Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filtering
Authors: Klaus-Rudolf Kladny
Bernhard Schölkopf
Michael Muehlebach
Venue: ICLR 2025 Poster (2025)
Keywords: Conformal Prediction
Generative Models
Risk Control
Active Learning
Language Models
Primary area: generative models

Abstract: Generative models lack rigorous statistical guarantees with respect to their predictions. In this work, we propose Sequential Conformal Prediction for Generative Models (SCOPE-Gen), a sequential conformal prediction method producing prediction sets that satisfy a rigorous statistical guarantee called conformal admissibility control. This guarantee means that the prediction sets contain at least one admissible (or valid) example, with high probability. To this end, our method first samples an initial set of i.i.d. examples from a black box generative model. Then, this set is iteratively pruned via so-called greedy filters. As a consequence of the iterative generation procedure, admissibility of the final prediction set factorizes as a Markov chain, where each factor can be controlled separately, using conformal prediction. In comparison to prior work, our method demonstrates a large reduction in the number of admissibility evaluations during calibration. This is crucial e.g. in safety-critical applications, where these evaluations must be conducted manually by domain experts and are therefore costly and time consuming. We highlight the advantages of our method in terms of admissibility evaluations and cardinality of the prediction set through experiments in natural language generation and molecular graph extension tasks.

Published as a conference paper at ICLR 2025
CONFORMAL GENERATIVE MODELING WITH IMPROVED SAMPLE EFFICIENCY THROUGH SEQUENTIAL GREEDY FILTERING
Klaus-Rudolf Kladny12, Bernhard Schölkopf Michael Muehlebach'
Max Planck Institute for Intelligent Systems, Tübingen
Tubingen Al Center
EELII Institute Tübingen
[kkladny, bs, michaelm) @uue mpg. de
ABSTRACT
Generative models lack rigorous statistical guarantees for their outputs and are there- fore unreliable in safety-critical applications. In this work, propose Sequential Conformal Prediction for Generative Models (SCOPE-Gen), sequential confor- mal prediction method producing prediction that satisfy rigorous statistical guarantee called conformal admissibility control. This guarantee states that with high probability, the prediction sets contain least one admissible (or valid) exam- ple. To this end, our method first samples an initial set of i.i.d. examples from a black box generative model. Then, this is iteratively pruned via so-called greedy filters. As a consequence of the iterative generation procedure, admissibility of the final prediction set factorizes as Markov chain. This factorization crucial, because it allows to control each factor separately, using conformal prediction. In comparison to prior work, our method demonstrates a large reduction the number of admissibility evaluations during calibration. This reduction is important in safety-critical applications, where these evaluations must be conducted manually by domain experts and therefore costly and time consuming. We highlight the advantages of our method in terms of admissibility evaluations and cardinality of the prediction sets through experiments in natural language generation and molecular graph extension tasks.
INTRODUCTION
Generative models have found extensive applications across various domains, including the generation of images (Rombach et al.) 2022). molecules (Vignac al. 2023), and natural language (Achiam al. 2023). While these models are becoming increasingly performant, caution is required when decisions based on generated outputs. This is particularly relevant for scenarios where errors have severe consequences. A prime example is the phenomenon of "confabulations" (or "hallucinations") in large language models-ree responses that lack factual support, potentially leading substantial harm if trusted (Bai et al., 2024; Weidinger et al.) (021). Therefore, developing effective measures to ensure strong statistical guarantees the predictions of these models is imperative.
The field devoted to obtaining rigorous statistical guarantees for the predictions of machine learning models is called risk control (Angelopoulos et al. 2022; 2021 Bates al. (021). prominent line of work within this field is called conformal prediction (Vovk et al.) 2005; Shafer & Vovk 2008). Conformal prediction techniques typically use heuristic uncertainty estimate from a black box machine learning model to construct a non-conformity measure (e.g.. Kato et al. 2023) that allows for generating prediction sets by selecting examples the prediction space y based on their non-confornity values. A typical guarantee is that with high probability, the true label y ) (as sampled from the generative process) for test example x is contained in this prediction set. Conformal prediction is appealing due to its simplicity and strong non-asymptotic, distribution-fie guarantees (Angelopoulos & Bates 2021). However, conformal prediction methods are typically designed for classification low-dimensional regression tasks and they suffer from the curse of

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[..] The cardian ailhonstte is within normal limits. [..] There no evidence of focal consolidation indicating pnetmonis
[.]] heaet marrkedly eularged. [.]
raising cunseen for [-.] aurtic ancarystn. [..] Focal cousolidation observed, suggesting paetmonii..
[-.] no evadense of vasenlar congestion. [..] unremarkable. [-.] localized consolidation observed to suggost pneumoniss
[...] Heart size normal, and mediastinal contours are unchanged. [-.] No sigus focal consolidation that would sngguse, puommonia.
Figure SCOPE-Gen for Radiology Report Generation. The sequential prediction procedure can be separated into two stages: In the generation stage (s 0), i.i.d. text reports (blue tokens) are drawn from the generative model. In the filter stage (s E {1,2}). the prediction set from the previous step - 1 is refined to remove examples with low quality (removing the false response in red) and examples with high similarity to already sampled texts (the answers in green are similar). Each step is performed via iterative (sampisg in given order (indicated by the purple circles), until the value of a non-confornity variable y exceeds a calibrated threshold X(e)
dimensionality when the prediction space ) is combinatorially large infinite, as it is the case for drug design or natural language generation.
Quach al. 2024) have recently introduced method called conformal language modeling (CLM) for addressing this problem. [ Rather than evaluating a non-conformity measure on each point the prediction space (which is intractable for textual data), CLM calibrates stopping rule parameter A that decides how many samples y are required from generative model G, conditionally on features x (for example, image text query). These samples then make up the prediction set, which fulfills poarect/non--allucinatee
a statistical guarantee with respect to containing at least one admissible example. The method further introduces rejection sampling ensure that the prediction set satisfies desired properties. The sampling is controlled by two calibration parameters A(1) and A(2) that ensure
1. Quality: If a new sample has too low quality, is rejected. The quality threshold is given by A(1)-
Diversity: a new sample from the generative model is too similar to an already sampled one, rejected. The similarity threshold is given by A(2)-
Conformal prediction cannot be applied with multi- linttiidimeiionnll calibration parameters, noted by AAneeoopouoss et al. (002)). To address this limitation, CLM calibrates all parameters = al. (023), a technique derived from the learn-then-test framework with fixed sequence testing for family error rate control (Angelopoulos)
(A(o): ((1)):((1) using Pareto testing [Laufer-Goldhter
al. (02T). In broad strokes, Pareto testing divides the calibration data into sets: The first set is used to estimate the Pareto frontier of different configurations for A over mean prediction set size (to be minimized) and admissibility (to be controlled). The estimated Pareto frontier is used construct a fixed sequence whose elements are tested in order, on the second data set. For testing, the null hypothesis corresponds to not controlling the admissibility at given level. The returned solution for À is the last configuration in the sequence for which this null hypothesis is rejected.
While CLM offers notion of admissibility control generative models, it has practical limitation. Specifically, during calibration, CL.M necessitates sampling and evaluating admissibility for fixed number of times per instance x in the calibration set. In safety-critical applications, such as medicine,
the factual integrity of admissibility checks based on n-gram (Lin 2004 Papineni et al. 2002) or
Notably, despite its name, CLM is not based conformal prediction in strict sense.
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machine learning methods (Smit et al. 2020) remains concern (hang al. 2024b). necessitating manual assessments by human domain experts for accurate calibration. Reducing the number of these costly admissibility checks is thus paramount (Settles 2009; Mosqueira- Rey et al. 2023).
