Dynamically structured holographic memory

We describe the DSHM (Dynamically Structured Holographic Memory) model of human memory, which uses high dimensional vectors to represent items in memory. The complexity and intelligence of human behavior can be attributed, in part, to our ability to utilize vast knowledge acquired over a lifetime of experience with our environment. Thus models of memory, particularly models that can scale up to lifetime learning, are critical to modeling human intelligence. DHSM is based on the BEAGLE model of language acquisition (Jones and Mewhort, 2007) and extends this type of model to general memory phenomena. We demonstrate that DHSM can model a wide variety of human memory effects. Specifically, we model the fan effect, the problem size effect (from math cognition), dynamic game playing (detecting sequential dependencies from memories of past moves), and time delay learning (using an instance based approach). This work suggests that DSHM is suitable as a basis for learning both over the short-term and over the lifetime of the agent, and as a basis for both procedural and declarative memory. We argue that cognition needs to be understood at both the symbolic and sub-symbolic levels, and demonstrate that DSHM intrinsically operates at both of these levels of description. In order to situate DSHM in a familiar context, we discuss the relationship between DHSM and ACT-R.

Problem Difficulty in Arithmetic Cognition: Humans and Connectionist Models

In mathematical cognition, problem difficulty is a central variable. In the present study, problem difficulty was operationalized through five arithmetic operators --- addition, subtraction, multiplication, division, and modulo --- and through the number of carries required to correctly solve a problem. The present study collected data from human participants solving arithmetic problems, and from multilayer perceptrons (MLPs) that learn arithmetic problems. Binary numeral problems were chosen in order to minimize other criteria that may affect problem difficulty, such as problem familiarity and the problem size effect. In both humans and MLPs, problem difficulty was highest for multiplication, followed by modulo and then subtraction. The human study found that problem difficulty was monotonically increasing with respect to the number of carries, across all five operators. Furthermore, a strict increase was also observed for addition in the MLP study.

Brain Mechanisms of Arithmetic: A Crucial Role for Ventral Temporal Cortex

Elementary arithmetic requires a complex interplay between several brain regions. The classical view, arising from fMRI, is that the intraparietal sulcus (IPS) and the superior parietal lobe (SPL) are the main hubs for arithmetic calculations. However, recent studies using intracranial electroencephalography have discovered a specific site, within the posterior inferior temporal cortex (pITG), that activates during visual perception of numerals, with widespread adjacent responses when numerals are used in calculation. Here, we reexamined the contribution of the IPS, SPL, and pITG to arithmetic by recording intracranial electroencephalography signals while participants solved addition problems. Behavioral results showed a classical problem size effect: RTs increased with the size of the operands. We then examined how high-frequency broadband (HFB) activity is modulated by problem size. As expected from previous fMRI findings, we showed that the total HFB activity in IPS and SPL sites increased with problem size. More surprisingly, pITG sites showed an initial burst of HFB activity that decreased as the operands got larger, yet with a constant integral over the whole trial, thus making these signals invisible to slow fMRI. Although parietal sites appear to have a more sustained function in arithmetic computations, the pITG may have a role of early identification of the problem difficulty, beyond merely digit recognition. Our results ask for a reevaluation of the current models of numerical cognition and reveal that the ventral temporal cortex contains regions specifically engaged in mathematical processing.

Impact of ageing on problem size and proactive interference in arithmetic facts solving

Arithmetic facts (AFs) are required when solving problems such as “3 × 4” and refer to calculations for which the correct answer is retrieved from memory. Currently, two important effects that modulate the performance in AFs have been highlighted: the problem size effect and the proactive interference effect. The aim of this study is to investigate possible age-related changes of the problem size effect and the proactive interference effect in AF solving. To this end, the performance of young and older adults was compared in a multiplication production task. Furthermore, an independent measure of proactive interference was assessed to further define the architecture underlying this effect in multiplication solving. The results indicate that both young and older adults were sensitive to the effects of interference and of the problem size. That is, both interference and problem size affected performance negatively: the time needed to solve a multiplication problem increases as the level of interference and the size of the problem increase. Regarding the effect of ageing, the problem size effect remains constant with age, indicating a preserved AF network in older adults. Interestingly, sensitivity to proactive interference in multiplication solving was less pronounced in older than in younger adults suggesting that part of the proactive interference has been overcome with age.

Efficiency of Arithmetic Procedures Modulates the Problem-Size Effect in Subtraction

The aim of this study was to examine whether differences in strategy selection and/or strategy efficiency can explain the modulation of the problem-size effect by arithmetic skill. More specifically, we wondered whether arithmetic skill increases the use of retrieval strategy in large problems, and/or enhances the efficiency of either retrieval or procedural strategies. The performance of highly-skilled (HS) and less highly-skilled (LS) individuals on a subtraction verification task was analyzed according to problem size and to the strategy reported on a trial-by-trial basis after each problem. The problem size effect was larger for LS individuals than for their HS peers, both in response time and in hit rate. Nevertheless, groups did not differ regarding the strategy reported for each subtraction size. As expected, problems in which retrieval strategy was reported were solved more quickly and more accurately than problems solved by procedural strategies. Responses using retrieval strategy were equally fast in the two groups, but HS individuals performed better than LS when using procedural strategies. The results therefore suggest that the differences in behavioral measures between groups might specifically be due to differences in the efficiency of procedural strategies.