Memory complexity

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Complexity of memory reflects the structural complexity of the neural network underlying a memory.

Simple memories may rely on a single connection that can be re-activated uniformly. Complex memories may involve a tangle of connections between a set of concepts that may be activated in a different sequence or constellation depending on the memory retrieval context.

Memory complexity correlates positively with:

Complex memories are hard to retrieve uniformly. For that reason, students should employ the minimum information principle. Simple memories are easier to recall, and are easier to store in long-term memory. In SuperMemo, complexity is represented by item difficulty.

In complex memories, individual synapses may behave like subcomponents of an electronic circuit and contribute to composite stability. For example, for sub-stabilities Sa and Sb, we may have: S=Sa*Sb/(Sa+Sb) (explanation)

The same item may be encoded differently by different students (e.g. depending on their mnemonic skills). This means that memory complexity is a neural network property, not a direct reflection of semantic properties of the item.

Moreover, item difficulty is student-dependent. This means that even if two students encoded the same item with the same complexity, the item difficulties measured by the spaced repetition algorithm may differ (e.g. when one of the students tends to work in the morning, while the other chooses the evening).

An atomic memory is the simplest possible memory, which follows perfectly exponential forgetting, and perfectly complies with the two component model of memory.

Memory complexity is the third component in the three component model of memory that extends the two component model from atomic memories to complex memories.

For more see:

This glossary entry is used to explain SuperMemo, a pioneer of spaced repetition software since 1987

Memory complexity: simple and complex memories
Memory complexity: simple and complex memories

Figure: Memory complexity illustrates the importance of the minimum information principle. When memorizing simple questions and answers, we can rely on a simple memory connection, and uniformly refresh that connection at review. Complex memories may have their concepts activated in an incomplete fashion, or in a different sequence that depends on the context. As a result, it is hard to produce a uniform increase in memory stability at review. Complex items are difficult to remember. An example of a simple item may be a word pair, e.g. apple = pomo (Esperanto). While a complex net of connection may be needed to recognize an apple. The connection between apple and pomo is irreducible (i.e. maximally simplified)

Uncertain course of stabilization in complex memories
Uncertain course of stabilization in complex memories

Figure: Uncertain course of the stabilization of complex memories. The picture shows a hypothetical course of stabilization, forgetting, generalization, and interference on the example of a single dendritic input pattern of a single concept cell. The neuron, dendrites and dendritic filipodia are shown in orange. The picture does not show the conversion of filopodia into dendritic spines whose morphology changes over time with stabilization. The squares represent synapses involved in the recognition of the input pattern. Each square shows the status of the synapse in terms of the two component model of long-term memory. The intensity of red represents retrievability. The size of the blue area represents stability. After memorizing a complex memory pattern, the concept cell is able to recognize the pattern upon receiving a summation of signals from the red squares representing a new memory of high retrievability and very low stability. Each time the cell is re-activated, active inputs will undergo stabilization, which is represented by the increase in the blue area in the input square. Each time a signal does not arrive at an input while the concept cell is active, its stability will drop (generalization). Each time a source axon is active and the target neuron fails to fire, the stability will drop as well (competitive interference). Due to the uneven input of signal patterns to the concept cell, some synapses will be stabilized, while others will be lost. Forgetting occurs when a synapse loses its stability and its retrievability and when the relevant dendritic spine is retracted. Generalization occurs when the same concept cell can be re-activated using a smaller, but a more stable input pattern. Retroactive interference occurs when a new input pattern contributes to forgetting some of the redundant inputs necessary for the recognition of the old input pattern. Stabilization of the old patterns results in the reduced mobility of filopodia, which prevents the takeover of a concept by new patterns (proactive interference). At the every end of the process, a stable and a well-generalized input pattern is necessary and sufficient to activate the concept cell. The same cell can respond to different patterns as long as they are consistently stabilized. In spaced repetition, poor choice of knowledge representation will lead to poor reproducibility of the activation pattern, unequal stabilization of synapses, and forgetting. Forgetting of an item will occur when the input pattern is unable to activate sufficiently many synapses and thus unable to reactivate the concept cell. At repetition, depending on the context and the train of thought, an item may be retrieved or forgotten. The outcome of the repetition is uncertain