CECN1 V1Rf

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V1 Receptive Fields and Hebbian Learning

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Project Documentation

(note: this is a literal copy from the simulation documentation -- it contains links that will not work within the wiki)

  • To start, it is usually a good idea to do Object/Edit Dialog in the menu just above this text, which will open this documentation in a separate window that you can more easily come back to. Alternatively, you can always return by clicking on the ProjectDocs tab at the top of this middle panel.

You will notice that the network (figure 8.7 in the text) has the two input layers, each 12x12 in size, one representing a small patch of on-center LGN neurons (Input_on), and the other representing a similar patch of off-center LGN neurons (Input_off). Specific input patterns are produced by randomly sampling a 24x24 patch from a set of four larger (800x600 pixels) images of natural scenes (you can view these scenes by clicking on the images v1rf_img1.jpg, etc in this directory in your file browser). The single hidden layer is 14x14 in size.

  • Let's examine the weights of the network by clicking on r.wt and then on a hidden unit.

You should observe that the unit is fully, randomly connected with the input layers, and that it has the circular neighborhood of lateral excitatory connectivity needed for inducing topographic representations.

  • Select act again in the network window, locate the ControlPanel, and do Train: Init, Step in the control panel, and observe the activations as the network settles in response to a sampled input pattern.

The hidden units will initially have a somewhat random and sparse pattern of activity in response to the input images.

You should observe that the on- and off-center input patterns have complementary activity patterns. That is, where there is activity in one, there is no activity in the other, and vice versa. This complementarity reflects the fact that an on-center cell will be excited when the image is brighter in the middle than the edges of its receptive field, and an off-center cell will be excited when the image is brighter in the edges than in the middle. Both cannot be true, so only one is active per image location. Keep in mind that the off-center units are active (i.e., with positive activations) to the extent that the image contains a relatively dark region in the location coded by that unit. Thus, they do not actually have negative activations to encode darkness.

  • Continue to do Step for several more input patterns.

Question 8.1 (a) What would you expect to see if the lateral, topography-inducing weights were playing a dominant role in determining the activities of the hidden units? (b) Are the effects of these lateral weights particularly evident in the hidden unit activity patterns? Now, increase the control panel parameter recurrent_wt_scale.rel to .2 from the default of .07 and continue to Step. This will increase the effective strength of the recurrent (lateral) weights within the hidden layer. (c) How does this change the hidden unit activation patterns? Why?

  • Set recurrent_wt_scale.rel back to .07.

We use this relatively subtle strength level for the lateral weights so the network can have multiple bumps of activity, not just one dominant one. This is important if there are multiple different edges with different orientations present in a given image, which is sometimes (but not always) the case.

If we let this network run for many, many more image presentations, it will develop a set of representations in V1 that reflect the correlational structure of edges that are present in the input. Because this can take several minutes to an hour (depending on your computer), we will just load a pre-trained network at this point.

  • Press LoadNet on the control panel, and select the v1rf_100.wts.gz file.

This loads network weights that were trained for 100 epochs of 100 image presentation, or a total of 10,000 image presentations.

  • Select r.wt, and then click on the lower right-most hidden unit.

You should see in the weights projected onto the input layers some faint indication of a right-diagonal orientation coding (i.e., a diagonal bar of stronger weight values), with the on-center (Input_on) bar in the middle of the input patch, and the off-center (Input_off) bar just adjacent to it on the right. Note that the network always has these on- and off-center bars in adjacent locations, never in the same location, because they are complementary (both are never active in the same place). Also, these on- and off-center bars will always be parallel to each other and perpendicular to the direction of light change, because they encode edges, where the change in illumination is perpendicular to the orientation of the edge (as depicted in figure 8.3).

  • Then click on the next unit to the left, and then the next one over, and click back and forth between these 3 units.

You should observe that the orientation shifts from being diagonal to more horizontal. As you click around to other units, you might also see a transition in the polarity of the receptive field, with some having a bipolar organization with one on-center and one off-center region, while others have a tripolar organization with one on-center region and two off-center ones. Further, they may vary in size and location.