Recognizing the need to enhance efficiency, we propose a method called Sequential Conformal Prediction for Generative Models (SCOPE-Gen), visualized in Fig- D This method differs in two major ways from CLM: (1) Prediction set generation is performed sequentially and can be split up into an initial generation stage and filter stage. The generation stage proposes i.i.d. candidates from the generative model (blue tokens in Fig. D. the filter stage applies so-called greedy filters in order to sub-sample the prediction set from the previous step. (2) We apply conformal prediction instead of learn- seem--thn-testt This can be done due to the fact that the admissibility of our final prediction set factorizes as a Markov chain. In this chain, each factor can be controlled separately. Thus, the desired level of admissibility for the final prediction set can be controlled by separately calibrating the individual prediction step parameters according to the Markov chain factorization.
Importantly, our prediction procedure has the significant advantage of reducing the number of admissibility checks involved in oracle-in-the-lopp scenarios (we explain this in detail in $ 4.2).
In summary, we highlight the following contributions:
We introduce Sequential Conformal Admissibility Control for Generative Models (SCOPE-Gen), a sequential conformal prediction approach that satisfies admissibility control ($ 2 for black box generative models ($
SCOPE-Gen requires significantly fewer queries of an admission function, in comparison to prior work. In addition, its computational complexity is lower (O(K) in comparison O(g"). where K is the number of calibration parameters (typically K = 3) and g is the size of a parameter grid).
We experimentally demonstrate the advantages of SCOPE-Gen in comparison to various baselines and prior work on molecular scaffold extension and natural language generation tasks (5
Overview. Section $ introduces (conformal) admissibility control, which is the main objective of
the present work. Thereafter, we present conformal prediction in Section $3 These sections set the stage for presenting our method in Section $ $4 Upon establishing the main principles, we demonstrate
the sub-sampling and non-conformity update functions used for filtering ($ [.1). the algorithmic
details of the calibration ($ 4.2).. Thereafter, we experimentally demonstrate the advantages of our
approach in comparison to prior work in Section $ followed by a section dedicated to related
work ($ 6). Finally, we conclude in Section $ 7
A discussion section is provided in App.
2 OBJECTIVE
We consider generating a prediction set Cx(X= = (Y.). parameterized by a calibration parameter A E K computed from labeled i.i.d. calibration set {(X,, Y')),, with feature variable X; and ground truth prediction Y.S The main objective of the present work is for Cx to be admissible for example, with high probability. Formally, we say that À satisfies (conformal) admissibility control at a given level a E (0, if
P(3Y Cx(X,+1): a(Y, Y1+1) = 1) 2 1-a,
(1)
where (X 1 is an additional independent sample from the same distribution as the calibration set and a : y² + {0,13 (no additional assumptions on a are imposed) measures admissibility between generated sample Y E y and YI )' (Fisch al. 2021 (3 For instance, could measure whether a textual response from a language model Y for the input X is similar to a ground truth textual response Yi+ For completeness, we demonstrate the relationship between admissibility control (T) and the more general notion called conformal risk control (Angelopoulos et al. 2022 in App. A For notational convenience, we introduce the set-level admissibillity
A(Cx(x), = 1 (Fy E Cx(x) a(y. v²) = 13.
(2)
We will generally drop dependence of A on and yf and simply write A(Cx) instead of A(Ca (x), v²). We also introduce the (total) udmissibility
A(A) = (A(((((XX*+ 1)41)),
(3)
"This means that an oracle can be queried on demand by the algorithm.
3 We note that y a is observed at test time.
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which is the quantity we desire to bound from below by 1 a.
3 PRELIMINARY: CONFORMAL PREDICTION
Conformal prediction (specifically, split conformal prediction (Papadopoulos et al., 2002 Lei
et al. 2015) provides a way of generating prediction set Ci {ye), parameterized by one-dimensional calibration parameter À E R. The typical setup in conformal prediction is to control (marginal) coverage, which is defined as
PP n+1 Cx(Xn-1)) 1
Conformal prediction techniques assume a (possibly random) non-conformity measure v(x, y). which typically chosen heuristic estimate for how incompatible and y are. For instance, if y is finite set of labels and corresponds to the feature variable (e.g.. an image), simple choice for v is consider the softmax scores of a classifier and use v(z, y) of non-conformity v and a calibration parameter A, the prediction set is constructed as
softmax(ar, y). Given choice
(x(x) fu y' v(x, v) S A}.
It can be shown that (4) is satisfied (independent of the choice of 1/) when calibrating as follows:
x (fv(1:)))) 1 : a) = -quantile (fu(E, 11)
- [1 =
(6)
n
where quantile denotes the empirical quantile of v/, evaluated at the calibration points {M( y1) }= We provide rigorous definition of the empirical quantile (6) in App. B
We note that can be seen as special case of admissibility control ( where the function a(v.y') )") 2 returns 1 if and only if and y' are identical. In the current study, we extend this concept to accommodate the typically vast output space y for instance, encompassing all possible sentences in natural language. This extension allows the function a to accommodate cases where y and y² are not identical but are semantically equivalent or similar. Without such a generalization, prediction sets would need to be excessively large to ensure admissibility control at the desired level (T. since they would have to account for all possible variations in structuring a sentence.
SEQUENTIAL CONFORMAL PREDICTION FOR GENERATIVE MODELS
SCOPE-Gen relies on i.i.d. calibration data {(r y/) from the true generating process. order to control A(A) (3) at level a, we utilize conformal prediction $ 3 The main challenge of our setting is that the output space y combinatorially large or even infinite. Hence, the prediction set determined in (5) (with À = À E I) is intractable. Thus, we construct prediction set directly from i.i.d. samples from a generative model G.
Sequential Prediction (Alg. 1.
The underlying idea of SCOPE-Gen is construct the prediction set C^ in multiple sequential steps s = O, 1, as shown in Alg. and Fig. On higher level, this process can be divided into two stages:
1. Generation Stage (s 0): An initial prediction set C(o) is generated by iteratively adding new i..dd samples from a generative model G, conditioned on æ (line[3) line line A new sample y is added until non-conformity value which is updated at each iteration of the while loop (line (1), exceeds the value of the calibration parameter > (line 12p. We assume that v is increasing at each iteration.
Filter Stage > 0): generated prediction set C(a-1) is filtered (or pruned) to C(a). as further reduce prediction set size (i.e., (C,,) S C(.-1y)). In this stage, filters & = 1,2 are be applied sequentially. Each filter is parameterized by an individual calibration parameter A(a) and is com- puted by means of a sub-sampling operation sub_ sample(C(s) C(--)). This sub-sampling is performed (line until the non-conformity value v exceeds A(a) (line analogous the generation stage) or there are no more samples left to add (line B).
Intuitively, X is the quantile level z with small correction for theoretical reasons (e.g.. An
gelopoulos & Bates 2021
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Algorithm 1: predict
Input: Condition z; generative model G; sub-sampling functions samplammmell..
update functions (update(s) 1 calibration parameters {>(a)
for == 0, 1,2 do
2
Co
(s) f Ø; V + j +
initialization
while rue do if s = then
y G
I| generation stage
else
if c/ C then break
II no samples left I/ filter stage
y sub__uuummaas (ub_sample C(--1))
10
V/ - (s (1
11
if > M(s) then
break
I/ threshold reached
C/ + (x) U4
-
13
14
-+1+1
return
C(2)
This sequential prediction provides a remedy for the intractibility the conformal prediction set as computed in (5). However, it poses the challenge that the total admissibility A(X) is parameterized by a muulti-dimensional calibration parameter X, which cannot directly calibrated via conformal prediction 6 This is due to the fact that conformal prediction crucially depends the assumption that the loss is controlled by a one-dimensional parameter (Angelopoulos et al. 2022).
