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Understanding the Logic of Direct Preference Alignment through Logic

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Pith's one-line read This paper proves that DPO-style preference losses have an exact logical form: each one can be decompiled into a propositional formula whose weighted-model-counting loss reproduces it, making loss design a matter of editing logic.

desk verdict A correct-by-construction algebraic re-encoding of DPA losses, but the claim that it captures the logic of the trained objective is undercut by the WMC independence assumption. read the letter →

arxiv 2412.17696 v2 pith:JM6ZE675 submitted 2024-12-23 cs.CL

Kyle Richardson , Vivek Srikumar , Ashish Sabharwal This is my paper · ORCID
classification cs.CL MSC 03B7068T2768T50
keywords directpreferenceoptimizationalignmentsemanticlossweightedmodelcountingstructureneuro-symboliclogiclandscapedecompilation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to show that the loss functions used in direct preference alignment (DPA), such as DPO and its variants, are not just optimization objectives but carry a hidden logical semantics. The authors propose a formalism called a preference structure, a triple of propositional formulas, and prove an exact translation: any DPA loss whose core equation is a ratio of disjoint multilinear polynomials can be decompiled into a preference structure whose semantic-loss ratio equals the original loss. If true, this makes the differences between DPO-style losses visible as logical entailment, reveals the loss landscape as a lattice of roughly 4.3 billion definable variants for DPO, and turns loss design into a matter of editing logical formulas and compiling them back. The paper demonstrates the approach by deriving new losses from first principles and reports a small-scale experiment in which one derived loss, cCPO, is competitive with CPO.

What carries the argument

The load-bearing object is a preference structure, written $P = (P, P_C, P_A)$: a core semantic formula $P$ that says something like 'if the model deems the loser valid, it should deem the winner valid,' a conditioning constraint $P_C$ that restricts which propositional models are counted, and an additive constraint $P_A$ that forces certain models always to be counted. Formulas are interpreted through weighted model counting, and the truth value of 'winner beats loser' is the ratio of counts of the satisfied and unsatisfied forms, whose log is the semantic loss ratio. Algorithm 1 decompiles a loss by translating its numerator and denominator into formulas, then assembling them via the implication construction of Proposition 2; Lemma 1 guarantees the compiled loss equals the original.

What would settle it

Take a loss whose published form includes one of the stripped terms, say DPOP with its $\max(0, \log P_{\mathrm{ref}}(y_w|x)/P_\theta(y_w|x))$ term or SimPO's $\gamma$ margin without the manual-reference rewrite, and find any assignment of model probabilities where the preference structure produced by Algorithm 1 yields a different loss value or gradient from the original; that difference would show the logic captures only an idealized core, not the trained objective.

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Extended reading notes

Core claim

The central claim, stated as Theorem 1, is that the preference structures in Table 4 correctly characterize the losses in Table 2 under the logistic-log semantic loss, meaning Eq. 6 holds: the core loss equation $\rho_\theta = \log(\rho^t_\theta/\rho^b_\theta)$ equals the semantic loss ratio $\log\big(\mathrm{WMC}(P_f;\theta)/\mathrm{WMC}(\neg P_f;\theta)\big)$ for the resulting preference structure. Lemma 1 supplies the mechanism: given any loss equation whose numerator and denominator are disjoint multilinear polynomials over atomic model predictions, Algorithm 1 returns a preference structure whose semantic loss ratio reproduces that equation. This is an exact, compositional translation between a class of DPA loss functions and logical programs over model predictions, so semantic relations among losses become logical entailment relations and new losses can be compiled from modified formulas. The same machinery extends to IPO and SliC by swapping the outer convex function, and to RRHF-style perceptron losses by switching to fuzzy-logic semantics.

Load-bearing premise

The load-bearing premise is that a loss is what its bare core equation says: a ratio of two disjoint products and sums built from individual model predictions, so that cross-entropy regularization, length normalization, margins, offsets, and max operations can be stripped away without changing the loss's logic.

