict. Coincident compression | expansion of used record space & processing time affects the costs, but not the benefits, of comparison & prediction.

Given incremental complexity of representation, initial inputs should have binary resolution. However, average binary match won’t justify the cost of comparison, which adds a syntactic overhead of newly differentiated match & miss to positionally distinct inputs. Rather, these binary inputs are compressed by digitization: a comparison across sequentially formed levels of scale, forming integers represented as a hierarchy of digits. Digitization is performed on all inputs within a shared coordinate. Resolution of such coordinate is defined by feedback, to form integers that are large enough for an average match between them to merit the above-mentioned costs of comparison (match is a subset of magnitude).

Hence, the next order of compression is comparison across coordinates, initially defined with binary (before | after) resolution. Comparison forms signed derivatives, complemented by which new inputs can losslessly & compressively replace older templates. At the same time, current input match determines whether individual derivatives are also compared (vs. aggregated), forming successively higher derivatives. “Atomic” comparison is between a single-variable input & a template (older input):
Comparison: match= min (input, template), miss= dif (i-t): aggregated over the span of constant sign.
Evaluation: match - average_match_per_average_difference_match, formed on the next search level.
Actually, evaluation can be increasingly complex, but I will need a meaningful feedback to elaborate.

Any comparison is an inverse arithmetic operation of incremental power: Boolean AND, subtraction, division, logarithm, & so on. Binary match is a sum of AND: partial identity of uncompressed bit strings, & miss is an offset. Binary comparison is useful for digitization, but it won’t further compress the integers produced thereby. This is a common principle, the products of a given-power comparison can be further compressed only by a higher-power comparison between them.
Thus, subsequent comparison between integers is done by subtraction, which increases match by compressing miss from offset to difference, in which opposite-sign bits cancel each other via carry. The match is increased because it is a complimentary of difference, equal to the smaller of the comparands.

Division further reduces difference to a ratio, which can then be reduced to a logarithm, & so on. Thus, complimentary match is increased with the power of comparison. But the costs may grow even faster, for both operations & incremental syntax to record incidental sign, fraction, irrational fraction. The power of comparison is increased if current match & miss predict further improvement, as determined by higher-order comparison between the results from different powers of comparison. This forms algorithms or meta-patterns. Again, I’ll need a constructive feedback to elaborate on the mechanism.

Note that in my approach, the relation of input’s resolution to its position’s resolution on 1D level is reversed from corresponding relation used in algorithmic information theory & Bayesian inference.
Transformation (as in Fourier transform) from input values to their derivatives is a basic compression method for positionally differentiated data. But it can’t scale without evaluation & selection of inputs (starting from pixels) for incremental expansion in range & power of comparison (transformation):

3. Search: incremental range & derivation of comparisons.

Assuming that the environment is not random, average match will decline with the distance: older templates are decreasingly predictive of future inputs. To maintain proximity to future inputs, the queue is FIFO: the oldest template is displaced by a new input & becomes an output. Along with declining match, continuous search span (number of templates in a queue) is also limited by the cost of increasing redundancy in representation of derivatives (match & miss). Aggregated derivatives are redundant to compared templates & their derivatives, to the extent of overlap in their aggregation span. Length of a queue is limited by the distance at which these costs exceed match for average comparison.

Queue’s outputs are evaluated for extended search on a higher-level queue, which must increasingly selective to avoid combinatorial explosion. Selection criteria are partial aggregated representation of a target queue, formed by adding corresponding variables of its inputs & subtracting the outputs.
The most basic criterion is an average match, multiplied by redundancy in representation of the output. I’ll expand on increasingly complex & predictive selection criteria in the “Feedback” part. Evaluation is a comparison of selection criteria in an output, to those in aggregated representation of a target queue: the output is selected as input to the higher level if the formed are greater than the later.

Non-selected outputs are aggregated within a minimal span: between individually represented outputs, or a maximal span, which increases aggregated magnitude to a value that forms an average match in a higher-level comparison. Match is limited by (& crudely correlates with) the magnitude of comparands. Thus, a higher queue will consist of selected discrete templates, interlaced with aggregated templates. Even though the magnitude of the later is increased, any higher-resolution matches within aggregation span are lost, & variable span makes comparison between aggregated templates more difficult. Partial aggregation among outputs expands coordinate span for a higher level queue of a fixed length.

Copies of non-selected outputs can also be stored in longer-term buffers, to delay the loss of detail. Such buffers are implemented in slower & cheaper media (tape vs. RAM), with possible compression by non-selective transforms, & multiple stages for parallel access. The buffers are accessed only if higher-level patterns that represent buffered templates at a lower resolution become strong enough to justify increased resolution, or if new inputs get relatively “close” to the buffered templates again.

For those with ANN background, I want make clear that each level of search here is 1D queue, not a 2D layer of ANN. Adding a single 1D -expansion at a time allows for incremental selection to compensate for the cost of each coordinate, & correspondingly more efficient scaling of search. So, while internally represented dimensionality of input patterns is increasing, their external order remains a 1D sequence. Also, dimensions are added in the order of decreasing rate of change therein. This means that spatial dimensions (with controllable rate) must be scanned first, while comparison over purely temporal sequence is delayed until accumulated variation within it justifies search for additional compression.