Markov Chain Factorization. We address this issue by noting that in sequential prediction procedure, the total admissibility A(A) factorizes as a Markov chain
A(A) = ((A(CA))) = 1) P(A(A,())) 11=-11110 A|A(Cs = P) = A(Cx,)) 1). (7)
= A(Aoo)
=: A(A(n))
A(((a))
This means that the probability that the final prediction set C(2) contains an admissible example is determined by the probability that the first step generates least one admissible example and the probabilities that none the consecutive steps filter out all admissible examples. Consequently, can control the total admissibility A()) at level by controlling each individual admissibility A()(s)) for univariate (s) E IR and for a E (0, 1, 1,2), separately, where the individual levels ((s) are chosen such that
I (1 (())) We discuss the choice of ((s) in App. D.
Employing Conformal Prediction. We proceed to show how control the individual admissibilites A(A(s)). First, we note that the prediction sets in SCOPE-Gen created each step such that they grow incrementally, meaning that Cy ccit1 where C/,)
conformal prediction to
(())
the prediction set C(.)) after j iterations of sampling in while loop of Alg. As result, conclude that admissibility can be reformulated for 0 as
P(A(C)) = 1) = IP < j samples are required to satisfy admissibility"),
(8)
and analagously for s Thus, just in vanilla conformal prediction 5 we generate the prediction set over integers that controls the right-hand side of (
(,,)()) E : N:
< (1,2,...ū},
where X is the calibrated parameter O6) and we recall that is increasing in 1, for fixed x! We see that sampling the prediction set C(e) by sampling argmax, C(.) many examples controls the individual admissibility A()(s) at level a(s). which is equivalent to adding new samples to C(s) until the con-conformity measure exceeds A(e)- as done in Alg.
We that computing (x)) would generally be intractable for non-inereasing

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Non-Conformity Measures. crucial aspect for the performance of conformal prediction methods lies in the choice the non-conformity measure, which is parameterized by the update function in Alg. T Here, only discuss the choice of this function at the generation level (i.e., update and refer to [4.] for the non-conformity measures used during filtering. For generation, we take inspiration from Quach al. (2024) and consider the following update functions:
j.
(count)
+ q(v) + 73,
(sum))
(10)
max {v, {(v)} + 75.
(max)
where ? O and q with g(y) > 0, Vy denotes a quality estimate of point y, such as an estimate of p(yla by the generative model. We note that the sum and max updates are slightly different from Quach et al. (2024) due to the + term. The reason is that our prediction sets are not naturally limited in terms of size. Without this size regularization, prediction sets could become large.
4.1 GREEDY FILTERS
A core ingredient of SCOPE-Gen lies in the greedy filters. The term greedy reflects the incremental growth of the set of filtered points, C(a). over the iterations j in Alg. [ We consider two types of filters: 1) quality filter and 2) diversity filter. Both of them are defined via sub-sampling function sub sub__saplle sample and a non-conformity update function update.
Diversity Filter. We take inspiration from farthest point (sub- samplingg which is common in computer vision applications (e.g., Moenning & Dodgson (2033) et (2017))
Uniform(C(E-1)),
if Cis) Ø
sub_sampl gatb_sampee(Cts
arg max min d(y/ v"), else. (VECC-1)\CC v²EC())
Intuitively, this method chooses the point in C(a-1) ((aa) with the maximum distance (as measured by some distance function d) from the already sampled subset C(.). if C(s) is non-empty. For empty C(.).
chooses a point of C(.-1). uniformly at random. For this filter, the update rule is specified as
dmax:
if
update(v.y)
min d(y. v/). else,
d'EC( Me)
where dmnx is an upper bound on the distance function (see App. D.2 for details).
Quality Filter.
Using quality function we choose the point C(--1) with maximum quality:
sub sub_ssmpll gub_sample(Css, C(-1))
argmax g(v').
y'EC CC))
For the update function of the non-conformity, we introduce the natural choice
update(y) -9(y)-
By default, if both filters are applied, first apply the diversity filter.
4.2 CALIBRATION
For calibration, we split the i.i.d. calibration data {(z1, v/) into three non-overlapping subsets:
Po: (( T {(x,, v/) : {( vi) Pmm
where n22)) = n. This step is paramount, since otherwise, the admissibility controls (7) are not independent. The calibration happens sequentially (s 0, 1, 2), similarly to the prediction step, where calibration for A(s) is performed using { v/) be 1)" We now proceed to explain the algorithmic implementation of the generation and filter calibration, displayed in Alg. 2 and Alg.

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(1)
(2)
ii
(8)
(4)
(max)
(1())1)1))
(a) generation:
wi utd Glz,
(b) filter:
x
alvl",tt v()
a(vl .2))
v sub sample(((-n)(z.))
Figure 2: SCOPE-Gen Savings on Admissibility Checks. Samples in brackets denote samples that do not need to be assessed for admissibility (the ones sampled after the first admissible one). For the generation step (a), the u are i..d. samples from the generative model G. For filter steps (b), the Vi (J) are examples from the previous prediction set C(a-1)(aze, ordered according to sub_samples
Generation Calibration (Alg. As outlined ($ 4). for each v, we generate i.i.d. samples y, from G Ii until the first y!" is admissible (line 3) The resulting non-conformity values i4 then used to calibrate ^(o)- In practice, we typically need to limit the maximum amount of samples drawn by max E N (line + to tackle "hard" cases, i.e., examples (x4, where the generative model is unable to generate an admissible prediction. For these examples, we cannot generate finite non-conformity values and set these values to oo (line (3). Provided that such examples occur infrequently, the conformal quantile Noy (6) not affected. Otherwise, SCOPE-Gen rejects the calibration common for methods in the field of risk control (e.g.. Angelopoulos et al. (2021)).
Filter Calibration (Alg. 3 The calibration of X > 0 is analagous to the calibration of the generation step (Alg. 2). However, we see from the factorization in (7) that filter steps must be calibrated on the condition that the prediction set of the previous step is admissible (A(Cx,, 1,) 1)).
Thus, we require sampling from the distribution with density
P(C(o-1) (A(C(e-1)) = 1) x 1 (A(C(o-1)) = 1) P(C(e-1));
(11)
where (1)(s-1)) denotes the density of the prediction set C(s-1) as calibrated in the carlier step 1. In practice, we sample from (11) through the acceptance-rejection method. To this end, first sample a prediction set for 8 (line 33. Instead of assessing its admissibility right away (leading to C(,-1)l admissibility checks), we can be more efficient by integrating these checks into the evaluation of the non-conformity value v4. Specifically, we gradually add samples to C(s) using sub_sampless (line B). Once an admissible example is encountered, no more checks need to be performed because we know that C(.-1) 1) is admissible, If (s--)) 1) is inadmissible, the sub-sampling is repeated until there are no more samples to add, i.e., [C(a)l = |C(e-1yl (line 6). In this case, no non-conformity value is generated (line l2p.
For all calibration steps, we thus only require to perform repeated sampling until the first admissible example is encountered, as visualized in Fig.
EXPERIMENTS
We compare our method against prior work and derived baselines empirically demonstrate the advantages of SCOPE-Gen on real-world natural language tasks and molecular generation task. As the motivation of the present work lies in sample efficiency, we generally focus on small calibration sets. The experiments in the main text consider the sum non-conformity measure with y 0.5 (1)). We show qualitative evaluations in App. G further quantitative evaluations and ablation studies
in App. F2 and an analysis of empirical admissibility (3) in App. F.
