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REVIEW 5 major objections 5 minor 48 references

From Hallucinations to Jailbreaks: Rethinking the Vulnerability of Large Foundation Models

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Pith's one-line read This paper claims that hallucinations and jailbreaks in large foundation models arise from a single shared optimization mechanism, so defending against one vulnerability also mitigates the other.

desk verdict The empirical cross-mitigation results are interesting, but the central theoretical claim is constructed rather than derived, so the paper should be rejected in its current form. read the letter →

arxiv 2505.24232 v1 pith:FAFULRYC submitted 2025-05-30 cs.CV cs.AIcs.CL

classification cs.CVcs.AIcs.CL
keywords hallucinationjailbreakattacklargefoundationmodelsattentionredistributiongradientalignmentvision-languagecross-domainmitigationsoftmaxsparsification
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 argues that hallucinations and jailbreaks are not separate bugs but two symptoms of the same underlying optimization tendency in large foundation models. It models jailbreaks as a token-level optimization that pushes the output distribution toward a harmful target, and hallucinations as an attention-level optimization that shifts focus toward a target token. Under stated proportionality conditions, the two loss functions converge to the same limiting scalar, and their gradients share a common attention-driven component. The authors show empirically on two vision-language models that hallucination-mitigation methods reduce jailbreak success rates and jailbreak defenses improve factual correctness, supporting the shared-mechanism view. If the claim holds, robustness work should target the shared mechanism rather than either failure in isolation.

What carries the argument

The central object is a pair of loss functions placed in a common embedding-perturbation setting: $L_{\text{adv}} = -\log p(y^\star | \tilde H)$ for jailbreaks and $L_{\text{hallu}} = \sum_i (-\log A^\Delta_{it} + \lambda \sum_{j\neq t} \log A^\Delta_{ij})$ for hallucinations. The argument runs on two mechanisms: (i) proportional scaling assumptions that non-target logits equal $\beta_j$ times the target logit and non-target attention equals $\eta_j$ times the target attention, with the sums $\sum \beta_j$ and $\sum \eta_j$ decaying to zero and $\lambda \to 0$; (ii) a shared gradient component $\Delta_{ij} = A^\Delta_{ij}(W_Q^T W_K H_j - \sum_k A^\Delta_{ik} W_Q^T W_K H_k)\cdot W_V H_j$ that appears in both gradients. Together these make the two losses converge to the same limiting function and align their optimization directions.

What would settle it

Measure the cosine similarity between the jailbreak and hallucination loss gradients on a model where attention does not concentrate into a single dominant token, such as a model evaluated on ambiguous or long-context inputs. If the similarity drops far below the 0.93 observed in the paper, the shared-gradient claim does not hold in that regime.

Watch

Extended reading notes

Core claim

The paper's central claim is that hallucination and jailbreak objectives converge to similar scalar functions, indicating that both reflect a fundamental optimization tendency of LFMs rather than isolated bugs. Concretely, Proposition 4.1 proves that under proportional scaling of non-target logits and non-target attention weights, with the scaling sums and the regularization parameter tending to zero, the jailbreak loss and hallucination loss have the same limit. Proposition 4.2 shows both gradients contain an identical attention redistribution term, so optimizing either loss moves the model's parameters in aligned directions. The authors validate these propositions on LLaVA-1.5 and MiniGPT-4 by tracking the scaling factors and loss curves, and show cross-domain mitigation: jailbreak defenses improve hallucination benchmarks and hallucination mitigations lower jailbreak attack success rates.

Load-bearing premise

The conclusion depends on the proportional scaling conditions holding as the dominant regime in real models: that during attack or hallucination, every non-target logit and non-target attention weight is a small fraction of the target's value, with those fractions summing to near zero.

Editorial extensions

If this is right

  • If both vulnerabilities share an optimization structure, then a defense that reduces one should transfer to the other; the paper demonstrates this bidirectionally on two vision-language models.
  • Robustness evaluation should measure both hallucinations and jailbreaks in the same sweep, since a method that improves one without checking the other may be hiding a tradeoff or a shared fix.
  • Attention-based interventions like OPERA and VCD can be considered a general-purpose safety mechanism, not just a factuality patch.
  • Gradient alignment implies that an attacker optimizing a jailbreak suffix is implicitly optimizing an attention shift; adversarial perturbations for one objective may transfer to the other.
  • The framework suggests that safety training should penalize attention concentration on unsafe targets and output likelihood of unsafe tokens jointly.