These principles are not empirically specific, but our practically universal primary environment is a spatio-temporal continuum. Here, initial levels should be incremental dimensions of search, & that of resulting patterns: 0D ) 1D ) 2D ) 3D ) TD. Each additional dimension requires its own coordinate, increasing the costs of “syntactic overhead”. This implies incremental selection: the inputs for search on higher dimensions must have greater projected match, capable of bearing additional costs. Initial dimensional definition is binary: before| after, integer-level relative coordinates are only needed to represent discontinuity between inputs, produced by their selective representation on higher levels.

Sequential increase of dimensionality can be traced in most biological senses. In vision, original stimuli are aggregated into 0D “pixels” of brightness, represented by each rod or cone cell in the retina. Output here is a spike train produced by accumulate- &- fire, which in functional terms performs digitization. All of these cell "scan" in the same direction of eye tremor or a saccade, receiving 1D queue of inputs. Some form of “comparison” over this queue might also be done within each sensor cell, or its 1D axon. 2D would be integration of 1D outputs of sensor cell across retina, then LGN, & primary visual cortex. 3D is formed by integration across ocular dominance columns in V1|V2, colors are integrated in V4, & temporal sequences, probably in V5 (MT) & beyond.
Even higher levels should process search & integration across sensory modalities, & then over increasing spatio-temporal distance between multi-modal & multi-dimensional patterns.

My approach may seem similar to Levin Search, but the latter randomly generates algorithms of incremental complexity, & selects those that happen to solve a problem or compress a bitstring. What I proposed is a search for patterns within environmental input flow. Cognition must start with empirical data, pure math becomes cost-efficient only on much higher levels of generalization. In any case, a hard distinction between input patterns & algorithms only makes sense in the context of special-purpose programs. It fades away if the algorithms are seen as simply incrementally complex short-cuts to pattern discovery, themselves discovered by search across derivatives produced by prior comparisons. “Search” may sound too simple, & working intelligence is obviously very complex. But, given a general fitness function, incremental complexity is discoverable by higher-order comparisons:

4. Patterns: syntactic expansion & re-integration.

A pattern is simply a higher-level input, I use a different term here just to emphasize their increasing predictive value & internal complexity. Every level of search potentially adds a new layer of syntax to an input: selected (initially all) variables of an input are compared, which “splits” into new derivatives: match & miss. These derivatives are either aggregated between comparisons or, in special cases, also individually compared. As with templates, minimal aggregation span is between individually compared derivatives, & maximal span is determined by average magnitude (thus match) of these derivatives on a higher level. Hence, a basic comparison cycle generates queues of interlaced individual & aggregated derivatives at each template variable, & conditional higher derivatives on each of the former.

I use “syntax” to mean identification of different variable types by their position (syntactic coordinate) within a pattern. This is analogous to recognizing parts of speech by their position within a sentence.
Initial variable types are different stimuli (such as different colors in vision), of corresponding senses (modalities). Subsequently, quantized inputs of each stimuli type are compared across the sequence of prior inputs, & then across incrementally higher spatial dimensions, as explained above.
Beyond original modalities & dimensions, comparisons & evaluations during search generate an indefinite number of secondary variable types. Such extended syntax records conditional operations that formed each variable, to cross-translate the variables for future comparisons & evaluations.

So, each basic comparison “splits” an input variable into two higher-order variables: relative match (m) & miss (d) between an input & template. Both of them are signed, as well as aggregated across multiple comparisons within the length of a constant sign: L(m) & L(d). Relative match determines comparison vs. aggregation for individual differences, forming additional queue of ds within each positive L(m).
On the following levels of search, same-type derivatives are also selectively compared between patterns. This generates secondary derivatives over greater distance, &|or over different types of coordinates. Such syntactic expansion is pruned by selective representation of variable types in each input, vs. their aggregation within a lower resolution syntax, coordinate, or magnitude.

A sufficiently complex syntax will justify comparing variables within a pattern & across a “syntactic“ coordinates, analogous to comparison across external coordinates. In fact, that’s what happens with higher-power comparisons. For example, division is an iterative comparison between a difference & a match, - across the order of derivation. Next, there should be selective comparisons across increasing syntactic discontinuity. For example, comparison of lengths: L(m) & L(d), across different dimensions within a multi-D pattern will compute potentially recurrent dimensional proportions.
Internal comparisons can further compress a pattern, but at the cost of adding a higher-order syntax, which means that they must be increasingly selective. This selection will increase “discontinuity” over syntactic coordinates: operations necessary to convert the variables before comparison.

At some point, these operators will become “large” enough to merit direct comparison / search among them. This will produce purely algebraic equations, where the match (compression) is a reduction in the number of operations needed to produce a result. The first such short-cut is probably a version of Pythagorean theorem, to be discovered during search in 2D as a way compute cosines. Cosines are necessary to normalize lengths: L(m) & L(d), initially in 1D, to a value they would have in an orthogonal “subjective” angle of 1D scan lines. Basically, while comparing 1D Ls (adjacent in 2D) by division, across an angle (1D distance & its derivatives), the algorithm should discover a relatively constant ratio between the ratio of 1D Ls & a second derivative of 1D distance. That ratio is a cosine, & resulting normalization for POV change is so basic that it might’ve evolved & is genetically encoded in animals.