We compare our method against CLM (Quach et al. 2024) and a baseline derived from it. CLM controls a different notion of admissibility than we do. Specifically, CLM controls
IP (A(Cx) = D(a) 2 1 - Pan] 2 1- 11
(12)
where Deal is shorthand for the calibration data {0,, " We note that 12 controls admissibil-
ity (T) at level a if a = B(1) + 3(2) - P()))12) (we show this in App. C. In order to tighten the gap.
which amounts to returning the entire output space
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Common Input: Data {(T, 1)) 2 admission function A; update function update
Algorithm 2: callbrate_.eneration
Algorithm 3: calibrate_fiiia Filter
Input: Generative model G
Input: Sub-sampling func. sub sample
m +
for -,,2, ((0)) do
for [[ 1); ((a-1):n(a--l [[1=1) + ((s)) do
3
((--1) ((C x4)
2 (()) +- 2-2 j +
4
(() + 2: + 0; 6
3 while A(C%)) do
while A(C()) = do
5
if 1/ max then break
if C/a) ((---)) then
6
7
break
y0) G
y0) ~ sub_ssamllsss sanb__
8
= update(u, ((),)
V + (v)
9
% C/) U
C+I + -(/) u (g10)
(6)
9
j マ ++
11
jtj+1
if C (0) < max then
10
if (()) < (C(e-1) then
1/ +
12
else
14
m t m+1
14
)(o) + X ((u))11) "000 a(()))
15 A + X ((u)) a(t))
15 return A(o)
16 return A(s)
we perform a grid search over combinations of B(1) and 8(2) that correspond to a and choose the configuration that minimizes admissibility (more details in App. D.3). We do this for each experiment separately and compare the optimal configuration to our method at level a.
Metries. 1) # Queries (1): Number required queries to the admission function during calibration. 2) Time (1): Runtime (in seconds) for entire calibration, excluding preprocessing (such as splitting data). 3) Set Size (L): Size of the final prediction set. 4) Frac. Reject ((): The fraction of rejected calibrations. For SCOPE-Ger this can occur if the conformal quantile (6) is not finite ($ 4.2) For CLM, this occurs the null hypothesis cannot rejected even once.
Baselines & Ablations 1) CLM (Quach et al., 2024). 2) CLM reduced max: This baseline assesses how CLM performs if we enforce a lower amount of admissibility checks during calibration by limiting max. Specifically, we choose max = 10 as limit. 3) SCOPE-Gen gen.onnly We only perform SCOPE-Gen using the generation stage and do not apply any filters. 4) SCOPE-Gen flipped: We apply the quality filter first and the diversity filter second ($ 4.1 config. [App. D.I]; when both filters used). We present 3) and 4) in App.
5.1
SETUP
For sake of demonstration, experiments shown here use automated admission functions. We leave experiments that involve admissibility checks made by human domain experts for future work 77 We provide general description in the main text and refer App. regardinn setup and App. B.2 for examples of each task. For SCOPE-Gen. we show config. (see App. D.I) in the main text.
Natural Language Generation. For all tasks, the default prediction upper bound chosen as max 20. We adopt three tasks from (unnh et al. (2024) related to natural language generation. 1) TriviaQA (Joshi et al., 2017): Open-domain question answering using L.Lam-22 (7B) (Touvron et al.) 2023). without fine-tuning- An answer y is admissible if it exactly matches one of the ground truth
answers yf. 2) MIMIC-CXR (Johnson et al. 2019): Radiology report generation using a pre-trained
We stress that admissibility control
still applies if human domain expert assesses admissibility.
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Table Quantitative Evaluations. All metrics =1 standard deviation of the different baselines from 300 repeated evaluations. For each evaluation, we first sub-sample calibration set of size 600 and calibrate each method coverage level a = 0.3 with sum non-conformity (TO). Then, we take means for each metric on test set of size 300, sampled from the remaining data. Best is bold.
Method
Metric
||
TriviaQA
MIMIC-CXR
CNN/DM
Molecules
# Queries
6.570 0.210
20.000 0.000
20.000 1 0.000
19.280 0.223
Time
2.710 0.019
113.677 10.891
105.907 + 13.137
15.853 1.441
CLM
Set Size
2,011 0.388
14.434 2.229
6.720 = 2.244
17.448 3.645
Frac. Reject
0.000 0.000
0.240 : 0.000
0.023 0.000
0.097
0.000
# Querres
4.187 0.106
10.000 0.000
10.000 + 0.000
7.109 + 0.069
Time
0.971 0.012
26.336 1.615
26.996 + 1.354
CLM reduced max
Set Size
2.463 0.776
16.226 1.790
6.190 1.792
Frac. Reject
0.020 0.000
0.817 0.000
0.207 0.000
1.000 0.000
# Queries
2.910 0.229
1.011
3.456 0.478
8.606 + 0.594
Time
0.026 0.001
0.072 0.030
0.061 0.013
0.093 0.002
SCOPE-Gen
Set Size
1.202 0.164
7.390 1.856
3. 3.669- 0.910
9.409 1.099
Frac. Reject
0.000 0.000
0. 0.203 1 0.000
0.057 0.000
0.097 0.000
vision transformer (Dosovitskiy 2020) and GPT2-small (Radford et al., 2019). Admissibility is assessed using soft Che labels (Smit al. 2020). 3) CNN/DM (Hermann et al. 2015): News article summarization. A fine-tuned T5-XL model (Raffel et al., 2020) is used and its outputs are compared to manually generated summaries. Admissibility is assessed via ROUGE-L (Lin 2004
Molecular Graph Extension. We use DiGress (Vignac et al. 2023 a discrete diffusion model for molecular graph generation that was trained on the MOSES data set (Polykovskiy et al. 2020),
which consists of 1, 1,936,962 diue-like compounds. We use molecule y from the calibration set and remove a single atom at random (subject to validity), leading to an "incomplete" compound x. We then condition DiGress x via masking to generate single-atom extensions y. An extension y is considered admissible (i.e., a(y, y') = (2)) if it exactly matches y'. For this experiment, we only apply a quality filter, where the quality function q corresponds to the quantitative estimate of drug-likeness (QED; Bickerton et al. (2012). The prediction upper bound is chosen as max = 40.
5.2 RESULTS
SCOPE-Gen consistently outperforms CLM in terms of amount of admissibility checks (# Queries) and runtime (Time), as can be seen in Tab. [ For instance, on MIMIC-CXR, SCOPE-Gen requires only 4_2 ~ 21% of the admissibility queries required for CLM. The "CLM reduced max" baseline demonstrates that counteracting this disadvantage by reducing the maximum sample size max comes high price to pay: The amount of rejected calibrations increases greatly (c.g., 81.7% MIMIC- CXR), while still being far from SCOPE-Gen in terms of performance. This decreased performance is due the fact that the admissibility guarantee in CLM holds for this specified ma x parameter, also during inference. In the inference phase, however, an upper bound on the prediction set size is often irrelevant, because no more admissibility checks must be performed. In addition, SCOPE-Gen consistently generates smaller prediction sets when the count or sum non-conformity updates are chosen (see (10). The only setting where CLM outperforms SCOPE Gen terms of prediction set size is for the max baseline, but not across all experiments (shown in App. F) An additional benefit of SCOPE-Gen in comparison to CLM is the vast reduction in computational demand for calibration: For MIMIC-CXR, SCOPE-Gen takes on average only 0.072 seconds for single calibration, in 0.072
comparison to CLM which takes 113.677 seconds on average (13.6777 As 10-4. 6.3).
6 RELATED WORK
Conformal prediction and the more general field known as distribution-free risk control have moti-
vated a plethora of developments related to various aspects such as causality (Lei & Candès 2021
Schröder et al.) (2224), non-exchangeable data (Barber et al. [2023] (Angllopoloss et al. [2224] 0012400ivvee Olieera et al., al.]| [2024). conditional coverage (Vovk] 2012; Lei & Wasserman (014 Cauchois et al. 2021
Deutschmann et al. 2023), and many others. The present work is also closely related to active

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learning (Settles 2009), which employs an oracle-in-the- framework reduce the number of queries made to the oracle. To reduce the scope of this section, we proceed to highlight advancements in the applications of risk control in the context of sequential filtering and generative models.
