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POThe Free energy approximation Equation in Restriction Boltzmann Machines
 

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  1. POThe Free energy approximation Equation in Restriction Boltzmann Machines
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    <p>According <a href="http://deeplearning.net/tutorial/rbm.html?goback=.gmr_70219.gde_70219_member_104223473#equation-free_energy_grad" rel="nofollow">a deeplearning tutorial</a>:</p> <p>The free energy in python is</p> <pre><code>def free_energy(self, v_sample): ''' Function to compute the free energy ''' wx_b = T.dot(v_sample, self.W) + self.hbias vbias_term = T.dot(v_sample, self.vbias) hidden_term = T.sum(T.log(1 + T.exp(wx_b)), axis=1) return -hidden_term - vbias_term </code></pre> <p>I am not very good at python, basically it get product expert of each visible unit as vector wx_b, calculate exp and plus 1 , calculate log and sum it for the hidden term.</p> <p>Which I believe is a little different than free energy equation in the Learning Deep Architectures:</p> <p>FreeEnergy(x) = −b′x − ∑log∑e^hi(ci+Wix). </p> <p>Where: </p> <ul> <li><code>hi</code> is the unit <code>i</code> hidden layer, </li> <li><code>ci</code> is the <code>i</code> hidden bias in vector c. </li> </ul> <p>It calculates exp and sum, calculate log respect to the sum value. after all sum all the product expert based on the number of visible unit.</p> <p>The above equation is eq.5.21 from <a href="https://wiki.inf.ed.ac.uk/twiki/pub/CSTR/ListenSemester1201112/bengio2009_deep_ai.pdf" rel="nofollow">Learning Deep Architectures for AI (Yoshua Bengio)</a></p> <p>Below is my draft of java implementation vis_v is the visible layer sample, hid_v is the hidden layer unit sample.</p> <pre><code>private double freeEnergy(RealVector vis_v, RealVector hid_v){ RealVector wx_hb= W.preMultiply(vis_v).add(hBias); double vbias_term= vis_v.dotProduct(vBias); double sum_hidden_term = 0; for(int i=0;i&lt; wx_hb.getDimension();i++){ RealVector vis_expert = hid_v.mapMultiply(wx_hb.getEntry(i)); double hidden_term= StatUtils.sum(vis_expert.map(new Exp()).toArray()); sum_hidden_term+=Math.log(hidden_term); } return -sum_hidden_term-vbias_term; } </code></pre> <p>Is this some kind of approximation? I am trying to implement the same thing in java, but am getting confused over it. Thanks in advance for any help!</p>
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    1. COYowser! That's a change from the usual kind of question we get on stackoverflow :) Let me take a deeper look to see what's what.
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    2. COAs an aside, there is a quick way to check your code: run it and see if it differs from the reference version...
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    3. COthanks, brice. I have run my code against some real example , it works. I believe the python example works too. I need to find out which one more optimize, it might help reduce the deep network error in future, even 0.1~0.2% is worth.
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