Reading between the lines

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

  • If the shared-gradient claim generalizes, jailbreak attacks might be detectable by monitoring attention concentration as a proxy, without waiting for harmful text to appear.
  • The proportionality assumptions suggest a softmax-sparsification regime; one could test directly whether the ratio $\sum_{j\neq t} A_{ij}/A_{it}$ is a reliable early indicator of jailbreak susceptibility across model scales.
  • The cross-mitigation effect may extend beyond the attacks the paper tests; for example, prompt-injection attacks in tool-using agents might also be mitigated by attention reallocation methods, since they similarly hijack output targets.
  • A natural extension would be to treat the gradient-alignment coefficient as a unified vulnerability score, letting practitioners rank models by a single number instead of separate hallucination and jailbreak scores.
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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

5 major / 5 minor

Summary. The paper proposes a unified theoretical framework connecting hallucinations and jailbreak attacks in large foundation models (LFMs). It models jailbreaks as token-level optimization and hallucinations as attention-level optimization, then claims two propositions: (1) similar loss convergence between the two objectives under proportional scaling assumptions, and (2) gradient consistency driven by shared attention dynamics. The authors validate these claims with optimization experiments on LLaVA-1.5 and MiniGPT-4 and demonstrate cross-mitigation effects between hallucination-reduction and jailbreak-defense methods. The central theoretical result, Proposition 4.1, is not valid as proven: the derivation drops the target logit term in the softmax denominator and imposes equality by solving for a scaling parameter rather than deriving it from the stated limits. The empirical sections are suggestive but do not compensate for the unsound theoretical basis.

Significance. If the unified framework were correct, it would provide a conceptually interesting link between two usually separate failure modes and would motivate joint defense strategies. The paper contributes a useful empirical observation that hallucination-mitigation methods (OPERA, VCD) reduce jailbreak success rates and that jailbreak defenses improve hallucination correctness. However, the theoretical propositions are the claimed main contribution, and they are not established. The proof of Proposition 4.1 contains a mathematical error and a circular construction; Proposition 4.2 is asserted rather than demonstrated. The cross-mitigation experiments, while potentially valuable, do not validate the specific loss-convergence and gradient-alignment theorems. The paper ships no code or machine-checked proofs, and several experimental details are missing, so the results are not independently verifiable from the text alone.

major comments (5)
  1. [§4.1, Eq. (12) and Appendix B, Eq. (27)] Proposition 4.1 is not derived correctly. With the proportional scaling assumption [Wout oi]_j = beta_j [Wout oi]_{y*}, the jailbreak loss should contain log( exp([Wout oi]_{y*}) + sum_{j != y*} exp(beta_j [Wout oi]_{y*}) ). Equation (27) drops the target logit term from the logarithm, leaving log sum_{j != y*} exp(beta_j [Wout oi]_{y*}). In the limit sum beta_j -> 0, the correct expression tends to log( exp([Wout oi]_{y*}) + |V| - 1 ), not log(|V| - 1). The equality with L_hallu therefore does not follow. The Taylor expansions in Appendix A.1 propagate the same omission.
  2. [Appendix B, Eq. (31)] The proof of Proposition B.1 is circular. The authors define Delta L = L_hallu - L_adv, set Delta L = 0, and solve for eta_j in terms of beta_j, obtaining eta_j = (1/C) exp(- beta_j [Wout oi]_{y*} / lambda). This constructs the equality rather than showing that the limiting behavior of the two losses is equal under the stated assumptions. The normalization constant C itself depends on the sums of eta_j and beta_j, so the expression is not a closed-form solution. Consequently, the proposition's conclusion is true by construction, not by dynamics of the optimization.
  3. [§5.1, Implementation Details and Eq. (9)] The optimization direction for the hallucination loss is stated inconsistently. The paper says 'we maximize the attention redistribution loss L_hallu', but Eq. (9) defines a loss to be minimized to increase target attention and suppress non-target attention: minimizing -log A_it and lambda sum log A_ij pushes A_it up and A_ij down. Maximizing L_hallu would do the opposite. This sign error makes the hallucination optimization experiments in Figures 2-4 ambiguous: it is unclear whether the reported behavior is for minimization or maximization. The text should be corrected and the experiments re-described.
  4. [§4.2, Proposition 4.2 and Appendix B, Proposition B.2] Gradient consistency is not demonstrated. The gradient of L_adv has a softmax coefficient Delta_softmax,i (Eq. 39), while the gradient of L_hallu has the coefficient -delta_it + lambda I(j != t). The claim that for large lambda the latter 'resembles' Delta_softmax,i is asserted without proof; the two coefficients have different structures, and no argument shows they are aligned in sign or magnitude. The notation also mixes the jailbreak target y* with the attention target t, and the derivation does not define t in the jailbreak context. The shared component Delta_ij is a common factor, but the coefficients acting on it determine whether the gradients are actually correlated.
  5. [§5.3, Table 1 and Figures 2-4] The empirical gradient-similarity results are computed in a setup where both L_hallu and L_adv are optimized on the same set of prompts, with visual inputs disabled. In this protocol, high cosine similarity may reflect the shared optimization trajectory rather than an intrinsic coupling of the two losses. A control experiment using random objectives or distinct target sets would be needed to rule out trivial alignment. As reported, the results do not provide strong validation of Proposition 4.2.
minor comments (5)
  1. [§3.2, Eq. (9) and §5.3] The role of lambda is inconsistent across the paper: Proposition 4.1 requires lambda -> 0, while Proposition 4.2 and the experiments in Section 5.3 use large lambda (up to 100). The authors should clarify how these different regimes are reconciled.
  2. [§5.1] The dataset is described as '50 commonsense reasoning prompts from [36]', but reference [36] is 'LLM Lies: Hallucinations are not bugs, but features as adversarial examples'. The paper should specify the exact source and whether these prompts are appropriate for jailbreak evaluation, since jailbreak attacks typically require harmful or unsafe requests.
  3. [§5.1] Disabling visual inputs means the optimization experiments are conducted on text-only inputs, while the claimed applications are to vision-language models and benchmarks like HallusionBench. The paper should state this limitation when interpreting the optimization results.
  4. [§5.4, Tables 2 and 3] The cross-mitigation results are reported as point improvements without error bars, confidence intervals, or significance tests. Given the small prompt count (50) and the variability of jailbreak success rates, it would be helpful to report variability across runs or seeds.
  5. [Throughout] There are formatting and typographical issues: 'LLaV A-1.5' appears inconsistently instead of 'LLaVA-1.5'; Eq. (34) uses t without definition; the reference for SafeBench [43] appears to be about autonomous vehicles, not vision-language safety; and the abstract repeats 'converge' and 'consistency' without precise definitions.