Risk Control and Sequential Filtering. Sequential (or iterative/cascading) filtering procedures are ubiquitous in the machine learning literature, demonstrated by. e.g.. Deng & Rush (2020); [aahmiri et al. (2021) Choi & Yang (2022). Among these, the method that most closely aligns with our approach is that Fisch et al. (2021). Similarly to the present work. |isch et al. (2021) sequentially filter a set of candidate solutions in order to obtain prediction set that controls admissibility ( In contrast to the present work, /Ficch al. (202T) consider classification scenario where filtering is done via increasingly complex classifiers to an initially assumed admissible set of candidates. This assumption contrasts with our setting, where we derive the initial set from a generative model without assuming admissibility. Moreover, Fisch et al. (202T) treat each candidate solution independently. dis- regarding the order of sampling within each filter stage, which contrasts with our greedy filters ($ 4. This is critical limitation when pruning prediction sets from generative models, as Fisch et al. (022) cannot take similarities between outputs into account.
Risk Control for Generative Models. One line of work constructs confidence intervals for generative
models in the pixel space of images (Horwitz& & Hoshen [022] Teneggi et al. (023). These studies focus on image-to- to-image tasks, such as denoising, where upper and lower uncertainty bounds of conformal prediction intervals on the target image can be visualized well. Conformal prediction
has also been applied to planning with diffusion models by utilizing conformal prediction for the reward estimate (Sun et al. (2024). Other applications include density estimation (Diamant et al. 2024) and detection of adversarial examples (Cai al.) 2020). Wang al. (2023) use generative models to create conformal prediction sets by determining a radius of a ball around each sample such that the union over all balls controls coverage. In contrast to our approach, the method proposed by Wang et al. (2023) is not suitable for non- non-Euclidean or high-dimensions data. Another work uses normalizing flows to approximate conditional coverage for regression (Colombo 2024).
Works other than the one by Quach et al. (024) that target language generation with different scope to ours include the approach by Ulmer et al.] (2024) who consider language modeling for non-exchangeable data, Gui et al. (2024) who focus conformal alignment of language models Kumar et al. 2023) who specifically consider multiple choice problems. Another concurrent line of work. followed by Cherian et al. (2024); Mohri & Hashimoto 2024); Liu & Wu (2024), provides guarantees on individual long-fore form-form-o text outputs by chunking them into sub-claims and removing false sub-claims. A critical assumption for such methods to be practical is that text responses indeed consist of multiple distinct claims with little coherence.
Detecting Hallucination without Guarantees. There is body of work focused on quantifying uncertainty and detecting hallucinations in language models, though these approaches do not directly achieve distribution-fin free risk control. Existing methods in this domain are based on notions such as semantic (Kuhn et al. 2023 Lin ct al. (224)) or task-specific uncertainty (Wang & Holmes 2024) and self-consistency (Zhang al. (024a). Although not explored in the present work, we believe that such approaches offer a promising opportunity for cross-por polss-pollnnation with ideas from conformal prediction in future work.
7 CONCLUSION
In the present work, we introduced SCOPE-Gen, a sample-efficient conformal prediction method for generative models. This method sequentially prunes an initial prediction set from a generative model using greedy filters, allowing the total admissibility to factorize as Markov chain. Consequently. each pruning step can be calibrated separately. Experimentally, SCOPE-Gen has shown to require fewer queries of an admissibility function to maintain control over the total admissibility at desired level, compared to prior work. This efficiency is particularly valuable in domains where admissibility assessments are costly, such those requiring evaluations by human domain experts. We hope that our work inspires further research in risk control for generative models, with a focus on integrating application-specifi constraints and desiderata, such sample efficiency.
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REPRODUCIBILITY STATEMENT
Our source code is available on GitHub at https://ggthubb.../ https//giiuub.ommuoo/lllllliiia com/ruudfivlllinnscpeeee Instructions for reproducibility are provided in the README file at the top level of the code directory. All parameters for running the experiments can be found in the config folders within the script folders of each experiment folder.
ACKNOWLEDGEMENTS
Michael Muehlebach is funded by German Research Foundation (DFG) under the project 456587626 of the Emmy Noether Programme. The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Klaus-Rudol Kladny.
REFERENCES
Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, lige Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidr, Sam Altman, Shyamal Anadkat, et al. GPT-4 Technical Report. arXiv preprint arXiv:2303.08774, 2023.
Time Series Prediction. Advances in Neural Information Processing Systems, 36, 2024. Anastasios Angelopoulos, Emmanuel Candes, and Ryan J. Tibshirani. Conformal PID Control for
Anastasios N. Angelopoulos and Stephen Bates. A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification. arXiv preprint arXiv:2107.07511, 2021.
Anastasios N. Angelopoulos, Stephen Bates, Emmanuel Candès, Michael Jordan, and Lihua
Lei. Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control. arXiv preprint arXiv:2 10.0005, 2021.
Anastasios N. Angelopoulos, Stephen Bates, Adam Fisch, Lihua Lei, and Tal Schuster. Conformal Risk Control. arXiv preprint orXiv:2208.004 022814 2022.
Zechen Bai, Pichao Wang, Tianjun Xiao, Tong He, Zongbo Han, Zheng Zhang, and Mike Zheng Shou. Hallucination of Multimodal Large Language Models: A Survey. arXiv preprint arXiv:2404.18938
2024.
Rina Foygel Barber, Emmanuel J. Candes, Aaditya Ramdas, and Ryan J. Tibshirani. Conformal Prediction Beyond Exchangeability. The Annals of Statistics, 51:816-888 8055, 2023.
Stephen Bates, Anastasios Angelopoulos, Lei Lihua, Jitendra Malik, and Michael Jordan. Distribution- free, Risk-controlling Prediction Sets. Journal of the ACM, 68, 2021.
Yoav Benjamini and Henry Braun. John W. Tukey's contributions to multiple comparisons. Annals of Statistics, pp. 1576-1556 1594, 2002.
G. Richard Bickerton, Gaia V. Paolini, Jérémy Besnard, Sorel Muresan, and Andrew L. Hopkins. Quantifying the chemical beauty of drugs. Nature Chemistry, 4:90-98, 2012.
Feiyang Cai, Jiani Li, and Xenofon Koutsoukos. Detecting Adversarial Examples in Learning- Enabled Cyber-Physiceh Systems using Variational Autoencoder for Regression. In IEEE Security and Privacy Workshops, pp. 208-214, 2020.
Maxime Cauchois, Suyash Gupta, and John C. Duchi. Knowing what You Know: valid and validated confidence sets in multiclass and multilabel prediction. Journal of Machine Learning Research, 22:1-42, 2021.
John J. Cherian, Isaac Gibbs, and Emmanuel J. Candès. Large language model validity via enhanced conformal prediction methods. Neural Information Processing Systems, 2024.
Young- Choi and Jeongsam Yang. Machine learning iterative filtering algorithm for field defect detection in the process stage. Computers Industry, 142:103740, 2022.

---

Published as a conference paper at ICLR 2025
Nicolo Colombo. Normalizing Flows for Conformal Regression. Uncertainty in Artificial Intelligence, 2024.
Gabriele Corso, Yilun Xu, Valentin De Bortoli, Regina Barzilay, and Tommi Jaakkola. Particle Guidance: Non-IID Diverse Sampling with Diffusion Models. International Conference Learning Representations, 2023.
Yuntian Deng and Alexander Rush. Cascaded Text Generation with Markov Transformers. Advances in Neural Information Processing Systems, 33:170-1 170-181, 2020.
Nicolas Deutschmann, Mattia Rigotti, and Maria Rodriguez Martinez. Adaptive Conformal Regres- sion with Jackknife+ Rescaled Scores. arXiv preprint arXiv:2305.19901. 2023.
Nathaniel Diamant, Ehsan Hajiramezanali, Tommaso Biancalani, and Gabriele Scalia. Conformalized Deep Splines for Optimal and Efficient Prediction Sets. International Conference on Artificial Intelligence and Statistics, pp. 1657-1665, 2024.
Alexey Dosovitskiy. An image worth 16x 16 words: Transformers for image recognition scale. arXiv preprint arXiv: 2010.11929, 2020.
Adam Fisch, Tal Schuster, Tommi Jaakkola, and Regina Barzilay. Efficient Conformal Predic-
tion via Cascaded Inference with Expanded Admission. International Conference on Learning Representation, 2021.
