On the ability of standard and brain-constrained deep neural networks to support cognitive superposition: a position paper

Abstract

The ability to coactivate (or "superpose") multiple conceptual representations is a fundamental function that we constantly rely upon; this is crucial in complex cognitive tasks requiring multi-item working memory, such as mental arithmetic, abstract reasoning, and language comprehension. As such, an artificial system aspiring to implement any of these aspects of general intelligence should be able to support this operation. I argue here that standard, feed-forward deep neural networks (DNNs) are unable to implement this function, whereas an alternative, fully brain-constrained class of neural architectures spontaneously exhibits it. On the basis of novel simulations, this proof-of-concept article shows that deep, brain-like networks trained with biologically realistic Hebbian learning mechanisms display the spontaneous emergence of internal circuits (cell assemblies) having features that make them natural candidates for supporting superposition. Building on previous computational modelling results, I also argue that, and offer an explanation as to why, in contrast, modern DNNs trained with gradient descent are generally unable to co-activate their internal representations. While deep brain-constrained neural architectures spontaneously develop the ability to support superposition as a result of (1) neurophysiologically accurate learning and (2) cortically realistic between-area connections, backpropagation-trained DNNs appear to be unsuited to implement this basic cognitive operation, arguably necessary for abstract thinking and general intelligence. The implications of this observation are briefly discussed in the larger context of existing and future artificial intelligence systems and neuro-realistic computational models.

Keywords: Artificial cognitive system; Brain-constrained modelling; Cell assembly; Concept combination; General intelligence; Multi-item working memory; Semantic representations.

Fig. 1

Superposition in standard (A) and brain-constrained (B) neural networks. The vertical arrays represent a neural network’s set of nodes, whose activity levels are indicated by grey scales and colour shadings. A: In standard feed-forward NNs trained with back-propagation, distinct sensory (or conceptual) items are learned as distinct vectors of graded activities over the same set of nodes (which here may be coding for visual features of objects, such as colour, shape, etc.). As any two such activity vectors are generally not orthogonal, their sum (co-activation) leads to a new vector from which the original components cannot be uniquely identified. In the example, superposing the learned representations for ‘green apple’ (V₁) and ‘yellow pear’ (V₂) produces an ambiguous vector V₃ (depicted as a “blend” of the two original items) which could also be the result of co-activating a ‘yellow apple’ and a ‘green pear’, or an infinite number of other pairs of items having some in-between colours and shapes. B: In the class of brain-constrained networks in focus here (trained with a biologically constrained Hebbian learning rule – see main text), the network correlates of distinct input items spontaneously emerge as distinct cell assembly (CA) circuits made up of mostly disjoint sets of strongly linked cells, each CA behaving as a functionally distinct unit having two activity states (“on” and “off”). In the example, activating the learned representation for a ‘green apple’ involves the full “ignition” of CA#1, depicted as a set of blue circles (active nodes) and arrows (links through which activity is reverberating). Similarly for the circuit (cor)responding to a ‘yellow pear’ (CA#2, red circles & arrows). As the most active cells of the two CAs – known as the CAs' kernels (Braitenberg 1978) – do not overlap, the network's activity states respectively induced by the ignition of CA#1 and CA#2 are quasi orthogonal (i.e., the strongly “on” nodes of one state are “off” in the other, and vice versa). Although two CAs may share a small portion of their constituent cells (light-blue and light-red circles), these are only weakly linked to the CA kernel (dashed arrows) and do not significantly contribute to its activity. Superposition thus leads to a network state (CA#1 + CA#2) in which both circuits are “on” but remain functionally distinct

Fig. 2

Examples of Cell Assembly (CA) circuits and their overlaps. Top: Five (out of 12 learned) CA circuits emerging in the six-layer deep brain-constrained network used for the present study, having structure, connectivity and learning mechanisms identical to that in (Garagnani et al. 2008). Each network layer (or “area”), depicted as a darker square, consists of 25 × 25 excitatory and 25 × 25 inhibitory (not shown) graded-response cells. Pixels’ brightness indicates cells’ activity levels. Training was implemented by repeated concomitant presentation of (binary) patterns to areas A1 and A6, each pattern activating 19 of the 625 cells. After 3,000 presentations, model areas A2–A5 exhibit distributed sets of cells strongly and selectively responding to each of the input pattern pairs; these cells form the emerging CA circuits. Note that the network response includes also less active cells, which form part of the CA’s “halo” (Braitenberg 1978): these cells are only weakly (and not reciprocally) linked to the strongly active CA cells, the CA’s kernel (see also Fig. 1B). The six areas are serially (next-neighbour) and recurrently linked (not depicted) via sparse, random and topographic projections (see Garagnani et al. for details). Bottom: mean and maximal overlap (% of shared cells) between the emerging CA circuits are plotted as a function of the threshold γ used to identify them: more precisely, a cell is considered part of a CA circuit if its activity during input stimulation (Top panel) reaches a given level, proportional to γ. Note that the maximal overlap between any pair of CA circuits remains below 5% for a wide range of threshold values (adapted from Garagnani et al. , their Fig. 8)

