Commentary on James R. Hurford

Abstract: 48 words

Main Text: 1,210 words

References: 261 words

Total Text: 1,554 words

I find merit in Hurford’s basic idea, that the ventral stream, or "what" cortical pathway, somehow classifies the objects or events to which attention is directed by the dorsal, "where" pathway. What I question is the form Hurford proposes for the nature of this classification. Hurford suggests a process analogous to the evaluation of a statement in formal logic. I suggest the process could be better understood as the evaluation of a probability.

That brain processes can by modeled using logical formalisms is an enduring theme. The desire to understand thought processes motivated the logical methods developed by George Boole. Famous work by McCulloch and Pitts (1943) demonstrated that neural networks could carry out logical operations. More recent work shows how cognitive processes could be built up from networks of neural elements that can learn basic logical functions (Valiant 1994). While the brain could implement logical operations in principle, convincing evidence that it does so in practice is lacking. For example, the initial hope that brain-like intelligence could be created using artificial systems based on logic (e.g. McCarthy 1968; Newel 1982) has been lost.

Other concepts have had more success in providing insight into brain function. Barlow (1969; 1972) suggested that neurons throughout the sensory hierarchy could be thought of as feature detectors, the responses of which are proportional to the probability that their trigger feature is present. Barlow’s original model was cast in terms of classical statistical inference. More recent incarnations of this idea involve Bayesian methods. Probabilistic models are distinctly better then those based on formal logic for understanding the response properties of sensory neurons. Research on multisensory neurons in the midbrain provide a case in point.

Multisensory interactions were first described by Newman and Hartline (1981), for neurons in the rattlesnake optic tectum that combine input from the visual and infrared pit-organ systems. Newman and Hartline categorized the responses of multisensory tectal neurons to visual and infrared stimuli presented separately (modality-specific) or together (cross-modal), near receptive field centers in both modalities. The ideal OR neuron had both modality-specific and cross-modal responses, while the ideal AND neuron had only cross-modal responses. They seemed to compute Boolean logical functions on their inputs. The analogy between the responses of multisensory tectal neurons and Boolean logical operators, however, could only be taken so far.

The cross-modal response of OR neurons could be larger than either of the modality-specific responses, and even larger than their sum. The modality-specific responses of AND neurons could be non-zero. Other neurons could not be fit into a Boolean scheme at all. For example, the responses of ENHANCED tectal neurons to a stimulus of one modality could be increased by a stimulus of another modality that was ineffective by itself. The responses of all types were significantly magnitude dependent. It would not be possible, on the basis of the data on multisensory neurons in the rattlesnake tectum, to develop a satisfying description of their response properties in terms of Boolean logic.

Later work by Meredith and Stein (1983; 1986; for review see Stein and Meredith 1993) provided a more general view of multisensory responses. They studied multisensory neurons in the deep layers of the mammalian superior colliculus (DSC), and described ENHANCEMENT as any augmentation of the response to stimulation of one sensory modality by the presentation of a stimulus of another modality. These responses are also magnitude dependent. Percent enhancement is larger when modality-specific responses are smaller. That property, known as INVERSE EFFECTIVENESS, provides the key to a model that can unify findings on multisensory interactions. This model is based not on logic, but on probability.

We modeled INVERSE EFFECTIVENESS on the hypothesis that multisensory DSC neurons use their inputs to compute the probability that a target, defined as a stimulus source, has appeared in their receptive fields (Anastasio et al. 2000). Specifically, we propose that DSC neurons compute P(T=1|S), where P is probability, S is sensory input of one or more modalities, and T is the target (T=1, target present; T=0, target absent). P(T=1|S) can be computed as a posterior probability using Bayes’ rule: P(T=1|S)=P(S|T=1)P(T)/P(S). By equating posterior probabilities with the responses of multisensory DSC neurons, the Bayes' rule model can simulate INVERSE EFFECTIVENESS. If a modality-specific stimulus is large, it provides overwhelming evidence of a target. The posterior probability of a target would be close to 1 and a stimulus of another modality would not increase it much. However, if a modality-specific stimulus is small, the posterior probability of a target can be close to 0. Integrating a stimulus of another modality can dramatically increase the probability that a target has appeared. The correspondence between posterior probabilities and the multisensory responses of DSC neurons strongly supports the hypothesis that DSC neurons compute the probability of a target given their multisensory inputs.

Of course, the brain does not compute using probability distributions, but through synaptic weights and neural activation functions. Borrowing techniques from the field of statistical pattern classification (Duda and Hart 2001), we developed simple neural models that are capable of computing posterior probabilities exactly, given well-described input distributions (Patton and Anastasio 2003). These models simulate ENHANCEMENT and INVERSE EFFECTIVENESS. For input distributions that are not well described, posterior probabilities can be estimated using neural networks (Bishop 1995). Thus, artificial neurons and networks are well suited to the computation of posterior probabilities, and it is reasonable to suppose that the brain is also.

Multisensory neurons in cortex have response properties similar to those in the DSC (Stein and Wallace 1996), and the hypothesis that multisensory neurons compute posterior probabilities could be extended to other brain regions. Cortical neurons, in general, could be thought of as feature detectors that compute the posterior probability that their feature has been detected, given their inputs. In his target article, Hurford suggests that neurons in the ventral ("what") stream of cortical processing evaluate the logical statement PREDICATE(X). X stands for an object or event in the environment that elicits sensory input S, the location of which is marked for attention by the dorsal ("where") stream of cortical processing. Presumably, neurons in the ventral stream would have two states, active or silent, corresponding to the "true" or "false" values of PREDICATE(X). By way of a concrete example, we might consider a hypothetical neuron in the ventral stream that evaluates APPLE(X), which would fire neural impulses at some fixed rate if the currently attended sensory input S corresponds to an apple, and would be silent otherwise. One problem with this scheme is that cortical neurons are not two-state elements, but show graded responses to their inputs. Another, more serious, problem is that sensory inputs, being neural, are stochastic, and therefore uncertain to some extent. It is hard to see how neurons in the ventral stream, or anywhere else in the brain, could ever be completely certain of exactly what has elicited their current pattern of input. Perhaps a better way to model the responses of such a neuron is P(X=APPLE|S). The activity of the neuron would then vary from zero up to some maximal level of firing, which would be proportional to the probability that object X, eliciting sensory input S, is an apple. The computation of probabilities seems a more realistic basis for perception than the evaluation of statements in logic.