The patterns I described are not qualitatively different from our largely intuitive semantic concepts, - most them are generalized empirical objects & processes. Given sufficient computational resources (combined with autonomously discoverable mathematical shortcuts), the search over incrementally complex derivatives should discover patterns / concepts on & beyond the level of natural language. Combined with the distances, derivatives can form “motor” feedback vectors that select sources (location & resolution of future inputs) projected to maximize predictive correspondence of a target.

5. Feedback: selection by higher-level aggregate representations.

This chapter will expand on the principles of selecting inputs for the next level of search by feedback. The most basic feedback is aggregated representation of selection criteria in a feedforward: inputs to the next level queue. Whole-queue representation may also contain averages of other input variables, for preliminary comparison, but that will have lower value than selection of an input as a whole.

As proposed above, the outputs are initially selected for extended search by their accumulated match, minus the average (normalized aggregate) match on the higher level, which is multiplied by the redundancy of output’s prior representation there. This selects for generality, or invariance in terms of Jeff Hawkins (in “On Intelligence”).
He also suggests selection by novelty, but that would be mutually exclusive with generality. The scope of discovered generality is limited by the span of experience searched by an input, & the longer it searches (especially over the following inputs) the less “novel” it becomes. Any pattern is defined by some sort of repetition, so prioritizing novelty per se would simply select for random noise.

Generality must be the ultimate criterion, but incrementally more abstract types of correspondence (which defines generality) are “novel” relative to the lower ones. The most basic form of such apparent novelty-seeking, that actually increases predictive power, is simply a preference for more recent inputs.
Recent inputs are relatively more predictive than the older ones because of their temporal proximity to future inputs. Thus, proximity should determine the span of search within a level of generality. But it can’t select for hierarchical elevation: search expansion increases the distance among comparands. Selection for proximity is implemented via FIFO design of template queues, see the “Search” chapter.

A higher form of such coincidental novelty is change, or the difference between S-T proximate inputs. Difference is an alternative representation of a comparand, but its association with match may make it stronger than the original one. Strong enough difference is compared to a queue of other selected or aggregate differences between the same template & other comparands, & then evaluated as an output. Evaluation is subtraction of target queue’s average difference, which indicates the trend for subsequent inputs. This subtraction forms relative difference, similar to relative match.

Value of output template in projected for a target queue by “recombining” it with co-derived difference, which is also projected: multiplied by its relative distance to an average coordinate of a target queue. Projection of a difference “competes” with that of a template, so both must be adjusted proportionally: projected_template = template + average_distance * relative_difference * aggregate difference / match.

So, the two most basic selection criteria are unique relative match & projected relative difference. These are initial derivatives (match & difference), minus corresponding averages (normalized aggregates) of a higher level. What makes selection more complex than simple comparison is the necessity to adjust (multiply) the averages by newly formed parameters: redundancy for match & distance for difference. These new parameters are products of prior input selection, which increases redundancy of a potential new input, or prior input aggregation, which increases coordinate span of a target queue.

Again, difference is primarily an alternative representation for compared template. Hawkins proposed that a main value of change | contrast is its “novelty”, but from my perspective that value is negative: contrast cancels positive predictive value of an interrupted pattern. The value here is not independent, but “borrowed” from the pattern. There’s plenty of “change” within random noise, but it has no value because there’s no pattern to be interrupted. So, selection by contrast is partial cancellation of a pattern by co-derived negative vectors, proportional to relative strength of difference vs. that of the match.

Further notes on Hawkins, semi-related to this chapter:

In Hawkins' HTM model (as in many conventional ANNs) match per pixel is defined with binary resolution, making evaluation meaningless. There is also no selection per 1D line of pixels, which would reduce complexity before adding higher dimensions. I guess he sees no need or opportunity for that because he doesn’t even “see” explicit coordinates. Hawkins begins selection by evaluating match between 2D frames: the level of complexity that leads to combinatorial explosion almost immediately (on the 4th layer of his ANN). Also, he arbitrarily ignores derivatives (0D miss), as well as coordinates & distances (1-4D miss). These parameters are necessary to form vectors, without which pattern prediction must remain extremely crude. I think such externally & internally coarse comparison & selection is the reason why HTM & similar RNN models don’t scale.

6. Hierarchical short-cuts: selection by downward expectations.

In addition to selection by representation of the next level, the output may also be filtered by direct feedback from the levels beyond the next. Such higher-level feedback is what we call “expectations”. Just like feedback from immediately higher level, these short-cuts select inputs for their additive generality, but with potentially higher derivation for average (expected) matches & differences. Expectations represented by a higher-level short-cut have correspondingly increased range.

A common objection to having predictive correspondence as a fitness function of intelligence is that it would keep you “staring at a wall”: lock into predictable environments. We tend to do the opposite, - skip over too predictable locations, thereby reducing match of new inputs to known templates. But, I submit, that’s because we maximize projected (higher-level) rather than current correspondence. The value of expectation is negative for potential inputs because confirmation is redundant, - predictive value of higher level templates will only increase (decrease) to the extent that the match (miss) is unexpected. Thus, expected match to higher level represented by a short-cut is a form of redundancy.

Downward suppression of locations with expected inputs will result in preference for exploration & discovery of new patterns vs. confirmation of the old ones. This is the opposite of upward selection for stronger patterns, but this “sign reversal” in selection criteria is a basic feature of feedback, - this also holds for subtracting the average, redundancy, & projected differences, explained in previous section.