Editorial extensions

If this is right

  • Every loss in Table 2 (DPO, CPO, ORPO, SimPO, DPOP, and the cross-entropy baselines) has an exact symbolic form in Table 4, so differences between losses can be read as logical entailment rather than algebraic coincidence.
  • Preference entailment is monotone in the loss: if one preference structure entails another, the semantic loss of the first is at least that of the second for any data and model, which orders the loss landscape as a lattice.
  • There are $4^{2^n}$ definable preference structures over $n$ atomic predictions, giving an upper bound of about 4.3 billion DPO-style losses for $n = 4$, most of them unexplored.
  • New losses can be produced by editing constraints: the paper derives unCPO, cCPO, and several unlikelihood losses this way, and in its case study cCPO reaches a 52.0% win-rate against CPO under a reward-model judge.
  • Reference-model losses acquire a clear semantic reading: adding a reference term turns the core formula into an implication guarded by the reference's winner prediction, which is why DPO's semantics is a conjunction of two such implications.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension would be to treat the stripped terms as explicit constraints: because the formalization removes cross-entropy regularization, length normalization, margins, offsets, and max operations before translation, the logical semantics describes an idealized core, and adding those terms back as formulas would test whether the logic also governs the objective actually trained.
  • The SimPO rewriting of $\gamma$ as a manual reference ratio assumes the preference data contains no transitive triples or cycles; a concrete testable extension is whether SimPO's semantic equivalence to DPO degrades on data that violates that condition.
  • The lattice order suggests a testable principle: semantically more constrained losses should be less vulnerable to alignment shortcuts such as driving both winner and loser probabilities to zero, which could be checked systematically across the unexplored losses in Figures 5 and 6.
  • The fuzzy-logic derivation of RRHF from the same core formula hints that the preference-structure formalism may generalize beyond probabilistic semantics, potentially connecting margin-based and perceptron-style losses into the same landscape.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes a formal framework for characterizing direct preference alignment (DPA) losses as symbolic logic. It introduces preference structures (P, PC, PA), a generalized semantic loss based on weighted model counting, and a decompilation algorithm (Algorithm 1) that translates a DPA loss's core equation log(ρt/ρb) into a preference structure whose WMC ratio equals the original ratio. The main formal results are Lemma 1 and Theorem 1, which assert that the structures in Table 4 correctly characterize the losses in Table 2 under the logistic-log semantic loss, plus Theorem 2 for IPO and SliC, a monotonicity result (Proposition 3), a count of definable structures, and a small-scale empirical case study of new losses around CPO. The paper also derives a loss lattice relating known and novel losses and reports a feasibility study with Qwen-0.5B.

Significance. The algebraic core of the paper is sound and useful: Algorithm 1 and Lemma 1 are correct as identities for the stated equation class, and the WMC calculations in Figure 3 and Table 4 check out. The framework offers a compositional, checkable translation between the algebraic form of DPA losses and logical formulas, and the monotonicity/lattice results are a genuine formal contribution. The paper also provides a Sympy-based construction (Figure 9) and a reproducible experimental protocol, which are strengths. However, the significance of the central claim hinges on whether the independent-atom WMC semantics in Eq. (2) is the right semantics for 'valid generation' by an LLM; the paper currently treats this as a modeling choice rather than a defended claim. If that semantics is not justified, the contribution reduces to algebraic rewriting of loss equations, which is interesting but not the 'logic of DPA' promised in the title.

major comments (3)
  1. [Section 4.1, Eq. (2); Theorem 1] The WMC semantics in Eq. (2) multiplies independent atom probabilities. For the atom set {M(x,yw), M(x,yl)}, it assigns positive weight to the joint event M(x,yw) ∧ M(x,yl). Under the interpretation of M(x,y) as 'y is a valid generation for x' in Figure 2B, the two events are not independent and, for a single sampled output, are mutually exclusive. Under the mutually exclusive joint, the ORPO structure from Table 4 (Pw = M(x,yw) ∧ ¬M(x,yl), Pl = M(x,yl) ∧ ¬M(x,yw)) has WMC ratio Pθ(yw|x)/Pθ(yl|x), which is the CPO ratio, not the ORPO ratio printed in Table 2. Thus the equality in Eq. (6) holds for the chosen algebraic factorization, not for the model's actual output distribution, and Theorem 1's claim that the structures 'correctly characterize the losses' is only an algebraic identity unless the paper supplies an argument that the product-form independent-atom semantics is the intended meaning of 'valid generation.' This is the load-bearing interpretive step and it is currently unstated.
  2. [Section 3, Table 2; Appendix A, Table 6] The decompilation operates on 'core loss equations' that remove cross-entropy regularization, length normalization, margins, offsets, α, max operations, and the β/λ weights. For SimPO, the rewrite γ = smref(yw,yl) introduces a manual reference model that is not part of the original loss, and the paper notes this is satisfiable only when the preference data contain no transitive triples or cycles. These are not harmless presentation details: the equality ρsem = ρθ in Eq. (6) is proved only for the stripped equations, so Theorem 1 should be restated as characterizing the idealized equations in Table 2, not the losses as implemented in the original papers. The authors should either prove that the stripped terms do not change the logical structure they identify, or explicitly limit all semantic claims to the core-equation class.
  3. [Section 5.2, Lemma 1; Proposition 2] The decompilation is correctness-by-construction. Because Algorithm 1 defines Pf := SEM(ρt) and ¬Pf := SEM(ρb) via the implication construction, the equality ρsem = ρθ is an identity; Lemma 1 and Theorem 1 are corollaries of the definitions and of the correctness of the SEM rules in Table 7. This is not an error, but it means the paper's semantic findings, such as CPO and ORPO sharing the same core formula P, are properties of the chosen encoding rather than empirical discoveries about the losses. The paper should state this more explicitly and identify what evidence would count against the semantic interpretation, for example a loss whose trained behavior contradicts the entailment relations in Figures 5 and 6.
minor comments (5)
  1. [Section 6.1, Figure 6] The claim that the lattice 'exhaustively captures all definable non-trivial single model losses and preference structures P ... that lie semantically in-between' is asserted without proof; Appendix E gives truth tables but no enumeration argument. Please either provide a proof of exhaustiveness or label the statement as a conjecture.
  2. [Appendix F, Table 5] The win-rate comparisons have overlapping error bars (for example, ℓcCPO is 52.0±0.6 against a 50% baseline, and subset win-rates such as ℓqfUNL on false-qa are 34.7±6.3). The conclusion that different losses have 'markedly different performance' is stronger than the data support; please report confidence intervals or significance tests, or temper the wording.
  3. [Appendix G] The copied prediction variables θ2 and ref2 for DPOP are representational devices, not actual model predictions, and the text says their values are set to 1 whenever the max term is inactive. Please mark these copies explicitly as part of the algebraic rewriting so that readers do not mistake them for semantic facts about the original DPOP loss.
  4. [Section 5.1 and Example 3] There are several typos and infelicities, including 'monototic' in Section 5.1 and 'the the winner' in Example 3; the paper would benefit from a careful proofreading pass.
  5. [Appendix B] The proof of Proposition 1 says to enumerate all 16 Boolean functions and verify that none works, which is acceptable but less transparent than a direct argument that no single formula over M(x,yw) and M(x,yl) can have WMC ratio Pθ(yw|x)/Pθ(yl|x); please expand the proof slightly.