Yu Gui, Ying Jin, and Zhimei Ren. Conformal Alignment: Knowing When to Trust Foundation Models with Guarantees. arXiv preprint arXiv:2405.10301, 2024.
Karl Moritz Hermann, Tomas Kocisky, Edward Grefenstette, Lasse Espeholt, Will Kay, Mustafa Suleyman, and Phil Blunsom. Teaching Machines to Read and Comprehend. Advances in Neural Information Processing Systems, 28, 2015.
Eliahu Horwitz and Yedid Hoshen. Conffusion: Confidence Intervals for Diffusion Models. arXiv preprint arXiv:2211.09795 2022.
Alistair EW Johnson, Tom Pollard, Nathaniel R. Greenbaum, Matthew Lungren, Chih-ying Deng. Yifan Peng. Zhiyong Lu, Roger G. Mark, Seth J. Berkowitz, and Steven Horng. MIMIC-CXR-JGG, large publicly available database labeled chest radiographs. arXiv preprint arXiv:1901 1901.07042 2019.
Mandar Joshi, Eunsol Choi, Daniel S. Weld, and Luke Zettlemoyer. TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension. arXiv preprint arXiv:1705.0355/ 2017.
Yuko Kato, David MJ Tax, and Marco Loog. A Review of Nonconformity Measures for Conformal Prediction in Regression. Conformal and Probabilistic Prediction with Applications, pp. 369-383, 2023.
Michael Kirchhof, James Thornton, Pierre Ablin, Louis Béthune, Eugene Ndiaye, and Marco Cuturi. Sparse Repellency for Shielded Generation Text-to-image Diffusion Models. arXiv preprint 10066224 2024.
Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar. Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation. International Conference on Learning Representations, 2023.
Bhawesh Kumar, Charles Lu, Gauri Gupta, Anil Palepu, David Bellamy, Ramesh Raskar, and Andrew Beam. Conformal Prediction with Large Language Models for Multi-Choice Question Answering. ICML 2023 workshop on Neural Conversational Al TEACH, 2023.
Salim Lahmiri, Anastasia Giakoumelou, and Stelios Bekiros. An adaptive sequential-fitterinn learning system for credit risk modeling. Soft Computing, 25:8817-8824, 2021.
Bracha
Adam Fisch, Regina Barzilay, and Tommi Jaakkola. Efficiently Control- ling Multiple Risks with Pareto Testing. International Conference on Learning Representations, 2023.
12

---

Published as a conference paper at ICLR 2025
Jing Lei and Larry Wasserman. Distribution-fre prediction bands for non non-parametric regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 76:71-96, 2014.
Jing Lei, Alessandro Rinaldo, and Larry Wasserman. A Conformal Prediction Approach to Explore Functional Data. Annals of Mathematics and Artificial Intelligence, 74:29-43, 2015.
Lihua Lei and Emmanuel J. Candès. Conformal inference of counterfactuals and individual treatment effects. Journal of the Royal Statistical Society Series B: Statistical Methodology, 83:911-938, 2021.
Chin- Yew Lin. Rouge: A package for automatic evaluation of summaries. Text summarization branches out, pp. 74-81, 2004.
Zhen Lin, Shubhendu Trivedi, and Jimeng Sun. Generating with Confidence: Uncertainty Quan- tification for Black-box Large Language Models. Transactions on Machine Learning Research, 2024.
Terrance Liu and Zhiwei Steven Wu. Multi-grow group Uncertainty Quantification for Long-form Text Generation. arXiv preprini arXiv:2407.21057, 2024.
Andreas Lugmayr, Martin Danelljan, Andres Romero, Fisher Yu, Radu Timofte, and Luc Van Gool. RePaint: Inpainting using Denoising Diffusion Probabilistic Models. Computer Vision and Pattern Recognition, 2022.
Carsten Moenning and Neil A. Dodgson. Fast Marching farthest point sampling. Technical report, University of Cambridge, Computer Laboratory, 2003.
Christopher Mohri and Tatsunori Hashimoto. Language Models with Conformal Factuality Guaran- tees. arXiv preprint 40X19:240..10978 2024.
Eduardo Mosqueira-Rey Elena Srnnandez-Pereiire David Alonso-Rios, José Ángel Fernández-Leal Human-ine -luman-in-the-lopp machine learning: state of the art. Artificial Intelli- gence Review, 56:3005-3054, 2023.
and
Roberto I. Oliveira, Paulo Orenstein, Thiago Ramos, and Joao Vitor Romano. Split Conformal Prediction and Non-Fxxcanngeabe Data. Journal of Machine Learning Research, 25:1-33 2024.
Harris Papadopoulos, Kostas Proedrou, Volodya Vovk, and Alex Gammerman. Inductive Confidence Machines for Regression. In Machine Learning; European Conference on Machine Learning, pp.
345-356, 2002.
Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu, BLEU: A Method for Automatic Evaluation of Machine Translation. In Annual Meeting of the Association for Computational Linguistics, pp. 311-318, 2002.
Daniil Polykovskiy, Alexander Zhebrak, Benjamin Sanchez-Lengeling, Sergey Golovanov, Oktai Tatanov, Stanislav Belyaev, Rauf Kurbanov, Aleksey Artamonov, Vladimir Aladinskiy, Mark Veselov, et al. Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models. Frontiers in Pharmacology. 11:666644, 2020.
Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J. Guibas. PointNet++: Deep Hierarchical Feature Learning on Point Sets in Metric Space. Advances in Neural Information Processing Systems, 30, 2017.
Victor Quach, Adam Fisch, Tal Schuster, Adam Yala, Jac Ho Sohn, Tommi S. Jaakkola, and Regina Barzilay. Conformal Language Modeling. International Conference on Learning Representations, 2024.
Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language Models are Unsupervised Multitask Learners. OpenAl blog, 1:9, 2019.
Colin Raffel, Noam Shazeer, Adam Roberts. Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer. Journal of Machine Learning Research, 21:1-67, 2020.
13

---

Published as a conference paper at ICLR 2025
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bjöm Ommer. High- Resolution Image Synthesis with Latent Diffusion Models. Conference on Computer Vision and Pattem Recognition, pp. 10684-006600 10695, 2022.
Maresa Schröder, Dennis Frauen, Jonas Schweisthal, Konstantin HeB, Valentyn Melnychuk, and Stefan Feuerriegel. Conformal Prediction for Causal Effects of Continuous Treatments. arXiv preprint arXivv2407.03094, 2024.
Burr Settles. Active Learning Literature Survey. Computer Sciences Technical Report 1648, University of Wisconsin-Madison 2009.
Glenn Shafer and Vladimir Vovk. A Tutorial on Conformal Prediction. Journal of Machine Learning Research, 9:371 17711 2008.
Akshay Smit, Saahil Jain, Pranav Rajpurkar, Anuj Pareek, Andrew Y. Ng, and Matthew P. Lungren. CheXbert: Combining Automatic Labelers and Expert Annotations for Accurate Radiology Report Labeling using BERT. arXiv preprint arXiv:2004.0916 2020.
Jiankai Sun, Yiqi Jiang, Jianing Qiu, Parth Nobel, Mykel J. Kochenderfer, and Mac Schwager. Conformal Prediction for Uncertainty-Aware Planning with Diffusion Dynamics Model. Advances in Neural Information Processing Systems, 36, 2024.
Jacopo Teneggi, Matthew Tivnan, Web Stayman, and Jeremias Sulam. How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control. In International Conference on Machine Learning, pp. 33940-33960, 2023.
Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open Foundation and Ffine-Tuneh Chat Models. arXiv preprint (rXiv:2307.09288) 2023.
Dennis Ulmer, Chrysoula Zerva, and André FT Martins. Non- -xhhanxcaeee Conformal Language Generation with Nearest Neighbors. arXiv preprint arXiv:2402.00700 2024.