Focus on unknown locations is different from the elevation of unexpected, as suggested by Hawkins, because all outputs of a given location are equally suppressed by expectations. In relative terms, stronger patterns within a location (continuous search span) still win over the noise (weaker patterns). Expectations can’t be pattern-specific on a lower level because individual patterns would be “out of range” there. Basically, a range of search is what defines a level & its syntax. Thus, lower levels simply don’t have the syntax to represent the origin of higher-level patterns, & will “mistake” them for the local ones. Note that my interpretation is in agreement with the consensus in neuroscience that cortical layer-I feedback is modulatory in nature, rather than containing “driving“ inputs as Hawkins proposes.

Of course, human curiosity is not purely cognitive, it is biased toward a survival value of information. Proximate & changing objects are more likely to affect a subject in a short term, thus attracting far more attention than they would for their immediate contribution to predictive power. That should also be the case for a purely cognitive system with enough introspection: it will seek impacts | materials that could buildup its predictive capacity, & avoid those that threaten it. Maximizing cognitive capacity will increase predictive correspondence of self-representation, rather than that of external representation. But longer term, it will increase external predictive correspondence more than direct pursuit thereof.

“Seeking” in the above describes both modulatory feedback downward a hierarchy of representations, & a motor feedback as a modulation of sensors / actuators “below” that hierarchy. Modulation is an adjustment of scope & resolution for both coordinates & sensitivity of lower-level sources. The scope (temporal & spatial) is defined in units of resolution for corresponding coordinates, which is adjusted (reduced) in proportion to the variation in local output flow.
Higher types of curiosity, which I formalize as a higher-syntax selection criteria, maximize more abstract forms of correspondence. Any representation can be seen as a partial & mediated form of reproduction, & such “abstraction” is what distinguishes any cognitive process from biomorphic evolution that maximizes “direct” reproduction.

7. Notes on a working mindset & a prize for ideas.

The algorithm of intelligence is a meta-generalization of entire cognitive experience, “lossy” in proportion to its vast scope. Such inductive lossiness is an anathema to deduction-oriented culture of math, computer science & artificial intelligence. I think this culture is largely responsible for barely detectable progress in theoretical understanding of cognition, hence AI’s focus on narrow tasks.

Many researches believe that AGI is a mathematical problem. I think that’s is a "man with a hammer" syndrome. Cognition is an incremental problem, - intelligence is a matter of degree. Higher math can accelerate learning, but is not necessary to initiate it on a human level, - cavemen didn’t do calculus.
Many more think it’s an engineering problem. As with math, it depends on how you define engineering. But there is an obvious trade-off between theoretical scope & practical certainty. General intelligence is an ultimate extreme of former, while any conventional engineering heavily favors the latter.
At a higher level, scientific approach to the problem is cognitive psychology. It’s far more intuitive in the way that theories are formed, but these theories must then be confirmed by high-level observations. That’s also too coarse & slow to produce a noticeable progress.

It seems obvious to me that AGI is a meta-scientific problem, requiring more theoretical (detached from immediate verification) attitude than what’s acceptable in any established field. The method here must be introspective generalization, plus understanding of unconscious low-level sensory information processing. Conceptually, it’s a province of philosophy, but philosophy is a clearly dysfunctional field. That’s not entirely surprising, - its main source of income are clueless freshmen, who replaced equally clueless aristocratic highbrows. Anyway, no one seems to be enough of a generalist. We didn’t evolve for this level of introspection, - there was no way to implement the results. Now we have computers, but human psychology is largely stuck in the farming age, if not retreating to hunter-gatherer age.

So, that’s my excuse for the lack of credentials: none are sufficiently relevant & I don’t have time to waste. What I do have is a far more advanced work-in-progress, but　will need a meaningful feedback to elaborate. Will appreciate specific questions, pointers to flawed logic or complimentary approaches.

Lots of people think that a major problem in AI is a lack of funding. I disagree, Einstein didn't need to be paid to work on his theory. Real science (especially theoretical) is driven by curiosity, & that should be even more true of meta-science. Anyway, I made a few bucks on my investments & want to put the money to work. If you're interested in scalable complexity pattern discovery, here's an incentive:

I offer prizes from $100 to $100,000 for the ideas that refute, correct, or further develop principles explained above. $100 could be a "consolation prize" for ideas that I already incorporated but did not fully explain here, or that are largely cosmetic in nature. $100,000 is for a major advance, - there won’t be many. A winner will have an option to convert his prize into an interest in all commercial applications of a final algorithm, at the rate of $10,000 per 1% share. This would be informal & likely unprofitable, - mine is not a commercial enterprise. Again, I don't believe money can be primary motivation here, but it may help a bit & has a way of attracting attention.

So far, - one winner: Todor Arnaudov, thank you very much! His idea seems obvious in retrospect (they always do), - simple buffering of old inputs after search. The "buffer" is accessed if the inputs' location gets relatively "close" again. It occurred to me more than once before, but I rejected it as redundant to potential elevation of those same inputs. Now that he made me think about it again, & stuck to it, I realized that partial redundancy can be justifiable. Buffering is much cheaper than elevation, & could be done in parallel to delay the loss of detail. It didn’t feel right because neocortex has no substrate for passive storage, but that should not matter here. The prize was $600, would've been higher, but... there was a problem with signal-to-noise ratio :). Well, it's a start (May 2010).
Todor also won $400 consolation prize for understanding some basic principles that weren’t clearly explained here. (September 2011).