Circularity Check

3 steps flagged · score 6.0 of 10

Decompilation is a correct-by-construction identity: Theorem 1's characterization is guaranteed by the implication-form encoding, and the CPO/ORPO 'shared semantics' is an artifact of that encoding.

  1. self definitional [Section 5.2, Eq. 6 and Algorithm 1; Section 6, Theorem 1]
    "The decompilation of a DPA loss ℓDPAx into a symbolic form can now be stated as finding a preference structure P whose particular semantic loss ℓslx is equal to ℓDPAx: ℓDPAx(θ,D) =ℓslx(P,θ,D), ρtθ/ρbθ = WMC(Pf;θ)/WMC(¬Pf;θ) (6). ... Algorithm 1: Pt ← SEM(ρtθ); Pb ← SEM(ρbθ); P ← SIMPLIFY(Implies(Pb,Pt)); PC ← SIMPLIFY(Or(Pt,Pb)); PA ← SIMPLIFY(And(Pt,Pb)); return P := (P,PC,PA) {ρθ = log WMC(Pf;θ)/WMC(¬Pf;θ), Lem. 1}."

    The characterization relation is defined in Eq. 6 as equality of the core loss ratio with the semantic loss ratio. Algorithm 1 then constructs the preference structure out of the very same polynomials: Pt is set to SEM(ρtθ), Pb to SEM(ρbθ), and the implication form of Proposition 2 makes Pf logically equivalent to Pt and ¬Pf to Pb. Consequently, WMC(Pf)/WMC(¬Pf) equals ρtθ/ρbθ identically, for any disjoint multilinear polynomials. Lemma 1 and Theorem 1 therefore assert that the construction satisfies the criterion by definition; they verify the encoder-inverter pair rather than derive an independent semantic fact about the losses. The 'correctly characterizes' statement is a tautology of the chosen encoding.

  2. renaming known result [Section 5, Proposition 2; Section 6.1, 'Single model approaches have an intuitive semantics']
    "Proposition 2. Given any two propositional formulas Pw and Pl, there exists a preference structureP such that Pw ≡ Pf and Pl ≡ ¬Pf. ... P := Pl → Pw, PC := Pw ∨ Pl and PA := Pw ∧ Pl. ... CPO and ORPO are both derived from the same core semantic formula P and implication first introduced in Figure 2."

    Proposition 2 shows that every pair of formulas can be encoded in the implication form P = Pl → Pw, with the actual pair-specific content pushed into PC and PA. Hence the shared core formula Implies(M(x,yl),M(x,yw)) for CPO and ORPO is guaranteed by the encoding for any two formulas Pw, Pl; it is not a discovered semantic commonality of those specific losses. The real difference between CPO and ORPO is relocated, by construction, into the conditioning constraint PC (one-true versus one-hot). Presenting the universal implication form as the 'core semantic formula' of both losses is a representational artifact of the chosen normal form rather than an independent characterization.