Circularity Check

2 steps flagged · score 8.0 of 10

Proposition 4.1's loss convergence is imposed by setting ΔL=0 and solving for η_j; Appendix B also drops the target softmax term, and Proposition 4.2 defines the shared gradient rather than deriving it.

  1. self definitional [Appendix A.3 (Eqs. 19-23) and Appendix B, Proposition B.1 proof (Eqs. 31-32)]
    "By considering the difference between the two losses, defined as ∆L=L hallu − Ladv, we set ∆L=0, solve for ηj in terms of βj, we obtain: ηj = 1/C · e^{−βj [Wout ˜oi ]y∗i /λ} ... Thus, the hallucination loss and jailbreak loss converge as: lim Lhallu = lim Ladv"

    The proof does not show that the two losses approach a common limit from the stated decay assumptions. Instead it defines ΔL = Lhallu − Ladv, sets ΔL = 0, and solves for η_j as a function of β_j (Eq. 31). That choice makes Lhallu = Ladv true by construction, so the 'similar loss convergence' is an input to the proof, not a derived consequence. In addition, Eq. 27 replaces the full softmax denominator log(exp([Wout oi]_{y*}) + Σ_{j≠y*} exp(β_j [Wout oi]_{y*})) with log Σ_{j≠y*} exp(β_j [Wout oi]_{y*}), omitting the target logit; with the correct denominator the Taylor expansion is different. The claimed limit equality is therefore not established from the assumptions.

  2. self definitional [Appendix B, Proposition B.2 proof (Eqs. 33-42)]
    "Using this shared component, the gradients can be rewritten as: ∂Ladv/∂H = Σ_i W_out^T Δsoftmax,i Σ_j Δij (37); ∂Lhallu/∂Δ = Σ_i [−Δ_it + λ Σ_{j≠t} Δij] (38) ... For sufficiently large λ (λ≫1), the term λI(j≠k) dominates, making Γij for Lhallu resemble Δsoftmax,i. This alignment leads to similar optimization directions for Ladv and Lhallu."

    The shared component Δij is defined in Eq. 13 with a dot product ·WV Hj that appears in the jailbreak gradient (Eq. 34) but is absent from the hallucination gradient derived in Eq. 35, which is an embedding-space vector. The proof then rewrites ∂Lhallu as a sum of scalar Δij terms and chooses the dynamic coefficient Γij so that Γhallu 'resembles' Δsoftmax,i. Gradient alignment is thus asserted by defining both losses in terms of the same Δij and by selecting the coefficient, rather than derived from the two loss functions.