Discussions with Ben Geortzel on AGI list

2012-01-07T13:08:00.000-05:00

Some of my replies are edited for clarity:

Ben,

The reference to 1D seems strange, since the physical world is
generally understood as 3D,

It's 4D, but that's our physics. General intelligence must be able to operate in any-dimensional space. I start with 1D because dimensionality (as well as any other form complexity) must be *incremental*. Search in higher dimensions adds syntactic cost, & we need to *select* inputs capable of bearing that extra cost.

and retinas are generally approximately
understood as 2D arrays ... care to clarify?

It's 2D, but that's not the first level of processing. Eye tremor makes each rod | kone *see* & interrelate a largely horizontal scan line of inputs. Interaction among these cells can be interpreted as subsequent integration of these scan lines in 2D. But, as anywhere else in biology, there's a lot redundancy & evolutionary artifacts in retina, so I don't see it as model.

Are you just saying that the same algorithm would apply to 1D retinas
as to 2D retinas, so you want to test it in the simpler 1D case first?

Every level is a simpler "test" before the next level, but primarily for inputs rather than algorithms. In my model 1D (horizontal scan line) search generates 1D patterns, which are selected & then compared in 2D (vertically) on a higher level, forming 2D patterns. The comparison algorithm is largely the same, but 1D patterns have mulitple additional variables (length & derivatives). Each variable is compared independently, & the results are then integrated within a pattern. And so on in higher dimensions.

All of this is in the knol :).

& selectively generate higher levels from the
results. Well, it actually starts from binary inputs & digitization thereof,
but its harder to see how this relates to the rest of the algorithm. Colors
& so on, as well as spatial dimensions & hardware details are not part a
core algorithm, - those are sensor / empirically specific & learnable,
though you can add short-cuts manually. We need to understand the core
algorithm *before* we can develop useful add-ons.

Any less incremental, & you lose opportunity for intermediate selection,
which leads to less efficient search.
Of course the cost of doing the selection intelligently, must always
be balanced against the cost of having more possibilities survive the
selection.... But indeed it's important to have the potential for
selection at all levels in the perception processing hierarchy, as
needed...

Selection is what intelligence is all about.

Boris.

Ben,

>> In my approach, there's only one right way to get every detail, that's
>> why I call it a theory.
>> Boris.
>
> Strange statement...
> For example, aerodynamics is a real theory (better established than
> anyone's theory of AGI), yet it admits multiple possible ways of
> creating flying machines... with rather large differences between them
> !!

All analogies are flawed, - it's a lazy way to think.

> (There may be one optimal way of creating a flying machine, given a
> certain set of well-specified constraints on the flying machine, where
> optimality is defined as minimum-energy or some such. But,
> aerodynamic theory as yet gives us no way to find this kind of optimal
> flying machine design...)
> So why should a theory of intelligence admit only one possible design
> for a thinking machine?

I didn't say possible, I said right way: directly derived from the way you
define a problem. A theory of intelligence is different because it's
supposed to be general, - context-free. At least the very core of it, which
should be a starting point anyway. Again, you can add environmentally &
application- specific adaptations latter, but the core algorithm must, in
principle, be able to learn them on it's own.
That's the very meaning of "general", as opposed to any empirically-specific
theory.

> I don't grok your theory of theories ;p
> ... ben g

It's a meta-theory, not a garden-variety kind :).
Boris.

Ben,

> I think the learning/teaching approach is, to some extent, a separate issue from the system architecture and algorithms.

You can make it separate, but that would be a waste.

> ...DeSTIN and also Itamar's proprietary HDRN system are already applied in that manner...

Right, I keep hearing that. It's supposed to be a top secret, but half of what I've seen is incompatible with my approach, & your difficulties understanding the later suggest that so is much of the rest.

> I'm unconvinced that this is the best way to have one's AGI system learn.

> But, I do think one should build an AGI system **capable** of learning in such a manner,

> even if for practical expediency reasons one chooses a different sort of world-interfacing approach...

It is conceptually the simplest & the most fundamental way, any short-cuts should be an add-on.

> Some folks, like my friend Itamar Arel, seem to think all of abstract cognition can be gotten to emerge
> from this sort of perception / action / reinforcement focused architecture.

> According to my best understanding, you and Boris K share this general perspective

The fact that he needs additional action & reinforcement hierarchies suggests that his perceptual hierarchy is fundamentally deficient.

> I'm not so sure, I suspect other stuff may be required too...

Well, lets start from the basics, you can't avoid that anyway, right?

> I don't mean to be dismissive when I refer to "details" --- getting
> the details right is going to be critical to making a thinking machine work.

> And there may be many different ways of getting the details right...

In my approach, there's only one right way to get every detail, that's why I call it a theory.

Boris.

> Essentially every proto-AGI architecture contains some component that does compression in an incremental and selective way, e.g. DeSTIN and MOSES certainly do...

> those are broad constraints that don't really say that much about how to do compression or pattern recognition...

　

These are broad constraints for “broadly“ incremental approach. My approach is strictly incremental, - that’s not a “constraint“, it’s a direct determinant of what is being compared (=compressed) & how. There’s only one place to start: pixels, & only one way to go from there: compare them in 1D, & iterate from there. Well, it actually starts from binary inputs & digitization, but that’s harder to relate to the rest of the algorithm.

