Learning transfer (i.e. accelerated learning over a series of structurally related learning tasks) differentiates species and age-groups, but the evolutionary and developmental implications of such differences are unclear. To this end, the relational schema induction paradigm employing tasks that share algebraic (group-like) structures was introduced to contrast stimulus-independent (relational) versus stimulus-dependent (associative) learning processes. However, a theory explaining this kind of relational learning transfer has not been forthcoming beyond a general appeal to some form of structure-mapping, as typically assumed in models of analogy. In this paper, we provide a theory of relational schema induction as a "reconstruction" process: the algebraic structure underlying transfer is reconstructed by comparing stimulus relations, learned within each task, for structural consistency across tasks-formally, the theory derives from a category theory version of Tannakian reconstruction. The theory also applies to non-human studies of relational concepts, thereby placing human and non-human transfer on common ground for sharper comparison and contrast. As the theory and paradigm do not depend on linguistic ability, we also have a way for pinpointing where aspects of human learning diverge from other species without begging the question of language.

In order to better protect and conserve biodiversity, ecologists use machine learning and statistics to understand how species respond to their environment and to predict how they will respond to future climate change, habitat loss and other threats. A fundamental modeling task is to estimate the probability that a given species is present in (or uses) a site, conditional on environmental variables such as precipitation and temperature. For a limited number of species, survey data consisting of both presence and absence records are available, and can be used to fit a variety of conventional classification and regression models. For most species, however, the available data consist only of occurrence records --- locations where the species has been observed. In two closely-related but separate bodies of ecological literature, diverse special-purpose models have been developed that contrast occurrence data with a random sample of available environmental conditions. The most widespread statistical approaches involve either fitting an exponential model of species' conditional probability of presence, or fitting a naive logistic model in which the random sample of available conditions is treated as absence data; both approaches have well-known drawbacks, and do not necessarily produce valid probabilities. After summarizing existing methods, we overcome their drawbacks by introducing a new scaled binomial loss function for estimating an underlying logistic model of species presence/absence. Like the Expectation-Maximization approach of Ward et al. and the method of Steinberg and Cardell, our approach requires an estimate of population prevalence, $\Pr(y=1)$, since prevalence is not identifiable from occurrence data alone. In contrast to the latter two methods, our loss function is straightforward to integrate into a variety of existing modeling frameworks such as generalized linear and additive models and boosted regression trees. We also demonstrate that approaches by Lele and Keim and by Lancaster and Imbens that surmount the identifiability issue by making parametric data assumptions do not typically produce valid probability estimates.

A complete theory of cognitive architecture (i.e., the basic processes and modes of composition that together constitute cognitive behaviour) must explain the systematicity property--why our cognitive capacities are organized into particular groups of capacities, rather than some other, arbitrary collection. The classical account supposes: (1) syntactically compositional representations; and (2) processes that are sensitive to--compatible with--their structure. Classical compositionality, however, does not explain why these two components must be compatible; they are only compatible by the ad hoc assumption (convention) of employing the same mode of (concatenative) compositionality (e.g., prefix/postfix, where a relation symbol is always prepended/appended to the symbols for the related entities). Architectures employing mixed modes do not support systematicity. Recently, we proposed an alternative explanation without ad hoc assumptions, using category theory. Here, we extend our explanation to domains that are quasi-systematic (e.g., aspects of most languages), where the domain includes some but not all possible combinations of constituents. The central category-theoretic construct is an adjunction involving pullbacks, where the primary focus is on the relationship between processes modelled as functors, rather than the representations. A functor is a structure-preserving map (or construction, for our purposes). An adjunction guarantees that the only pairings of functors are the systematic ones. Thus, (quasi-)systematicity is a necessary consequence of a categorial cognitive architecture whose basic processes are functors that participate in adjunctions.

Classical and Connectionist theories of cognitive architecture seek to explain systematicity (i.e., the property of human cognition whereby cognitive capacity comes in groups of related behaviours) as a consequence of syntactically and functionally compositional representations, respectively. However, both theories depend on ad hoc assumptions to exclude specific instances of these forms of compositionality (e.g. grammars, networks) that do not account for systematicity. By analogy with the Ptolemaic (i.e. geocentric) theory of planetary motion, although either theory can be made to be consistent with the data, both nonetheless fail to fully explain it. Category theory, a branch of mathematics, provides an alternative explanation based on the formal concept of adjunction, which relates a pair of structure-preserving maps, called functors. A functor generalizes the notion of a map between representational states to include a map between state transformations (or processes). In a formal sense, systematicity is a necessary consequence of a higher-order theory of cognitive architecture, in contrast to the first-order theories derived from Classicism or Connectionism. Category theory offers a re-conceptualization for cognitive science, analogous to the one that Copernicus provided for astronomy, where representational states are no longer the center of the cognitive universe--replaced by the relationships between the maps that transform them.