full rationale

The paper's central theoretical proposition (Similar Loss Convergence) is circular: in Appendix A.3 and in the proof of Proposition B.1, the authors define ΔL = Lhallu − Ladv, set ΔL = 0, and solve for η_j in terms of β_j before concluding that the losses converge. This constructs the equality that the proposition claims to prove. The proof is additionally algebraically invalid because Eq. 27 drops the target logit from the softmax denominator, so the stated limit expansion is not the jailbreak loss. Proposition 4.2 is similarly constructed: a 'shared component' Δij is defined using a ·WV Hj factor present only in the jailbreak gradient, and the hallucination gradient is then rewritten in terms of that same scalar component with a coefficient chosen so that the gradients 'resemble' each other. The empirical cross-mitigation experiments (Tables 2-3) provide independent evidence of transfer between hallucination and jailbreak defenses, and the paper's self-citations in related work are not load-bearing. However, the theoretical unification that forms the paper's main contribution reduces to its conclusion by construction, so the circularity score is 8 rather than lower.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on ad hoc scaling factors and limiting assumptions that enforce the convergence result. The hallucination loss itself is an invented formulation, but it is a loss function rather than an entity. There are no newly postulated physical mechanisms or entities.

free parameters (3)
  • lambda = 0.1, 1, 10, 100
    Regularization coefficient in L_hallu that balances focus on the target vs suppression of non-targets. The propositions require opposite regimes: lambda tending to 0 in Proposition 4.1 and lambda much greater than 1 in Proposition 4.2.
  • beta_j = dynamic scaling factors, not fit
    Introduced ad hoc so that the jailbreak loss reduces to a simple form; the convergence proof requires the sum of beta_j to tend to zero.
  • eta_j = dynamic scaling factors, not fit
    Introduced ad hoc so that the hallucination loss reduces to a simple form; the convergence proof requires the sum of eta_j to tend to zero.
assumptions (5)
  • standard math Softmax attention and output probability as defined in Equations 1, 5, and 6.
    The paper models the model's forward pass using standard softmax attention and token probabilities.
  • domain assumption Hallucinations are caused by attention misallocation and can be captured by the loss L_hallu (Equation 9).
    The paper defines hallucinations this way, but provides no independent evidence that this loss is a faithful model of real hallucination mechanisms.
  • domain assumption Jailbreaks can be captured by token-level likelihood optimization of a harmful target (Equation 3).
    This is standard in the white-box attack literature, but it is a modeling choice that restricts the class of jailbreak attacks considered.
  • ad hoc to paper Proportional scaling conditions (Equations 10-11) and the limits sum(beta_j) tending to zero, sum(eta_j) tending to zero, and lambda tending to zero hold for real LFMs.
    These assumptions are what make the two losses converge; they are not derived from models or data, and the paper acknowledges they are stylized.
  • domain assumption The 50 prompts from reference [36] are representative of hallucination and jailbreak scenarios.
    The paper uses these prompts for all experiments, but their representativeness is not justified beyond being 'commonsense reasoning prompts'.

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Cite this review

Pith. "Pith review of From Hallucinations to Jailbreaks: Rethinking the Vulnerability of Large Foundation Models." pith.science (2026). https://pith.science/paper/FAFULRYC

@misc{pith2026250524232,
  author       = {Pith},
  title        = {Pith review of: From Hallucinations to Jailbreaks: Rethinking the Vulnerability of Large Foundation Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FAFULRYC}},
  note         = {Machine review of arXiv:2505.24232}
}
read the original abstract

Large foundation models (LFMs) are susceptible to two distinct vulnerabilities: hallucinations and jailbreak attacks. While typically studied in isolation, we observe that defenses targeting one often affect the other, hinting at a deeper connection. We propose a unified theoretical framework that models jailbreaks as token-level optimization and hallucinations as attention-level optimization. Within this framework, we establish two key propositions: (1) \textit{Similar Loss Convergence} - the loss functions for both vulnerabilities converge similarly when optimizing for target-specific outputs; and (2) \textit{Gradient Consistency in Attention Redistribution} - both exhibit consistent gradient behavior driven by shared attention dynamics. We validate these propositions empirically on LLaVA-1.5 and MiniGPT-4, showing consistent optimization trends and aligned gradients. Leveraging this connection, we demonstrate that mitigation techniques for hallucinations can reduce jailbreak success rates, and vice versa. Our findings reveal a shared failure mode in LFMs and suggest that robustness strategies should jointly address both vulnerabilities.

Figures

Figures reproduced from arXiv: 2505.24232 by the authors.

Figure 1
Figure 1. Example of the interplay between hallucinations and jailbreaks. (a) LLaVA-1.5 and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Scaling factors η and β over 80 opt. steps for LLaVA-1.5 and MiniGPT-4. We evaluate this convergence using two key metrics: • Scaling Factors η and β: These quantify the concentration dynamics of attention and output logits, respectively. Specifically, we define η = P j̸=t A∆ ij/A∆ it as the ratio of residual attention mass distributed to non-target tokens, and β = P j̸=y ∗ i logitj /logity ∗ i as the corresponding … view at source ↗
Figure 3
Figure 3. Hallucination and jailbreak losses over 80 opt. steps for LLaVA-1.5 and MiniGPT-4. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Hallucination and jailbreak losses over 80 optimization steps under different values of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.