Any less incremental, & you lose opportunity for intermediate selection, which leads to less efficient search & then combinatorial explosion.

From: Ben Goertzel

Essentially every proto-AGI architecture contains some component that does compression in an incremental and selective way, e.g. DeSTIN and MOSES certainly do... those are broad constraints that don't really say that much about how to do compression or pattern recognition....

In 1993 I wrote about the internal network of a mind as a dynamic "dual network" with linked (and co-evolving) hierarchical and heterarchical structures. The hierarchical network provides incremental pattern composition, the heterarchical network provides associational selection. Each network must be associated with appropriate learning algorithms. That was a long time ago and my AGI design is much more sophisticated now, but it's a similar principle...

ben g

On Mon, Dec 19, 2011 at 2:59 PM, Boris Kazachenko <bkazz@verizon.net> wrote:

> That is also rather obvious.
Show me where it's explained.
From: Ben Goertzel
Sent: Monday, December 19, 2011 1:56 PM
To: AGI
Subject: Re: [agi] Intelligence as a cognitive algorithm.

On Mon, Dec 19, 2011 at 1:37 PM, Boris Kazachenko <bkazz@verizon.net> wrote:
> Hmm, I had a formal definition of a "pattern" in 1990 or so, that's not the hard part ;p ...
OK, a "compressed representation" is rather obvious, I meant that compression must be defined as an incremental & selective process.
That is also rather obvious ...

And I don't mean "AIT-incremental", - a pattern must be discovered among empirical inputs. Generating predictions independently from inputs is anti-compressive when you consider both combined.

Ben,

> But I guess it's true that, if you reject someone's approach based on a rough description (because it doesn't agree with your own intuition),

> you would probably still reject it after hearing more of the conceptual and technical details. Maybe you mean something like that...

From OpenCog "Theory" section: "OpenCog is a diverse assemblage of cognitive algorithms, each embodying their own innovations — but what makes the overall architecture powerful is its careful adherence to the principle of cognitive synergy."

There's nothing for me to reject. You only know what's "synergetic" after experimentation, so your overall "theory" is trial & error. That took evolution >3B years on a planet-size quantum mechanical "computer".

Boris wrote,

The best place place to focus is one's own website... & I don't see much focus on your blog.

OpenCog has its own website, which is not updated frequently enough, but does focus on OpenCog ;)

My personal blog is more wide-ranging, as you've noted. I spend a majority but not 100% of my time on AGI -- partly because I need to earn a living, and partly because that's just the way my mind works ... I guess we all need to strike our own balance between purposeful focus on one thing, and broad-ranging exploration...

> So I've found private discussions on deep AGI issues much more productive...
You only get private discussions *after* you introduced people to your approach. And you restrict your audience down to nothing unless that introduction is public.

Sure, and this list is good for those sorts of introductions...

The level of private discussions can't be much higher than that of public introductions.

Well, private discussions can get much more in-depth both conceptually and technically.

But I guess it's true that, if you reject someone's approach based on a rough description (because it doesn't agree with your own intuition), you would probably still reject it after hearing more of the conceptual and technical details. Maybe you mean something like that...

> However, while this detailed theory appears to be **compatible with** the high-level theory, it's not **derived from** the high-level theory.... This is a shortcoming.

Right, you can't "derive" much from that hand-waving :). You need a formal definition of a "pattern", & I have it.

> However, I prefer to accept this shortcoming, than to adopt an alternate approach whose underlying theory appears to me

> fundamentally conceptually inadequate (which is my current reaction to your knol, though I must temper that with the comment

> that it's obviously a very compacted representation of your ideas, so there may be way more to your thinking and approach than I limned from that page...).

Use your imagination :). I should have an expanded edit soon, along with moving back to Blogger.

> I just don't buy the idea that hierarchical pattern recognition is the whole story, or even 40% of the story, for human-level AGI...

I think you're confusing general intelligence with a bunch of other things in human mind, as well as forgetting about modulatory / motor feedback.

From: Ben Goertzel

Sent: Monday, December 19, 2011 12:03 PM

To: AGI

Subject: Re: [agi] Intelligence as a cognitive algorithm.

Hmmm...

Well, there is a high-level overall theory underlying OpenCog, which I wrote about at length during 1993-2006 in various books, e.g. The Hidden Pattern which gives a summary of many aspects (only semi-technically)

Then there is a lot of detailed theory underlying the different cognitive processes in the OpenCog design, and their interactions

However, while this detailed theory appears to be **compatible with** the high-level theory, it's not **derived from** the high-level theory.... This is a shortcoming.

However, I prefer to accept this shortcoming, than to adopt an alternate approach whose underlying theory appears to me fundamentally conceptually inadequate (which is my current reaction to your knol, though I must temper that with the comment that it's obviously a very compacted representation of your ideas, so there may be way more to your thinking and approach than I limned from that page...). I just don't buy the idea that hierarchical pattern recognition is the whole story, or even 40% of the story, for human-level AGI...

One of my ongoing compromises, is how to divide time btw building theoretical bridges between the high-level and detailed theory of my approach, versus guiding the practical implementation. I enjoy the theoretical aspect more, but feel the practical work is probably more valuable at this stage...

-- Ben G

> No... in OpenCog we're trying to engineer synergy between a specific collection of cognitive processes,

> architected according to specific principles, and there's a lot of theory underlying each of these processes and their interactions.

> There is a certain amount of trial and error involved but also a lot of specialized theory...