Transitive inference, class inclusion and a variety of other inferential abilities have strikingly similar developmental profiles-all are acquired around the age of five. Yet, little is known about the reasons for this correspondence. Category theory was invented as a formal means of establishing commonalities between various mathematical structures. We use category theory to show that transitive inference and class inclusion involve dual mathematical structures, called product and coproduct. Other inferential tasks with similar developmental profiles, including matrix completion, cardinality, dimensional changed card sorting, balance-scale (weight-distance integration), and Theory of Mind also involve these structures. By contrast, (co)products are not involved in the behaviours exhibited by younger children on these tasks, or simplified versions that are within their ability. These results point to a fundamental cognitive principle under development during childhood that is the capacity to compute (co)products in the categorical sense.

Describes a sequence of methods to improve the running-time of the Isodata and K-means algorithms. The methods are compared on a range of remotely-sensed data sets, and show consistent and dramatic speedups.

Standard feedforward and recurrent networks cannot support strong systematicity when constituents are presented as local input/output vectors. To explain systematicity connectionists must either: (1) develop alternative models, or (2) justify the assumption of similar (non-local) constituent representations prior to the learning task. I show that the second commonly presumed option cannot account for systematicity, in general. This option, termed first-order connectionism, relies upon established spatial relationships between common-class constituents to account for systematic generalization: inferences (functions) learnt over, for example, cats, extend systematically to dogs by virtue of both being nouns with similar internal representations so that the function learnt to make inferences employing one simultaneously has the capacity to make inferences employing the other. But, humans generalize beyond common-class constituents. Cross-category generalization (e.g. inferences that require treating mango as a colour, rather than a fruit) makes having had the necessary common context to learn similar constituent representations highly unlikely. At best, the constituent similarity proposal encodes for one binary relationship between any two constituents, at any one time. It cannot account for inferences, such as transverse patterning, that require identifying and applying one of many possible binary constituent relationships that is contingent on a third constituent (i.e. ternary relationship). Connectionists are, therefore, left with the first option which amounts to developing models with the symbol-like capacity to represent explicitly constituent relations independent of constituent contents, such as in tensor-related models. However, rather just simply implementing symbol systems, I suggest reconciling connectionist and classical frameworks to overcome their individual limitations.

Operations on basic data structures such as queues, priority queues, stacks, and counters can dominate the execution time of a parallel program due to their frequency and their coordination and contention overheads.There are considerable performance payoffs in developing highly-optimized, asynchronous, distributed, cache-conscious, parallel implementations of such data structures.Such implementations may employ a variety of tricks to reduce latencies and avoid serial bottlenecks, as long as the semantics of the data structure are preserved.The complexity of the implementation and the difficulty in reasoning about asynchronous systems increases concerns regarding possible bugs in the implementation.In this paper, we consider black box procedures for testing whether a parallel data structure behaved correctly.We present the first systematic study of algorithms and hardness results for such testing procedures, focusing on queues, priority queues, stacks, and counters, under various important scenarios.Our results demonstrate the importance of selecting test data such that distinct values are inserted into the data structure (as appropriate).In such cases, we present an O(n) time algorithm for testing linearizable queues, an O(nlog n) time algorithm for testing linearizable priority queues, and an O(np') time algorithm for testing non-linearizable queues, where n is the number of data structure operations and p is the number of processors.In contrast, we show that testing such data structures for executions with arbitrary input values is NP-complete.Our results also help clarify the thresholds between scenarios that admit polynomial time solutions and those that are NPcomplete.Our algorithms are the first nontrivial algorithms for these problems.

Human cognition is said to be systematic: cognitive ability generalizes to structurally related behaviours. The connectionist approach to cognitive theorizing has been strongly criticized for its failure to explain systematicity. Demonstrations of generalization notwithstanding, I show that two widely used networks (feedforward and recurrent) do not support systematicity under the condition of local input/output representations. For a connectionist explanation of systematicity, these results leave two choices: either (1) develop models capable of systematicity under local input/output representations or (2) justify the choice of similarity-based (non-local) component representations sufficient for systematicity.

No abstract available.