(This is an essay I wrote and cross-posted on my blog as well, and is not my journal)
The ancient south Indian city of Madurai, shimmering like a polestar in the divine firmament and inspiring an eternally compounding repository of knowledge, music, and art from time immemorial, reverberates with pristine generative energy. For more than two and half thousand years, this celestial land has woven the study of the self, carnatic music, and art into a tapestry of the most ancient spirituality, defying definitive description by even the most erudite of scholars, and transcending material concern & transient emotion. A beacon of resplendent temples, to take a walk inside this city is to immerse the self in a universe parameterized by the deepest of aesthetic emotions and sublime bliss, igniting the subtle consciousness and be transported into an abode of supreme peace.
Even a hundred full lives are perhaps not enough to experience the scale and depth of knowledge stored here, which seems to emanate from a cosmic residence of infinite compassion and a seat of consummate wisdom.
A pride of majestic peacocks always colored Madurai. Revered as an enduring symbol of wisdom and adorned as a sacred motif all over the intricate and radiant temples across this historic town, this iconic personification of philosophical acumen is my most beloved spirit animal. Every visit to Madurai was a chance to sight and feed a peacock. A sense of connection to that which is beyond any lexicon; a bond with long and deep memories, represented as a sight that was both inexplicably spectacular and inviolably lucid at the same time.
But even upon a couple of days after arriving in Madurai during this visit, there was no peacock to be seen. Not a single one. A most vexing and saddening void. On the final day of the visit, I took a walk early in the morning, lamenting the deprival of seeing his kindred spirit animal. Where was it? Feeling ever more crestfallen, I walked through the misty Pasumalai Hills, still hoping to meet one. A gentle drizzle was now falling across the brilliant green landscape.
It was still quite early in the morning. The melancholic yearning condensed as teardrops, falling from my cheeks as gently and quietly as the drizzle accompanying his walk. Teardrops that fell unostentatiously in a manner, but spoke loudly, perhaps in an entirely different way. No sooner did the tears start flowing down my cheeks than a gorgeous peacock swooped down from a nearby Banyan tree, howling mellifluously and walking in parallel alongside me. A sanguine expression now splashed all across my face, tears now morphing into one of profound bliss. The peacock then jumped on to an adjacent parapet wall, standing as a commander would survey and gaze the vastness of the Madurai landscape in front of him. Karthikēyan, after all, was always adored as the philosopher-warrior and rode a peacock.
Time appeared to stand still with the magnificent sight in front of me as the morning sun broke through the cinereal clouds and exalted the peacock's brilliant feathers. It was no wonder perhaps that the first tonic note in Carnãtic music -- shadjam (Sanskrit word for the tone that forms the relative reference and thus gives rise to six other tones), was thought to have been conceived by meditating and observant sages drawing deep inspiration from the sound of the peacock. Somewhere from the beneath the Pasumalai Hills came a rendition of a flutist playing the cherished pancharatna kriti jagadānandakāraka in rāgam Nattai and Ādi tālam. The song that was not just an invocation and transcendent celebration of the consciousness that moves the universe in the direction of supreme bliss, but also now forged in the image of the rising sun irradiating the dazzling peacock — a state of spiritual opulence and of mystical testimony that signaled a perfect alignment of the seven chakras. It was time to drive to walk to the Mīnākṣī temple.
Identities constructed by the ego
I walked into a relatively emptyMīnākṣī Sundaresan temple. Sandalwood incense seemed to permeate the entire temple complex, adorned by oil lamps that must have been lit well before sunrise. I sat on the ground, on the right side of the chamber enclosing the inner sanctum santorum, wondering how Muttusvāmi Dīkṣita might have composed his mellifluous compositions as he once sat inside the very temple of this ancient temple. 'Who might you be, to compare yourself to Muttusvāmi Dīkṣita?', asked an inner voice. Afterall Shankara was explicit in his thesis that humility was the gateway for all knowledge.
I glanced at the walls of the inner sanctum santorum, whose thousands of sculptures enacted in rousing detail the divine wedding of Mīnākṣī and Sundaresan, orchestrated by the great sages and attended by the Devas. It was perhaps this sight, I told myself, that might have been the source of such deep-rooted generative power and inspiration. Muttusvāmi Dīkṣita suddenly became no more than a receptacle, an instrument that produced ageless melodies by a mind that rapturously received this numinous energy. The sense of I, an effect of a personal identity forged by the egoic forces vaporized in light of the knowledge and awareness that the generative power stemmed from the sublime forces at work in the world, whose energy no doubt preceded the very origin of time.