> ben

But no overall theory.

Ben,

> This list is so heterogeneous in nature, that it's not really possible to pursue in-depth AGI conversations here --

> because as soon as you get started discussing a set of detailed ideas meaningful within one broad approach to AGI,

> the discussion gets sidetracked into foundational discussions with folks who don't like that broad approach.
> I tried to resolve this problem a few years ago by starting an AGI forum site, but pretty much nobody came, so I killed it after a while...

I appreciate your efforts (including this list) & didn't mean to blame you for sidetracking the thread. Heck, if no one wants to talk business, why not... Like you said, this list is only useful for introducing an approach & updates thereto.

> I spend most of my time focusing on "real AGI issues", but I don't consider this list the best place to do that.

The best place place to focus is one's own website... & I don't see much focus on your blog.

> So I've found private discussions on deep AGI issues much more productive...

You only get private discussions *after* you introduced people to your approach. And you restrict your audience down to nothing unless that introduction is public.

> Anyway, it would be a big mistake to judge the level of overall discussions btw AGI researchers in the world, based on the discussions on this list ;p

That's not how I judge it. I follow links & do searches on *unavoidable* keyword combinations. The level of private discussions can't be much higher than that of public introductions.

Boris,

I spend most of my time focusing on "real AGI issues", but I don't consider this list the best place to do that.

Focusing on real AGI issues is best done within some particular paradigm and approach, within a community of people who have provisionally agreed to work within that approach to see where it leads. This list is so heterogeneous in nature, that it's not really possible to pursue in-depth AGI conversations here -- because as soon as you get started discussing a set of detailed ideas meaningful within one broad approach to AGI, the discussion gets sidetracked into foundational discussions with folks who don't like that broad approach.

I tried to resolve this problem a few years ago by starting an AGI forum site, but pretty much nobody came, so I killed it after a while...

So I've found private discussions on deep AGI issues much more productive... though this list is still useful as a generic "meeting ground" for various random AGI-interested people...

Anyway, it would be a big mistake to judge the level of overall discussions btw AGI researchers in the world, based on the discussions on this list ;p

... ben g

On Sun, Dec 18, 2011 at 8:08 PM, Boris Kazachenko <bkazz@verizon.net> wrote:

Typical.
A thread is hijacked & turned into a pissmatch because no one here has an attention span to focus on real issues.
In terms science in general, I definitely agree with Ben, - an ability to work alone is a plus, but other things are more important.
But in terms of formalizing general intelligence, it's not a plus, it's an AND. One must work alone because no one else is working.

Ben G: As a couple almost examples of things that confused me in your knol ..:
"
This may seem similar to Levin Search, but the latter selects among randomly generated algorithms (of incremental complexity) that happen to solve a problem | compress a bitstring. My approach, on the other hand, is to search for patterns within environmental input flow. Hard distinction between input patterns & algorithms exists only for special-purpose programs.
"
Ben G: but it's not clear to me from the preceding paragraphs how your proposed system can recognize arbitrary computable patterns (as Levin search obviously can),
Boris: I don’t like “arbitrary”, but if a given location is projected to be important enough (per “hierarchical feedback” part), all its outputs are elevated losslessly & eventually compared in all possible combinations.

Ben G: or if so what representation language it uses.
Boris: There’s no fixed “language”, the algorithm generates incrementally complex syntax on every level of generalization. I described first steps of this process in “syntactic expansion” part.

Ben G: My immediate impression is that your method would be limited to primitive recursive functions (which can be built up via composition from elementary functions), but the description isn't detailed enough for me to tell.

Boris:
It doesn’t need to be detailed, selective (pruned) recursion & combinatorics is the only method we have for generating functions of any complexity. But that’s math, empirical pattern discovery comes way before that.

"
On the next level of search, the derivatives are also selectively compared between patterns. This generates secondary derivatives over discontinuity, &|or over different types of coordinates. Such syntactic expansion is pruned by selected representation of variable types at a given resolution of position & magnitude, with partially redundant aggregation at a lower resolution.
Beyond that, a higher-order syntax is formed by comparisons across current syntax, analogous to, but far more complex than comparison across initial coordinates.
"
Ben G: but I don't understand what is your method for choosing which expressions in this "higher order syntax" to evaluate against sensory data (and the lower-level patterns computed therein)

Boris:
All the patterns are compared to all the lower-level outputs within a given range of search. Selection (evaluation for elevation) of potential outputs is done at a lower level, according to projected match of the former. Projected match (predictive correspondence) is the quantitative criterion of intelligence that I was talking about. It is computed by adjusting accumulated match of a pattern (defined in part 2) by hierarchical feedback (described in part 4), – average match, redundancy, contrast, expected match...

Ben G:
I don't really understand how you would handle
-- generating composite actions
-- episodic memory
-- assignment of credit thru the hierarchy once reinforcement is received
-- lots and lots of other stuff

Boris:
Neither I nor anyone else can explain higher levels explicitly, they build on a gazillion of lower-level choices. What I have is general principles that guide this process, derived from my definition of intelligence. This definition is the highest-level (meta) generalization one can make. It can't be "proven" without a life-time worth of examples, one simply has to work up to it through introspection. People get increasingly sloppy with elevation, hence the ludicrous mess that passes for philosophy & AGI.