1 more flagged steps
  1. self definitional [Section 4.1, Assumption 1 and Eq. 2; Section 5.2, Example 7 and Table 4]
    "Assumption 1 (compositionality). When translating the preference log ratios ρθ from Table 2 to propositional formulas Pw and Pl, every unique model prediction PM(·) in ρtθ and ρbθ is treated as a unique weighted proposition forming an atomic variable. ... WMC(P;θ) := Σ_{w|=P} Π_{w|=Xi} Pθ(Xi) · Π_{w|=¬Xi}(1−Pθ(Xi)) (2)."

    Under Eq. 2, the formula SEM(ρtθ) = M(x,yw)∧¬M(x,yl) for ORPO receives probability Pθ(yw|x)(1−Pθ(yl|x)), exactly the numerator of ORPO's core equation, only because the atoms are multiplied as independent. For a single LLM, generating yw and generating yl are mutually exclusive events, so the faithful joint model would give P(M(x,yw)∧¬M(x,yl)) = Pθ(yw|x), making ORPO's structure reduce to CPO's ratio Pθ(yw|x)/Pθ(yl|x). The 'one-hot' semantics attributed to ORPO is therefore a property of the independent-atom counting convention chosen in Assumption 1, not of the loss evaluated on the model's actual output distribution.

full rationale

The paper is a formalization whose main correctness theorem is true by construction. Eq. 6 defines 'correctly characterizes' as equality between the core loss ratio and the semantic loss ratio; Algorithm 1 takes the numerator and denominator of that very ratio, translates each to a formula, and applies the universal implication form of Proposition 2, which makes Pf ≡ Pt and ¬Pf ≡ Pb. Lemma 1 and Theorem 1 therefore certify an identity, not a prediction. The interpretive claims built on this identity are correspondingly forced: the shared implication core of CPO and ORPO is an artifact of the universal encoding, and the one-hot constraint that distinguishes ORPO from CPO depends on treating winner and loser predictions as independent atoms, an assumption that does not hold for a single LLM's mutually exclusive outputs. This is genuine partial circularity in the central semantic claim. However, the paper also contains substantial non-circular content: the loss lattice, the entailment ordering, the enumeration of definable preference structures, and the small-scale empirical study of newly compiled losses against CPO are external and self-contained results. The only self-citation (Richardson & Wijnholds 2024) is in related work and is not load-bearing. Weighing these, the central 'logic of DPA' claim reduces by definition and by the chosen counting semantics, but the framework's generative and empirical contributions remain independent; a score of 6 reflects partial circularity rather than complete collapse.

Assumptions & free parameters 2 free parameters · 5 assumptions · 3 invented entities

The central formalization pulls in standard Boolean algebra and WMC, plus domain assumptions: independent atomic predictions, the disjoint multilinear polynomial equation class, and a chosen implication-form encoding. The SimPO γ rewrite and DPOP variable copying are representational devices needed to fit variants into the framework, and the empirical case study depends on grid-selected hyperparameters. The conceptual core is a translation scheme whose correctness is guaranteed by construction; what the framework adds is the symbolic form and the relations it induces, not a parameter-free prediction of an external constant.

free parameters (2)
  • Experimental hyperparameters selected on dev set = Learning rate in {1e-6, 3e-6, 8e-6, 9e-7}, epochs in {3, 5, 8}, batch in {32, 128}, CE weight λ in {0, 0.01, 0.1, 0.3…
    The empirical claim that ℓcCPO is competitive is conditioned on per-loss grid search over these values; the exact chosen values for each reported row are not given.
  • DPA weight β and CE weight λ in experiments = β = 1; λ around 0.01 to 0.1 found most effective
    These hyperparameters are set by hand or grid search rather than derived; the formal results do not depend on them, but the empirical comparison does.
assumptions (5)
  • domain assumption Propositional model predictions are independent weighted atoms: Pθ(M(x,y)) = Pθ(y|x), and WMC multiplies their weights.
    Introduced in Section 4 to give logical formulas a probabilistic semantics; real predictions from a single conditional model are not generally independent events.
  • domain assumption The core equation ρθ of every DPA variant considered is a ratio of disjoint multilinear polynomials in prediction variables.
    Section 5.2 restricts the equation class; DPOP needs variable copying and RRHF needs fuzzy logic, so the central algorithm does not cover all variants as originally written.
  • ad hoc to paper SimPO's margin γ can be represented as a log ratio smref(yw,yl) of a manual reference model.
    Section 3; requires setting Pmref(yl|x) = Pmref(yw|x)/exp(γ) and assumes the preference data has no transitive triples or cycles, so this is a representational device rather than an independent model.
  • ad hoc to paper The preference structure implication form (P = Pl → Pw, PC = Pw ∨ Pl, PA = Pw ∧ Pl) is the canonical encoding of any pair of formulas.
    Proposition 2; this choice forces every loss to display an implication core, so observed commonalities among losses partly reflect the encoding.
  • standard math Boolean algebra, weighted model counting, and the quotient rule for logarithms are standard background.
    Used throughout; standard mathematical background.
invented entities (3)
  • Preference structure (P, PC, PA) independent evidence
    purpose: Captures winner and loser semantics through a core formula plus conditioning and additive constraints; central representation for decompiling losses.
    It has explicit denotational semantics, compiles into testable loss functions, and the paper evaluates one such variant (ℓcCPO), so it has an empirical handle even though it is a formal construction.
  • Manual reference model mref for SimPO
    purpose: Represents SimPO's margin γ as a reference log ratio so that SimPO fits the DPO form.
    A notational device defined by Pmref(yl|x) = Pmref(yw|x)/exp(γ), with no independent data or predictions beyond re-encoding γ.
  • Copied prediction variables θ2 and ref2 for DPOP
    purpose: Restore multilinearity for DPOP's squared terms by duplicating variables.
    A syntactic device that duplicates variables; it does not correspond to additional model predictions.