Clement Vignac, Igor Krawczuk, Antoine Siraudin, Bohan Wang, Volkan Cevher, and Pascal Frossard. DiGress: Discrete Denoising diffusion models for graph generation. International Conference on Learning Representationss, 2023.
Luke Vilnis, Yury Zemlyanskiy, Patrick Murray, Alexandre Tachard Passos, and Sumit Sanghai. Arithmetic Sampling: Parallel Diverse Decoding for Large Language Models. In International Conference Machine Learning, pp. 13120-3536, 2023.
Vladimir Vovk. Conditional validity of inductive conformal predictors. In Asian Conference
Machine Learning, pp. 475-490, 2012.
Vladimir Vovk, Alexander Gammerman, and Glenn Shafer. Algorithmic Learning Random World, volume 29. Springer, 2005.
Zhendong Wang, Ruijiang Gao, Mingzhang Yin. Mingyuan Zhou, and David M. Blei. Probabilistic Conformal Prediction using Conditional Random Samples. International Conference on Artificial Intelligence and Statistics, 2023.
Ziyu Wang and Chris Holmes, On Subjective Uncertainty Quantification and Calibration in Natural Language Generation. arXiv preprint arXiv:2406.00 05213, 2024.
Laura Weidinger, John Mellor, Maribeth Rauh, Conor Griffin, Jonathan Uesato, Po-Sen Huang, Myra Cheng, Mia Glaese, Borja Balle, Atoosa Kasirzadeh, et al. Ethical and social risks of harm from Language Models. arXiv preprint arXiv:21 2021.
Jiaxin Zhang, Zhuohang Li, Kamalika Das, Bradley A Malin, and Sricharan Kumar. SAC3: Reli- able Hallucination Detection in Black-Box Language Models via Semantic-aware Cross-check Consistency. arXiv preprint arXiv:2311.01740 2024a.
Kai Zhang, Rong Zhou, Eashan Adhikarla, Zhiling Yan, Yixin Liu, Jun Yu, Zhengliang Liu, Xun Chen, Brian D. Davison, Hui Ren, et al. A Generalist Vision-Languaa Foundation Model for Diverse Biomedical Tasks. Nature Medicine, pp. 1-13, 2024b.
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Appendix
Table of Contents
Relationship between Risk Control and Admissibility Control
16
B Definition of the Empirical Quantile
16
Bounding Conformal Admissibility by Learn-then- Test Admissibility
16
Implementation Details
17
D.1 Parameter Configuration
D.2 Distance Upper Bound
17
D.3 Grid Specification for CLM
17
E
Experimental Details
18
E.1
Sctup Details
18
E.2
Examples
18
F
Additional Experiments
F.1
Admissibility Analysis
19
F2
Further Quantitative Evaluations & Ablations
20
G
Qualitative Results
25
1
TriviaQA].
25
MIMIC CXR
26
Yost-Evaluating Admissibility
28
Discussion & Limitations
30
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A RELATIONSHIP BETWEEN RISK CONTROL AND ADMISSIBILITY CONTROL
Conformal risk control (Angelopoulos et al. 2022 considers the generation of prediction set Cx with calibration parameters computed from labeled i.i.d. calibration set {(x, Y.) new input/conditioo x with label Yn+1 and a loss function L. The desired property of interest for Cy called risk control, defined as
(X 12+1 < a;
(13)
where a > 0. A classic example is the coverage loss ((Cx (z), Li & Cx(x)} (ook et al. 2005), which gives (13) the simple interpretation that Cx contains Ya+1 with probability a. In the present work, we consider the loss
((Cxa)),') 1By E Cx(x) a(v. =1.
(14)
When inserting
14 into
13 our definition of admissibility control arises naturally:
E ( E Cx(Xn+1) aaY, Y, x+1) 1}}
Eyy E Cx(X.+1) a(Y, Y m+1) 1}] -a
P(AY Cx(Xx+1) a(Y, x2+1) 1)
B DEFINITION OF THE EMPIRICAL QUANTILE
We define the empirical 8-quantile for ō IR at 1-dimensional real-valued data points {a:)i_.
{ q
quantile ([=:)=m 8)
inf 2 E RUf
Σ 1[x S g) 2 nd
(15)
Intuitively, 15 corresponds to the no smallest element in {xi empirical quantile (15) is set to co.
J if 6 < 1. Otherwise (8 > 1), the
C BOUNDING CONFORMAL ADMISSIBILITY BY LEARN-THEN-TES. ADMISSIBILITY
Proof. Let B(1) E (0, and ((2) (0, 1) be chosen arbitrarily, such that B(1) + ((2) B(1) = a.
We further suppose that the learn-then-test guarantee
IP (A(CA) = Dem) 2
{1) 2 3(2)
(16)
is satisfied. We now show that the admissibility is bounded from below as
[[[(A(()) 1}] 2 1-a.
To this end, we observe that the admissibility
E [1 (A(C2) = (} = E EP((((())) = 1 Deal)
can be split into two parts
E 1 [P((())) = 1|Dma] 2 (())P(((CA) = Daa]]
(17)
E [[P[A((N)) 1/Daal < 1 (()CP(A((C)) 1 Deal]
(18)
We note that (18) is bounded from below 0. We further bound 17 follows
E (TP (A(Cx) 1/D Btn HP (A(Cx)
1 Dawl]
(1 (1-Ba)) [A(()) Deal] 8(1)
(1 (1-)(,)) 3(a)).
where the last inequality holds by the learn-then-test guarantee (6)
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D IMPLEMENTATION DETAILS
D.1 PARAMETER CONFIGURATION
The most straightforward choice is to equally distribute the risk among prediction steps, resulting in
(c)) 1 (1-11_))
(19)
where K is the amount of prediction steps (typically, K 3). We note that (19) is somewhat analagous to a Bonferroni correction in that it also equally distributes a correction. In practice, when working with upper bound the sample size max (outlined in $ $4.2) however, lower admissibility levels can often attained by different choice of (ss)- Specifically, we choose a larger risk level for the generation step 0) and distribute the remaining risk equally among the other step(s) (s E {1, 2)). We assess two different configurations of SCOPE-Gen, which we name config. 1 and config For config. 1, we choose M 5 and set
(0) (1 - ao-)
and
(()) = 1 - a)) ()) vs 0.
For config. 2, the same setup for config. 1, with the only difference that only use the diversity filter (i. e., = 2). In addition, we add prediction set count penalty to the diversity update function, resulting in
update(u.g) {
dmux: -
if
-
-
min d(y, v/) + 7al Go)le V'C (x)
else,
with 74 = 0.1.
D.2 DISTANCE UPPER BOUND
All distance functions in the present work are derived from text-based similarity functions such as ROUGE (Lin 2004). Such metrics typically range from 0 and functions simply by negating them (such that they range from -1 to 0). Thus, for such metrics, we obtain distance lower bound by choosing d -1 If d is not bounded, bounded distance d, for example by taking
convert them distance
turn it into
d(y. 1 + d(y,)r)
assuming positivity of d.
D.3 GRID SPECIFICATION FOR CLM
In general, we observe empirically that coverage is minimized when 8(2) is much smaller than 3(1) (usually for B(2) B10) For given a, the grid over ((2), denoted B by selecting 10 equidistant points between a/15 and a/5.. This can be mathematically represented as follows:
a/5 2/5-a/1 a/15 :i= 0,
B
a/15 +
9
The corresponding values Bi) accordingly are
1 - - B
( (2)
3(1) =
i = 0, 1,
1 3 (i)
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E EXPERIMENTAL DETAILS
E. SETUP DETAILS
Natural Language Generation. All of our experiments regarding natural language generation
roughly follow the setup from (Quach et al. 2024). Thus, we only highlight differences to the setup considered there:
TriviaQA. We remove duplicates automatically rather than calibrating parameter to do this, in order to improve statistical efficiency of both methods. For CLM, we set the diversity parameter λ(2) 0.5 such that all duplicates are removed and for SCOPE-Gen, we use a fixed diversity filter at the end of the prediction pipeline, which removes duplicates.