It was at this moment that I saw an elderly lady walking over to me, holding a bamboo basket of jasmine flowers. She wore a dark green Kanchipuram saree and wore a pair of diamond-studded earnings that glistened as if it was extracted from the sun itself. Her face had a kind of effusive glow, and she exuded a sort of tranquility that made it seem as if she'd been meditating her entire life. "You must be Karthik! My name is Lalitha and I live in this town, and my son saw you taking pictures of a peacock on Pasumalai this morning! You are here quite early in the morning", she said smilingly as she sat down on the floor next to me. "Yes amma, I'm Karthik and I'm from Bangalore. I'm waiting for the inner sanctum santorum to open", I replied. "You look like you've been in deep thought", she enquired, "Are you a student?". "I am always a student, amma", I confided hastily, "I was wondering what might have inspired Muttusvāmi Dīkṣita to write his compositions on the divine mother when he used to sit here in this very spot. I felt that his immense generative power came to him because he was a receptacle of the spirit that animates this magical place, and it made me question the egoic forces that construct the sense of I in my generative thinking", I replied.
"Ah I see," she remarked serenely. We sat for a couple of moments in silence, standing up briefly to make way for the morning procession of temple elephant Gajaraja. "Listen, child, to fully understand and process the answer you found to question on Muttusvāmi Dīkṣita, you have to follow the significance of Kamaksi, Minaksi, and Visālākśi. I'll tell you the importance of Kāmākśi, and maybe my two sisters who'll be here shortly can tell you the other two", she said, talking as gently as if I was an infant.
I. Kāmākśi & Model Representation
"My child, as you already know, the word Kāmākśi means she whose one glance is enough to awaken the desire for knowledge. The highest metaphysical reality, whose transcendental absolute form is expressed by the great sages using the beeja mantras or seed incantations during meditation. In the laws of causality, she is the primordial cause of all speech and is meditated upon by the yogis and yoginis who house her in the cave of their hearts. Adi Shankara writes in this composition Soundarya Lahari (the flood of beauty) that a single glance from her is akin to the lotus flower rising through the mud of material bondage and opening to the radiance of the bright sun. No water or dirt ever sticks on the surface of the lotus flower's petals or leaves, in the same way as no vicissitude of life can stain the being of an enlightened soul. Her form is well-marked with auspiciousness and is of imperishable patience. She is also the union of the wealth of spiritual prosperity, the illuminating knowledge of the nondual, and the strength of perseverance and grit."
I felt a flood of insight drench the deepest recesses of my mind upon listening to this description. In latent variable probabilistic graphical models, one often depicts a joint distribution of the posterior as a plate notation, containing both observed and latent variables. Connections between the observed and latent variables are conceptualized by an intuition of how the data might have been produced, both by observation of the context in which the data are collected, as well as a scrutiny of the actual data itself. Every graphical model the mind could conjure immediately separated neatly into the configuration, parameter, and evidentiary spaces.
Just as there is the illuminating knowledge of the nondual, any evidentiary space of a graphical model can only be as meaningful as the depth and nuance of the awareness of the context in which any data is accumulated. Just as there is the strength of perseverance and grit, any configuration space of a parametric graphical model is informed only by an intuition of the number of latent clusters, with the awareness that all estimation of latent variables must fit within the number of latent clusters so assigned. And just as there is the resultant wealth of spiritual prosperity, so is the richness of the parameter spaces governed directly by the construction of the evidentiary and parameter spaces.
"Amma, it is almost as if she instructs the generative apparatus of the ego in a way that erases prior decadent identities of the self, into a new identity forged by the illuminating fire of the knowledge of the nondual, molded by the strength of perseverance and grit and yielding a wealth of spiritual opulence", I said with joy.
For example, consider a Gaussian mixture model. We make an assumption - each data point is generated by two hidden latent variables that we do not directly observe. The hidden variables are Gaussian means , each of which is drawn from a Gaussian (or normal) distribution and a mixture proportion , where each is a nonnegative, vector where . We first obtain a dummy assignment as if it were coming from the multinomial mixture , and then draw the point from the particular Gaussian distribution . We can now see why a corresponding Gaussian distribution generates each data instance , and a mixture of Gaussians generates the entire dataset .