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Pith. "Pith review of Understanding the Logic of Direct Preference Alignment through Logic." pith.science (2026). https://pith.science/paper/JM6ZE675

@misc{pith2026241217696,
  author       = {Pith},
  title        = {Pith review of: Understanding the Logic of Direct Preference Alignment through Logic},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JM6ZE675}},
  note         = {Machine review of arXiv:2412.17696}
}
read the original abstract

Recent direct preference alignment algorithms (DPA), such as DPO, have shown great promise in aligning large language models to human preferences. While this has motivated the development of many new variants of the original DPO loss, understanding the differences between these recent proposals, as well as developing new DPA loss functions, remains difficult given the lack of a technical and conceptual framework for reasoning about the underlying semantics of these algorithms. In this paper, we attempt to remedy this by formalizing DPA losses in terms of discrete reasoning problems. Specifically, we ask: Given an existing DPA loss, can we systematically derive a symbolic program that characterizes its semantics? We propose a novel formalism for characterizing preference losses for single model and reference model based approaches, and identify symbolic forms for a number of commonly used DPA variants. Further, we show how this formal view of preference learning sheds new light on both the size and structure of the DPA loss landscape, making it possible to not only rigorously characterize the relationships between recent loss proposals but also to systematically explore the landscape and derive new loss functions from first principles. We hope our framework and findings will help provide useful guidance to those working on human AI alignment.

Figures

Figures reproduced from arXiv: 2412.17696 by the authors.

Figure 1
Figure 1. Can we uncover the hidden logic of DPO? Here we show the decompilation of the DPO loss into a symbolic expression that expresses its high-level model behavior, along with a semantically modified version that we can compile into a novel DPO variant. We study how to translate between such loss and symbolic spaces to understand existing preference algorithms (e.g., by inspecting their semantics) and derive new algorith… view at source ↗
Figure 2
Figure 2. What do formal representations of loss functions tell us? We show (A) two symbolic formulas related to single model preference learning with their semantics paraphrased in informal English. When grounded in model behavior, they tell us about the structure of the model’s output probability distribution (B) and where predictions belong in that distribution (relative to some threshold ϵ). We will later show that these … view at source ↗
Figure 3
Figure 3. and correspond to the ✓s in the truth table rows (column 3). The weighted model count of these interpre￾tations, denoted as P✓, then corresponds to the WMC formula in Eq 2. Based on Eq 4, the semantic loss can be computed as the sigmoid of the log ratio of the counts of ✓ and × (i.e., the propositional models corresponding to the negation of P), both of which can be turned into a semantic loss by adding a −log. For … view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: How do we decompile losses? A visualization of our compositional decompilation procedure and main results using the example loss ℓORPO. First the original input loss (upper left) is stripped down to its core loss equation (lower left, log removed), which is then semant…
Figure 5
Figure 5. Figure 5: What other losses are there? Here we show the loss land￾scape for single model preference approaches using a loss lattice showing losses (nodes) structured according to strict entailment (❁) and their core formulas P (boxes) with ✓ being the known losses. See Appendix …
Figure 6
Figure 6. Figure 6: What are interesting DPO variants to explore? Extending the loss lattice in [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: A Boolean representation (in the style of [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: Boolean semantics of DPO and SimPO (column 5) and some novel variants of (columns 6-8) representing the different semantic regions in [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: An example showing how to compute the simplified sym￾bolic formulas in preference structures for ORPO (see [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: An illustration (A) of how to semantically satisfy losses ( ✓ ) and the corresponding log probability behavior during train￾ing (B) and evaluation (C). deed, we see in [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]