Fig. 3

Cell assemblies in deep brain-constrained neural networks, and their superposition. A: Snapshots of current and recent network activity during self-sustained reverberation of each of the five cell-assembly circuits shown in Fig. 2. (Left): Each of the five rows depics a snapshot of the network activity (including the two input areas) taken when one of the five CAs circuits showin in Fig. 2-Top was fully active (“ignited”) and exhibited reverberant activity in absence of any input. The activity within the circuit was self-sustained, and the system was in a fixed-point attractor state (though minor oscillations around the fixed point were observed). Also note that only a subset of the cells identified in Fig. 2-Top as forming the CA circuits is showing high activity levels; in particular, the most “peripheral” areas A1 and A6 (where the input patterns were presented during training) contain only a few active CA cells, suggesting that the kernel of the CA circuits lies mainly in the four “central” areas (A2-A5) of the arhictecture. The reason for the only partial binding (and reconstruction) of the stimulus patterns into the cell assembly is to be found in the sparse – as opposed to ‘all-to-all’ – between- and within-area connectivity of the network: due to the low density of recurrent and between-area projections, some of the cells directly stimulated by the inputs to areas A1 and A6 happen to be linked neither to other co-active cells in such areas nor to (CA) cells the patterns indirectly activate in other layers. (Right): Each of the five snapshots shows the recent history of the total within-CA activity (calculated as the sum of the responses of all cells belonging to a CA circuit) for the twelve CAs the network had learned. Specifically, each of the six smaller quadrants displays the raster plots of the within-CA activities during the last 150 simulation time steps. Within a quadrant, each row shows (using a suitably normalised gray scale) the total activity within each CA circuit (first row for CA #1, second row for CA #2, etc.). Thus, for example, a vertical segment at a given time point reveals that a greater-than-zero portion of CA cells was active in that area. Significant persistent per-area activities within any of the 12 CA circuits are thus visible as bright “bands” on the relevant rows (as CAs #6 – #12 are not depicted, only the first five rows show activity). Note that, consistent with the previous observation of the CA kernels being mostly in the four central model areas, self-sustained CA activities tend to be weaker in the two peripheral areas (A1, A6) – see, e.g., the low percentage of the input pattern reconstructed by reactivation of CA #4 in area A1 (only 2–3 cells out of the original 19-cell pattern), as indicated by the almost invisible gray band in the corresponding quadrant (see red dashed oval). B: Representative example of CA superposition. Overall network activity is plotted at nine ordered time points (arbitrarily chosen) during an episode of two CA-circuits’ dynamic superposition. (Left): snapshots of current network activity (six areas and two input patterns). (Right): raster plots of total within-CA activities for the corresponding network states shown on the left. Initially (time t₀) the network is in a stable state, showing persistent, self-sustained activation of CA #5 (note the bright bands in the fifth row, right-hand side panel). At time t₁ the inputs to A1 and A6 are set to the patterns that led to the emergence of circuit CA #2 (cf. Figure 2-Top). During the following time steps (t₂-t₃), the second CA circuit (CA #2) ignites, with its cells ‘lighting up’ first in A1 and A6 and then rapidly extending to  the central areas. By time t₄, activity is stable and shows superposition of CAs #2 and #5 (note the corresponding activity bands on rows 2 and 5 in all network areas – Right). In this example, the strengths of the internal links of the second assembly were insufficient to allow this circuit to enter a state of self-sustained reverberant activity: when external stimulation is removed (time t₅), activity within CA #2 starts to fade (again from network “periphery” towards “centre”), as the gaps appearing – and growing increasingly larger (t_6-7) – at the rightmost ends of the raster plots on the second row show. By time t₈, the network has returned to its initial state, with CA #5 still being “on” (self-sustained). This demonstrates that co-ctivation of CA #2 interfered only minimally with CA #5’s own activity: thanks to the strong links connecting the circuit’s kernel cells, the minor perturbation in CA #5’s halo (see orange-dashed ovals) caused by CA #2’s full ignition did not affect CA #5’s overall “on” state. Hence, the two CAs behaved as distinct, bi-stable functional units, and their superposition caused no loss of information about the identity of the co-active circuits