The configuration space of this model would be the number of Gaussians , and the hyperparameter . Setting this space is all about deciphering how many clusters there might be are that are useful in some way.
The parameter space would consist of the latent variables and the per cluster mean . This is all about can I cluster the data into clusters based on the spirit of bhakti bhava.
And the evidentiary spaces are the observed variables , speaks to partitioning a set of useful clusters into subclusters, where the context under which the data is being observed assumes prime importance.
Latent Variable Model Space
śrī vidya (meditation of the nondual)
clairvoyance of observation
depth and nuance of the awareness of the context in which any data is accumulated
śrī saptamātrike (meditation of perserverance & grit)
endurance of disciplined practice
an intuition of the number of latent clusters and hyperparameters, with the awareness that all estimation of latent variables must fit within the number of latent clusters so assigned
śrī lakśmi (meditation of inner opulence)
expansion & accumulation of inner wealth
cohesive wholesomeness of the estimated latent variables in a manner that is consistent with astute understanding of the data
"My dear child, I think you found an answer to your question about what inspired Syama Sastri", replied a beaming Lalitha, before we were interrupted by a rendition of first nagaswaram of the morning. "My child, I will have to be there for the gomata ceremony, you may see my sisters shortly. If so don't fail to ask them the significance of Mīnākṣī and Visalaksi", she suggested. "How will I recognize them amma", I asked, once again noticing the glittering diamond-studded lotus earnings on her. "Oh, that is very easy, we're triplets and looks very alike", she answered with a grin, before patting me on my head and walking away around the inner sanctum santorum.
II. Mīnākṣī & Model Inference
The nadaswaram accompanyists now started to play what sounded like a kriti in bilahari rāgam, though I could not identify which kriti it was. I began silently reading the great poet Kaviratna Kālidāsa's musical composition of shymala dandakam, feeling as if his description of nonduality was like observing the synchronized dance of two particles conjoined by quantum entanglement over a distance of many multiverses. I must have fallen into a dreamless nap state, for I was woken up by a gentle tap on my shoulder. "Karthik, isn't it?", she enquired, sitting down next to me. "My child, I'm one of Lalitha's sisters, and my name is Mātangi. She asked me to tell you the significance ofMīnākṣī, would you like to tell you now?", she asked with a laugh", and I said yes excitedly. I was positively astonished by how similar she looked to her sister, even as she wore a red saree and sported almost identical diamond-studded lotus earnings. "Are you stunned by how similar my earnings look like the ones my sister wore this morning?", she asked with a roar of a laugh. I could only respond with a smile torn somewhere between timidity and awe
"Oh dear one, the name Mīnākṣī means she whose eyes are shaped like that of a fish. Fish have a uniquely ultrawide panoramic view, don't they? It symbolizes the metaphysical reality whose watch over you is without beginning and knows no end. Her gaze is unending, shinning like a thousand effulgent suns by day and the splendor of a full moon at night. She is the embodiment of the highest metaphysical reality that is without attributes, whose qualities are like that of an ocean of eternal compassion, assisting in the removal of fear and the endowment of all knowledge. She is the sustaining and persevering force behind any spiritual practice and enters all its nooks and crevices."
I felt another wave splash against my face as if interrupting my parched stupor with a nourishing dash of refreshing hydration. There are many kinds of approximate inference routines for latent variable models. Of these, two of the most popular are Markov Chain Monte Carlo (MCMC) methods and variational inference. It is the case, almost universally that the conjugate priors are set via a setting of the hyperparameters well before the inference routine begins. Though practically all inference routines are sensitive to the initialization of these conjugate priors, all we do in latent variable models is to wait for the data to override the priors as the number of iterations in the inference routine keeps increasing. But shouldn't one also insert some cognitive input inside the very inference loop before proceeding with the next iteration? As I thought about this, a vivid image flashed in my mind of Mīnākṣī occupying every prior for every data point in every inference routine, overriding the effect of the data and correcting priors for each data point consistent with the goals of interpretative cohesion and wholesomeness.
Amśa (constituent parts)
nirantara saksi bhavati (eternal witness)
A watch over provisional attributes of consequence and a check for interpretive cohesiveness
Examine the posterior for data points by examining a latent variable of interest after each iteration
Examine the posterior for data points by examining variational parameters of interest after every variational update
samyāka upāstite (corrector of perceptual errors)
Correction of errors in inference that might lead to interpretive dilution and imbalance
Tweak the conjugate priors characterizing the latent variable of interest for affected data points to achieve interpretive cohesion. Disregard the updates derived from the data.