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Reference graph

Works this paper leans on

43 extracted references · 17 canonical work pages · cited by 1 Pith paper

  1. [1]

    DPO and reference approaches For DPO we see a simi- lar derivation

    Given that the same core semantic formula above can be recovered between the fuzzy and probabilistic approaches, we see this as giving additional motivation to using our preference structure rep- resentations. DPO and reference approaches For DPO we see a simi- lar derivation. Given the same core formula from Table 4: PDPO := Implies( And(Ref(x,yw),M(x,yl...

    work page 2024

  2. [2]

    arXiv preprint arXiv:2311.10702,

    arXiv

  3. [3]

    Prompting is programming: A query language for large language models

    Beurer-Kellner, L., Fischer, M., and Vechev, M. Prompting is programming: A query language for large language models. Proceedings of the ACM on Programming Lan- guages, 7(PLDI):1946–1969,

    work page 1946

  4. [4]

    However, the semantics of the resulting formulas are less transparent and often hidden in the weights

    schemes, as is commonly done in standard WMC encodings (Chavira & Darwiche, 2008). However, the semantics of the resulting formulas are less transparent and often hidden in the weights. We instead propose to define below a novel (unweighted) encoding for preference that doesn’t require additional variables, thereby facilitating a compositional and transpa...

    work page 2008

  5. [5]

    See again Figure 3 for how to interpret the corresponding losses. Proof. By the definition of preference entailment, we have P (1) f |= P (2) f . This means that for any d, P 1 (d) |= P 2 (d), which implies that for any θ, WMC P (1) (d); θ ≤ WMC P (2) (d); θ . From the definition of preference en- tailment, we also have ¬P (2) (d) |= ¬P (1) (d). Follow- i...

    work page 2018

  6. [6]

    (2024)), all of which were originally implemented using the logistic log-loss, i.e., each ℓx = − log σ(βρθ)

    Details of the original losses from Table 2 and others (adapted from Meng et al. (2024)), all of which were originally implemented using the logistic log-loss, i.e., each ℓx = − log σ(βρθ). We also include details about whether cross-entropy regularization (CE term) and length normalization (length norm.) were used (yes ✓, no ×) along with other details (...

    work page 2024

  7. [8]

    Declarative Design of Neural Predicates in Neuro-Symbolic Systems

    Hinnerichs, T., Manhaeve, R., Marra, G., and Dumancic, S. Declarative design of neural predicates in neuro-symbolic systems. arXiv preprint arXiv:2405.09521,

    work page Pith review arXiv

  8. [9]

    New desiderata for direct pref- erence optimization

    Hu, X., He, T., and Wipf, D. New desiderata for direct pref- erence optimization. arXiv preprint arXiv:2407.09072,

    arXiv

Show all 43 references
  1. [10]

    For example,ℓunCPO and ℓcfUNL attempt to make both the winners and losers false by driving their probability in the direction of zero (as shown in in both training (b) and evaluation (c)), whereas ℓcfUNL keeps both probabilities high to make both true. When viewing learning as...

    2024

  2. [11]

    T., Moazam, H., et al

    13 Understanding the Logic of Direct Preference Alignment through Logic Khattab, O., Singhvi, A., Maheshwari, P., Zhang, Z., San- thanam, K., Vardhamanan, S., Haq, S., Sharma, A., Joshi, T. T., Moazam, H., et al. Dspy: Compiling declarative language model calls into self-impro...

    arXiv

  3. [12]

    What makes good data for alignment? a comprehensive study of automatic data selection in instruction tuning

    Liu, W., Zeng, W., He, K., Jiang, Y ., and He, J. What makes good data for alignment? a comprehensive study of automatic data selection in instruction tuning. arXiv preprint arXiv:2312.15685,

    arXiv

  4. [15]

    Smaug: Fixing failure modes of pref- erence optimisation with dpo-positive

    Pal, A., Karkhanis, D., Dooley, S., Roberts, M., Naidu, S., and White, C. Smaug: Fixing failure modes of pref- erence optimisation with dpo-positive. arXiv preprint arXiv:2402.13228,

    arXiv

  5. [16]

    Online dpo: Online direct preference optimization with fast-slow chasing

    Qi, B., Li, P., Li, F., Gao, J., Zhang, K., and Zhou, B. Online dpo: Online direct preference optimization with fast-slow chasing. arXiv preprint arXiv:2406.05534,

    arXiv

  6. [17]

    Unintentional unalignment: Likelihood displacement in direct preference optimization

    Razin, N., Malladi, S., Bhaskar, A., Chen, D., Arora, S., and Hanin, B. Unintentional unalignment: Likelihood displacement in direct preference optimization. arXiv preprint arXiv:2410.08847,

    arXiv

  7. [19]

