Advaita Vedānta

On this reading the eternal Brahman gained here is liberation itself, but reached by a definite sequence. Sacrifice removes sin and brings purity of mind; the purified mind grows fit for Self-knowledge, gained through hearing and the other means; and only that knowledge yields Brahman. Because the verse speaks of a path and lets time pass, the liberation meant is gradual, krama-mukti, not direct release; to read it as immediate liberation would clash with the scripture of the path. The non-sacrificer lacks even one of the named sacrifices, whether the twelve or the five daily obligatory ones, and so forfeits even the common world, let alone the world of the Self.

Śaṅkarācārya · Śrī Ānandagiri · Śrī Nīlakaṇṭha · Dhanapati Sūri

Viśiṣṭādvaita

Here the stress falls on staying engaged in the discipline of action while merely keeping up the body with the sacrificial remnant; such people go to the eternal Brahman. 'This world' that the non-sacrificer loses is read specifically as the human goal belonging to the world of matter, the lawful pursuit of duty, wealth, and pleasure; and since liberation is the topic as the highest human aim, the verse points to that lower, material aim by the words 'this world' precisely to deny it to the one who drops the obligatory and occasional actions preceded by the great sacrifices. The supplementary gloss presses the same logic: the absence-of-sacrifice forfeits the worldly fortune, the various lesser human ends are denied, and liberation, the supreme human goal, is closed off as well.

Rāmānujācārya · Vedānta Deśika

Bhedabheda

This reading takes the remnant plainly as the leftover of the material substance applied in sacrifice, eaten as nectar. It adds an explicit double route to the goal: the actions performed even by those who long for fruit become causes of the attainment of Brahman, either directly or through succession. It then frames the whole sweep of sacrifices as 'spread out in the mouth of Brahman,' all of them born of action, and says that knowing this brings release.

Śrī Bhāskara

Dvaita

This source does not comment on the surface promise and warning of the verse at all but is occupied with a fine technical question carried over from the surrounding verses: the nature of offering the vital breaths into the vital breaths, and how restraint of food bears on it. It reads the drying up of the vital breaths as the contracting of the senses' functions into the sense-powers, distinguishes this restraint-by-food from the earlier withdrawal-by-hearing, and weighs whether 'restrained in food' should count as a separate sacrifice, preferring the explanation grounded in scripture over a merely supplied one.

Śrī Jayatīrtha

Śuddhādvaita

The Pushtimarga reading takes the remnant as prasada, the grace-laden leftover of the Lord himself, so that tasting it does more than cleanse fault; the seeker is gathered into the divine company. One source develops this devotionally: it is by remembrance of the Lord that works are made complete, and the 'nectar that remains over' is precisely that remembrance of Bhagavan; the non-sacrificer is the one without the sacrifice that has the form of the Lord's manifestation and command, and so even this world, where he is censured, is not won by him, let alone the imperishable beyond.

Vallabhācārya · Śrī Puruṣottama

Kashmir Shaivism

Here the imagery is turned wholly inward and esoteric. The 'remnant of the sacrifice' is the gladdening of one's own instruments, the senses and inner organs; the 'nectar' is the resting in one's own Self, made of supreme, objectless bliss. Those who enjoy this are joined, as they wish, with the state of Brahman. The source deliberately declines to spell out the secret further, saying that this hidden savour, when held within, becomes for the rightly prepared seeker, ripened by the tradition and a graceful teacher, a matter of inward chewing-over that yields the taste of the real meaning.

Ācārya Abhinavagupta

Bhakti

These devotional commentators read the remnant as the permitted, not-forbidden food enjoyed after sacrifice, by which, through knowledge, the doer reaches eternal Brahman; one stresses that this Brahman is the fruit specifically aimed at, while the enjoyment of the remnant is a fruit not deliberately sought. The warning is read plainly: this man-world of only slight happiness is not even attained by the non-sacrificer, so the world of the gods and the like is all the more beyond him; therefore sacrifices must by all means be done. One source, the Marathi commentary, makes the knowledge explicit and lyrical: the knowledge emerging at the close of sacrifice is pure and beginningless, enjoyed by souls devoted to Brahman together with the recital 'I am Brahman,' and those content with this nectar become masters of true immortality and are easily absorbed into the Supreme.

Śrīdhara Svāmī · Śrīla Viśvanātha · Śrīla Baladeva · Sant Jñāneśvar

Modern

These modern commentators keep the purification-to-knowledge logic but draw out wider meanings. One reads 'sacrifice' in its broadest sense: any act stripped of attachment to its fruit becomes a yajna, the Mimamsa rules about partaking of the remnant then apply to all of them, and the line that the non-sacrificer has no success even in this world carries a social principle, that unless everyone sacrifices something dear, the shared life of the world cannot go on by all getting equal opportunity. Another gives the teaching an inward, non-sectarian devotional turn: yajna is giving happiness to others without selfish motive, the resulting experience of evenness is itself the 'nectar of the remnant,' and the human body and every duty done purely as duty exist for sacrifice alone; by living so a person becomes detached and tastes the deathlessness that is already his true nature, while one who lives only for himself binds himself and forfeits even this world.

Swami Sivananda · Lokmanya Tilak · Swami Ramsukhdas