Tweak the conjugate priors characterizing the latent variable of interest for affected data points to achieve interpretive cohesion. Disregard the updates derived from the data
sarva yantrātmike (universal instrumentation)
An instrument to reason over the entire joint distribution, observing both the observed and the latent, at every stage
Human-in-the-loop sampling updates. Pause at every iteration and reflect on the observed data and the estimated latent variable.
Human-in-the-loop sampling updates. Pause at every iteration and reflect on the observed data and the estimated latent variable.
III. Visālākśi & Model Criticism
As instructed, I ate the prasādam in the outer courtyard and made my way back to Pasumalai Hills. I could hardly wait to come back to listen to the third piece this mystical puzzle. It was already almost noon by the time I started to walk back to Pasumalai, and the level of humidity in the air seemed to suggest the arrival of summer. I walked past a vegetable and fruit produce market and looked at carts of mangoes being readied for sale. There were no mangoes anywhere in the world as sumptuous and kingly as those in south India, I told myself, chuckling slightly at the thought of those whose otherwise overfed stomachs somehow still making room for an afternoon mango. I took a blissful nap that afternoon, waking up only to find that many peacocks were now walking all over Pasumalai Hills, including two peacocks that were exhibiting the outstretched glory of their magnificent feathers. It was time to go back to the Mīnākśi temple.
No sooner did I enter the temple this time than did I find a lady sitting down in a yellow sari, and her face looked identical to the sisters I met in the morning. I was certain that she was the third triplet, for she wore the same type of diamond-studded earnings. "Amma, my name is Karthik", I said, as I sat down next to her. "Of course dear one, I was busy in the morning, and I heard about you from my sisters you met this morning. We are almost identical, aren't we?", she said. "Namaskāram, Gowri amma!!", yelled a passerby who was carrying what looked like a large canister of milk.
"Ok, so let me tell you about the significance of Visālākśi. The word means she whose glance causes the expansion and broadening of the spirit. She represents that primordial cosmic expanse of infinite compassion, whose disposition is one of supreme peace and profound tranquility. She is the ascending and descending scale of the generative apparatus of the evolving identity of the self and embodies spiritual evolution wrapped by the nectar of understanding and love". By now I was positively smitten by the idea that even criticism must be cloaked in the warmth of compassion, both towards the self and to all others.
"Amma, the many vicissitudes and vagaries of life notwithstanding, excessive and harsh criticism, both of the self and others is decidedly the handiwork of the ego running amok. Perhaps a broadening and expanding liberal spirit can never be achieved unless one cultivates the discipline of compassion", I said. "Of course, my child", replied Gowri amma. "The Sattva guna cannot inhabit any place that is devoid of compassion and tolerance.".
We stood silently for a moment, as my mind floated to the concept of model criticism in Bayesian machine learning. Every time a model is specified, the specification and representation encode assumptions about the nature of the data generation process itself. A good critique of the estimated model, perhaps, should systematically check the assumptions so made before estimating the model, without resorting to acerbic commentary and resisting the tendency sweep untested assumptions under the carpet.
It is quite telling that the concept of model criticism involves both frequentist and Bayesian ideas. No dualist and duelist rejection is made of frequentist approaches. An understanding of the limitations and soundness of generative assumptions is possible only by broadening one's toolkit beyond purist Bayesian thinking by taking sampling techniques from the frequentist literature. In other words, one has to check the fervent Bayesian religiosity at the door and adopt a more liberal statistical stance.
I smiled broadly at Gowri amma, who seemed to have noticed that I was deepy moved. "My dear boy, please go inside the sanctum santorum now before the temple closes for the evening. See you again next year!", she exclaimed, patting me on my forehead. "Thank you so much amma!", I replied, thanking her and her sisters for their incredible generosity. I then walked into the sanctum santorum.
Nādaswaram music accompanied the chanting inside the sanctum santorum, and the rāgam being played was madhyamāvati. A group of women standing next to me was singing a song called Dharma Samvardhani. "Who's composition?", I quickly enquired. "Muttusvāmi Dīkṣita", came the reply. And it was in that moment that I felt a gaze coming towards me from inside the sanctum santorum, and the moola murti of Mīnākśi was now wearing a familiar looking diamond-studded lotus earning, as tears of joy flowed from my eyes, and the universe seemed to dissolve in a nectar-ocean of supreme bliss.