Receptive Field View

Although this examination of the individual unit's weight values reveals both some aspects of the dimensions coded by the units and their topographic organization, it is difficult to get an overall sense of the unit's representations by looking at them one at a time. Instead, we will use a single display of all of the receptive fields at one time.

  • To view this display, select the Get RFs button in the control panel, which gathers the data and displays it in the .T3Tab.ReceptiveFields display.

You will now see a grid view that presents the pattern of receiving weights for each hidden unit, which should look generally to figure 8.8 in the textbook (the network was retrained so the weights are different). To make it easier to view, this display shows the off-center weights subtracted from the on-center ones, yielding a single plot of the receptive field for each hidden unit. Positive values (in red tones going to a maximum of yellow) indicate more on-center than off-center excitation, and vice versa for negative values (in blue tones going to a maximum negative magnitude of purple). The receptive fields for each hidden unit are arranged to correspond with the layout of the hidden units in the network. To verify this, look at the same 3 units that we examined individually, which are along the bottom right of the grid view. You should see the same features we described above, keeping in mind that this grid log represents the difference between the on-center and off-center values. You should clearly see the topographic nature of the receptive fields, and also the full range of variation among the different receptive field properties.

Question 8.2 'Which different properties of edges are encoded differently by different hidden units? In other words, over what types of properties or dimensions do the hidden unit receptive fields vary? There are four main ones, with one very obvious one being orientation -- different hidden units encode edges of different orientations (e.g., horizontal, vertical, diagonal). Describe three more such properties or dimensions.

You should observe that the topographic organization of the different features, where neighboring units usually share a value along at least one dimension (or are similar on at least one dimension). Keep in mind that the topography wraps around, so that units on the far right should be similar to those on the far left, and so forth. You should also observe that a range of different values are represented for each dimension, so that the space of possible values (and combinations of values) is reasonably well covered.

Probing Inputs

We can directly examine the weights of the simulated neurons in our model, but not in the biological system. Thus, more indirect measures must be taken to map the receptive field properties of V1 neurons. One commonly used methodology is to measure the activation of neurons in response to simple visual stimuli that vary in the critical dimensions (e.g., oriented bars of light). Using this technique, experimenters have documented all of the main properties we observe in our simulated V1 neurons -- orientation, polarity, size, and location tuning, and topography. We will simulate this kind of experiment now.

This will bring up a table containing 4 events, each of which represents an edge at a different orientation and position.

Question 8.3 Explain the sense in which these probe stimuli represent edges, making reference to the relationship between the Input_on and Input_off patterns.

Now, let's present these patterns to the network.

  • Select act in the network window, then do ProbeStep in the control panel, and continue to ProbeStep through the next 3 events, and note the relationship in each case to the weight-based receptive fields shown in the grid log.

You should observe that the units that coded for the orientation and directionality of the probe were activated.

If you are interested, you can draw new patterns into the probe events, and present them by the same procedure just described. In particular, it is interesting to see how the network responds to multiple edges present in a single input event.

Recurrent Connectivity Effects

Finally, to see that the lateral connectivity is responsible for developing topographic representations, you can load a set of receptive fields generated from a network trained with recurrent_wt_scale.rel set to .01.

  • Do LoadWeights in the control panel and select v1rf_rec01.wts.gz and then do Get Rfs to generate the rf display of these weights.

You should see little evidence of a topographic organization in the resulting receptive field grid log, indicating that this strength of lateral connectivity provided insufficient neighborhood constraints. Indeed, we have found that these patterns look similar to those with networks trained without any lateral connectivity at all.

There appears to be an interaction between the topographic aspect of the representations and the nature of the individual receptive fields themselves, which look somewhat different in this weaker lateral connectivity case compared to the original network. These kinds of interactions have been documented in the brain (e.g., Das & Gilbert, 1995; Weliky, Kandler, & Katz, 1995) and make sense computationally given that the lateral connectivity has an important effect on the response properties of the neurons, which is responsible for tuning up their receptive fields in the first place.

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