    L., Stew- art, R., and Stark, K

    14 Understanding the Logic of Direct Preference Alignment through Logic ´Slusarz, N., Komendantskaya, E., Daggitt, M. L., Stew- art, R., and Stark, K. Logic of differentiable logics: Towards a uniform semantics of dl. arXiv preprint arXiv:2303.10650,

    arXiv

  8. [21]

    Uller: A unified language for learn- ing and reasoning

    van Krieken, E., Badreddine, S., Manhaeve, R., and Giunchiglia, E. Uller: A unified language for learn- ing and reasoning. In International Conference on Neural-Symbolic Learning and Reasoning, pp. 219–239. Springer, 2024a. van Krieken, E., Minervini, P., Ponti, E. M., and Ver...

    arXiv

  9. [22]

    Aligning large language models with human: A survey

    Wang, Y ., Zhong, W., Li, L., Mi, F., Zeng, X., Huang, W., Shang, L., Jiang, X., and Liu, Q. Aligning large language models with human: A survey. arXiv preprint arXiv:2307.12966,

    arXiv

  10. [24]

    Xu, H., Sharaf, A., Chen, Y ., Tan, W., Shen, L., Van Durme, B., Murray, K., and Kim, Y . J. Contrastive preference optimization: Pushing the boundaries of llm performance in machine translation. arXiv preprint arXiv:2401.08417,

    arXiv

  11. [25]

    Direct preference knowledge distillation for large language models

    Yixing, L., Yuxian, G., Dong, L., Wang, D., Cheng, Y ., and Wei, F. Direct preference knowledge distillation for large language models. In arXiv preprint arXiv:2406.19774,

    arXiv

  12. [26]

    Rrhf: Rank responses to align language mod- els with human feedback without tears

    Yuan, Z., Yuan, H., Tan, C., Wang, W., Huang, S., and Huang, F. Rrhf: Rank responses to align language mod- els with human feedback without tears. arXiv preprint arXiv:2304.05302,

    arXiv

  13. [28]

    Zhao, Y ., Joshi, R., Liu, T., Khalman, M., Saleh, M., and Liu, P. J. SLiC-HF: Sequence Likelihood Calibration with Human Feedback. arXiv preprint arXiv:2305.10425,

    arXiv

  14. [29]

    M., Stiennon, N., Wu, J., Brown, T

    Ziegler, D. M., Stiennon, N., Wu, J., Brown, T. B., Radford, A., Amodei, D., Christiano, P., and Irving, G. Fine-tuning language models from human preferences. arXiv preprint arXiv:1909.08593,

    1909 arXiv

  15. [30]

    Original losses Further details of the original losses in Table 2, along with other variants such as R-DPO (Park et al., 2024), ODPO (Amini et al.,

    A. Original losses Further details of the original losses in Table 2, along with other variants such as R-DPO (Park et al., 2024), ODPO (Amini et al.,

    2024

  16. [31]

    and DPKD (Yixing et al., 2024), are shown in Table

    2024

  17. [35]

    where we can replace each P . with the corresponding WMC equations for each mark, then simplify the resulting equation (i.e., the core loss equation) to arrive at a compact loss equation that can be directly used for implementation. Losses used in experiments Employing the pro...

    2024

  18. [36]

    Figure 8 shows the Boolean semantics of DPO/SimPO and some novel variants based on the ref- erence form of ORPO (ℓORPO-ref), qfUNL (ℓqfUNL-ref) and l5 (ℓl5-ref)

    This reveals a wide range of novel variants of DPO that we leave for future experi- ments and study. Figure 8 shows the Boolean semantics of DPO/SimPO and some novel variants based on the ref- erence form of ORPO (ℓORPO-ref), qfUNL (ℓqfUNL-ref) and l5 (ℓl5-ref). Computing pref...

    2017

  19. [37]

    Specifically, we focus on losses around the known lossℓCPO, which we treat as a natural baseline to compare against

    in Sympy (Meurer et al., 2017). Specifically, we focus on losses around the known lossℓCPO, which we treat as a natural baseline to compare against. All experiments are performed using a 0.5 billion parameter LLM, Qwen-0.5B (Bai et al., 2023), tuned using trl (von Werra et al.,

    2017

  20. [38]

    While these experiments are small scale and limited in scope, they are merely meant to suggest possible uses our frame- work and open questions

    on the ultrafeedback dataset; following standard practice, losses were implemented with a weighted cross-entropy regularizer term. While these experiments are small scale and limited in scope, they are merely meant to suggest possible uses our frame- work and open questions. W...