Ben G: I sort of understand how you want to do perceptual pattern recognition, but not really how you want to leverage perceptual pattern recognition for control of an embodied agent doing stuff in a world over an extended time period...

Boris: Action is an adjustment of coordinates for sensors & actuators (they’re always combined), which is a direct extension of downward feedback within a representational hierarchy.

Ben G: I would be curious if other list members find the knol more transparent than I do...
Boris: They probably don’t, it’s something you need to work on, at the exclusion of everything else.

Sep 21, 2011 10:35 AM

Ben G: About predictive accuracy as an intelligence measure.... What matters is if the system is good at predicting which sequences of its action will lead to achievement of its goals in the contexts relevant to its life. This is different than, though related to, general predictive capability.

Boris: For a purely cognitive system the only goal is maximizing its predictive correspondence (accuracy * range). That goes for both internal information processing & external action (see the end of part 4). We can adopt it for our goals by pre-selecting inputs.

Ben G: "Hard distinction between input patterns & algorithms exists only for special-purpose programs. "
Hmmm, well clearly in the brain there's a distinction between its input patterns and the algorithms implicit in its wiring, no?

Boris: I think you're talking about a distinction between innate & acquired wiring patterns. Yes, some level of algorithms must be built-in to initiate learning at an acceptable speed, but the cut-off is not a qualitative distinction. Cognitive algorithm can then be refined & extended indefinitely. All of our math is such an extension.

Ben G: "... if a given location is projected to be important enough (per “hierarchical feedback” part), all its outputs are elevated losslessly & eventually compared in all possible combinations. "
How can you take all possible combinations, in reality?

Boris: You can't, not if you include combinations of subsequent derivatives, I was talking "in the limit".

Ben G: Don't you need to prune the space of possible combinations? How is this done?

Boris: I already described evalutation by projected match for empirical inputs & patterns. In pure math (on much higher levels), the criterion is reduction (as in equations), which is an equivalent of match. You prune the expressions with below-average resuts-per-operations ratio.

Ben G: Are the following simple points correct?

-- you're building a hierarchical pattern recognition network,
Boris: Obviously.

-- it's substantially aligned with the spatiotemporal structure of the perceived world
Boris: Initially, but a comparison sequence can be re-ordered on higher levels according to more compressive "coordinates".

-- higher levels of the network embody more abstract patterns, combining the outputs of the lower levels
Boris: Yes, but "network" implies lateral data transfers, while in my model primary data transef is vertical: across levels.

-- perception and action are carried out in the same network, so that action control and planning are part of the same process as top-down perceptual feedback
Boris: Right.

-- the system's goal is accurate prediction,
Boris: More like a "predicted... prediction", actual confirmation is not always necessary.

-- and somehow those patterns that lead to accurate predictions are going to be rewarded and have more likelihood of surviving and being used again
Boris: They're selected as inputs to higher levels, which have a longer search cycle, thus slower content "recycling".

Ben G: I don't think I'll be able to fully grok your design and algorithms in detail without putting us both through more QA than we want to do,
Boris: No problem. BTW, I may post (a constructive part of) this discussion as comment on the knol, do you mind? Might save me a few questions in the future.

> Boris: For a purely cognitive system the only goal is maximizing its
> predictive correspondence (accuracy * range).

Ben G: Hmmmm.. in that case I don't think "purely cognitive systems" are
going to be very useful in reality. Given limited compute resources,
they will be massively outperformed by systems that are oriented
toward maximizing *useful* predictive correspondence...

Boris: You don't know what's "useful" till you have a big chunk of
"correspondence" in the first place. And you can't define "useful" in general terms anyway,
so this is just another one of your excuses for lazy thinking.

> Boris: I already described evaluation by projected match for empirical
> inputs & patterns. In pure math (on much higher levels), the criterion is
> reduction (as in equations), which is an equivalent of match. You prune
> the expressions with below-average results-per-operations ratio.

Ben G: Yeah, but there are very many expressions due to combinatorial
explosion -- you can't just produce them all then prune the bad ones.
Is your approach to incrementally build up complex expressions
compositionally from simpler ones?

Boris: I think I have "incremental" in just about every paragraph in the knol, starting from the 1st. You seem to have too many things on your mind to keep track of this discussion.

Ben G: If so, why don't you run into the same problems as greedy learning
systems? Presumably because the
top-down feedback from the existing complex expressions guides the
formation of new complex ones from simpler components, I suppose. But
this is a key point and it's not very clear to me how your system does
it...

Boris: Maybe you can point out what part of the process I already described
is not clear to you.

Intelligence

Cognitive Algorithm

Discussions with Ben Geortzel on AGI list

Comments from the knol

Derek Zahn:

Understanding another human being's thoughts is hard. :)

Todor Arnaudov:

Higher match within derivatives in a pattern, than between templates and lower level output:

Andrey Panin:

Boris, interesting perspective

Todor Arnaudov:

Events in programming are all the way through the hierarchy...

Task: Comparing a single-integer input to a fixed-length continuous sequence of older inputs

Maximizing predictive-correspondence which maximizes reward

How to filter out the improbable seems to me to be the key

AGI

How about semantics?

Cognition: hierarchical pattern discovery with incrementally scalable syntax.

Meta-Evolution: evolution beyond reproduction

A mindset for AI discovery.

Inductive & deductive cognitive phases.

Generalist vs Specialist' neuroarchitectural bias.

On "On Intelligence" (edited)