    2023

  21. [39]

    To avoid repeating the process of instruction tuning, we started from the trained Qwen model released in the TRL library6

    that was initially tuned on 6k pairs from the deita dataset of (Liu et al., 2023). To avoid repeating the process of instruction tuning, we started from the trained Qwen model released in the TRL library6. Hyper-parameters and model selection The following are the standard set...

    2024

  22. [41]

    This suggests that different types of preference data rely on a different semantics of preference, which requires a tuning approach that’s tailored to those differences

    varies quite considerably across models and loss types. This suggests that different types of preference data rely on a different semantics of preference, which requires a tuning approach that’s tailored to those differences. We conjecture that such a phenomenon is likely to b...

    2024

  23. [42]

    extend and relax classical logic by allowing truth values to have a continuous range. In these systems, traditional Boolean operators take the form of continuous functions, based on the theory of t-norms (Klement et al., 2013), which provides a means for directly translating l...

    2021

  24. [1975]

    Self-exploring language models: Active preference elicitation for online alignment

    Zhang, S., Yu, D., Sharma, H., Zhong, H., Liu, Z., Yang, Z., Wang, S., Hassan, H., and Wang, Z. Self-exploring language models: Active preference elicitation for online alignment. arXiv preprint arXiv:2405.19332,

    arXiv

  25. [1977]

    D., Zheng, Z., Calandriello, D., Munos, R., Rowland, M., Richemond, P

    Tang, Y ., Guo, Z. D., Zheng, Z., Calandriello, D., Munos, R., Rowland, M., Richemond, P. H., Valko, M., Pires, B. ´A., and Piot, B. Generalized preference optimization: A unified approach to offline alignment. arXiv preprint arXiv:2402.05749,

    arXiv

  26. [2007]

    G., Wu, Y ., Michalewski, H., Saurous, R

    Dohan, D., Xu, W., Lewkowycz, A., Austin, J., Bieber, D., Lopes, R. G., Wu, Y ., Michalewski, H., Saurous, R. A., Sohl-Dickstein, J., et al. Language model cascades. arXiv preprint arXiv:2207.10342,

    arXiv

  27. [2015]

    Insights into align- ment: Evaluating dpo and its variants across multiple tasks

    Saeidi, A., Verma, S., and Baral, C. Insights into align- ment: Evaluating dpo and its variants across multiple tasks. arXiv preprint arXiv:2404.14723,

    arXiv

  28. [2017]

    and Riedel, S

    Minervini, P. and Riedel, S. Adversarially regularising neu- ral nli models to integrate logical background knowledge. arXiv preprint arXiv:1808.08609,

    arXiv

  29. [2018]

    Miranda, L. J. V ., Wang, Y ., Elazar, Y ., Kumar, S., Pyatkin, V ., Brahman, F., Smith, N. A., Hajishirzi, H., and Dasigi, P. Hybrid preferences: Learning to route instances for human vs. ai feedback. arXiv preprint arXiv:2410.19133,

    arXiv

  30. [2019]

    I., Zhao, H., Das, A., Tang, W., Yao, D

    Winata, G. I., Zhao, H., Das, A., Tang, W., Yao, D. D., Zhang, S.-X., and Sahu, S. Preference tuning with human feedback on language, speech, and vision tasks: A survey. arXiv preprint arXiv:2409.11564,

    arXiv

  31. [2020]

    G., Rowland, M., Piot, B., Guo, D., Calandriello, D., Valko, M., and Munos, R

    Azar, M. G., Rowland, M., Piot, B., Guo, D., Calandriello, D., Valko, M., and Munos, R. A general theoretical paradigm to understand learning from human preferences. arXiv preprint arXiv:2310.12036,

    arXiv

  32. [2021]

    Direct language model alignment from online ai feedback.arXiv preprint arXiv:2402.04792,

    Guo, S., Zhang, B., Liu, T., Liu, T., Khalman, M., Llinares, F., Rame, A., Mesnard, T., Zhao, Y ., Piot, B., et al. Direct language model alignment from online ai feedback.arXiv preprint arXiv:2402.04792,

    arXiv

  33. [2022]

    Donadello, I., Serafini, L., and Garcez, A. D. Logic ten- sor networks for semantic image interpretation. arXiv preprint arXiv:1705.08968,

    arXiv

  34. [2023]

    Qwen technical report

    Bai, J., Bai, S., Chu, Y ., Cui, Z., Dang, K., Deng, X., Fan, Y ., Ge, W., Han, Y ., Huang, F., et al. Qwen technical report. arXiv preprint arXiv:2309.16609,

    arXiv

  35. [2024]

    Logically consistent language models via neuro-symbolic integration

    Calanzone, D., Teso, S., and Vergari, A. Logically consistent language models via neuro-symbolic integration. arXiv preprint arXiv:2409.13724,

    arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.