MIMIC-CXR. We slightly modify the admissibility criterion due to insufficient implementation details available. Following the approach by Quach et al. (2024), which uses exact CheXbert prediction matches as labels, we obtain few admissible examples ( 30%). To address this problem, adjust the setup by extracting soft labels from the CheXbert model (using weights from the original work). Specifically, we employ a labeling function based on the F1 score
2
FI
(20)
recall precision
where both precision and recall are computed from 14 clinically relevant lahels output by the CheXhert model. This Fl score aligns with the evaluation metric used in the original work by Smit et al.) (2020).
We consider prediction admissible if FI 0.6, manually chosen threshold. We compare all baselines using the predictions of this model.
Molecular Graph Extension. The weights of the used DiGress model can be found the official GitHub page In order to condition the generated molecular graphs on a given substructure, we employ a form of masking in the reverse diffusion process (from noise to data distribution). This is similar to masking approaches in computer vision, such as the one proposed by Lugmayr et al. (2022). However, unlike Lugmayr et al. 20022) mask the given graph structure directly (rather than applying noise to it) and do not repeat the reverse diffusion process multiple times.
Analagously TriviaQA, we filter duplicates automatically. In addition, we treat invalid predictions by setting their quality estimate to O. Invalid molecules are molecules that cannot be represented in a valid resonance form according to Kekulé's rules.
In order to check whether two molecules are identical (criterion for admissibility), we convert both molecules their canonical SMILES representations and check whether these are identical.
E.2 EXAMPLES
We demonstrate one specific example per experiment, where we show both condition æ and ground truth output y²
TriviaQA:
The condition x is question in natural language, the ground truth target y is short phrase in natural language (with multiple aliases that are all considered admissible).
"Sunset Blvd",
"Which Lloyd Webber musical premiered the US on 10th December 1993?"
"West Sunset Boulevard",
"Sunset Boulevard",
"Sunset Bulevard",
"Sunset. Blvd."
y'
CNN/DM:
The condition x a lengthy news report in natural language, the ground truth target yf is manually generated summary (in natural language) of .r.
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"Laving hern the recemving med of 6-1 tampiin difrat li that could be jus tifally ned with lucalash by puclize. watching 8-1 lest sggnggate adbuntage
unardd beat thiir chau-
into Tel defieii come the snd of the reverse encouster too could acud wayy lass spoplectic lhe cuptrciacion of Gati side [od] 2. was the flsst thme that pocto who bad been unbestea as this son toumuscuree
tundday 7-4 agaro- 2005
lae last and
until tunsday uight... had reaited too quariee huols of the chat- plons Iregon sinoe the 2306-09 arancn.
y
E
The condition x is a anterior to posterior or posterior to anterior chest X-ray image (recorded from the front or from the back, but from the side). including a text prompt in natural language, which contains all text prior to either the "FINDINGS", "IMPRESSION or "FINDINGS AND IMPRESSION" keyword of the ground truth report. The ground truth target y' is all text starting from the identified keyword.
MIMIC-CXR:
FINAL REPORT
IOSTORY:
- year man fever,
poesmonii
TECENIQUE Poctable crect chess eaclograph
Right contral vamous is in vis- Lie position at the mid SVC, and the left PICC line máds near the caveatrial puretion. Gastttc tube below the disphrngm and mis the body of the stomacc. Low voluases seen. Previous has improzed,, and disstuall cont ous are normal.
FINDINGS:
whe obtained
COMPARISON: Cleo ralingaph from
contance
congre- and mo-
IMPRESSION: No focal consoidatioo, to pusamonis.
y
x
Molecules: The condition is given valid scaffold (i.e. subgraph that adheres to the grammar of valid molecules) that results as a random removal of a single atom (including all of its connections; highlighted in cyan) from a compound y in the calibration set.
HN
T
y
F ADDITIONAL EXPERIMENTS
F.1 ADMISSIBILITY ANALYSIS
We demonstrate the empirical admissibility levels for the MIMIC-CXR experiment at admissibility level a = 0.3, varying calibration set size n and the used non-conformity measure. We use cross-validation like algorithm (Angelopoulos Bates (202T): Fig. 12) to generate histograms. The rest of the experimental setup is identical to the setup used for all other experiments (see caption of Tab. [
As shown in the histograms of Fig. 3 for all non-conformity measures, the admissibility achieved by SCOPE-Gen (config. 1 [App. D.I blue) is slightly conservative for low sample sizes and converges to the desired level as the calibration set size is increased from 300 to 1200. This is similar for CLM (orange), where the achieved admissibility (using the optimization strategy described in $ also becomes less conservative for large sample sizes. However, in contrast SCOPE-Gen, CLM is
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300
600
1200
Non-conforuiiyy tocasure: FIET
CLM Meon
15
Focquaoa
Non-conformityy measure: sum
15
Rleprrug
Non-conformity measure:: count
10
0.7 Mean Acinisabiilit
0.7
0.9
Moon Admisshilry
Moom Admicsibiliity
Figure 3: Admissibility Analysis for MIMIC-CXR, For all non-conformity scores, SCOPE-Gen (config. [see App. D.I]: blue) becomes less conservative with respect to the desired admissibility level 1 - a (red dashed line) as the amount of calibration samples increases, as typical for methods based on conformal prediction. For CLM (orange), in contrast, conservativeness depends much on the chosen non-conformity measure.
generally more conservative. addition, this conservativeness is highly influenced by the choice of non-conformity measure: While the CLM gap becomes tighter for the and sum non-conformities, this is not the case for the count non-conformity, where a large gap persists even for n = 1200.
A further observation is that SCOPE- Gen tends reject far fewer calibration sets small calibration set size (n 300). This can be seen from the bars at coverage 1., which indicate calibration sets that are rejected (rejecting calibration amounts returning the entire output space ) (see $ which results in 100% admissibility). We see that the blue bar (SCOPE-Gen) tends to be smaller than the orange bar (CLM).
F.2 FURTHER QUANTITATIVE EVALUATIONS & ABLATIONS
We demonstrate further experiments that showcase the performance for the different non-conformity measures (count and max (7 0.1) in addition to sum (7 0.5); see (10). including two more baselines (baselines 3) and 4) introduced in $ 5) for admissibility levels both configurations SCOPE-Ges (see App. D.I.. While for some experiments, choosing smaller values for is feasible (e.g., TriviaQA, can be seen in App. G.I). this is possible for all experiments due to the performance of the underlying model. Specifically, if model does not generate single admissible example within the upper limit max for more than fraction of examples,
{0.3, 0.35, 0.4) and
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see that generating prediction sets that fulfill admissibility of level smaller than cannot be possible, irrespective of the calibration method that used. We observe such issues for CNN/DM and Molecules when using admissibility levels smaller than 0.3. Thus, restrict our numerical experiments to larger admissibility levels.
We in Tab. that typically either SCOPE-Gen (config. and config. 2, see App. D.I.
of its ablations performs best in terms of the considered evaluation metrics. We see that occasionally, SCOPE-Gen gen. only generates the smallest prediction sets on average. We hypothesize that this may have to do with the fact that SCOPE-Gen gen. will tend to be slightly less affected by variance in the estimation of the threshold, since SCOPE- gen. has more data estimate the latter. In terms of the non non-conformity update function, we see that general recommendation in favor of one over any other cannot be made. For example, considering that SCOPE-Ger config. generates the smallest prediction sets for the sum non-conformity. but the fewest admissibility checks are achieved for the same method when using the count non-conformity. For = 0.3 and MIMIX-CRR SCOPE-Gen config. 2 generates the smallest prediction sets, using max non-conformity.
setting a = 0.3 for TriviaQA, we see
Table 2: Further Quantitative Evaluations. See Tab. for experimental setup. Best is bold.
Method
||
Metric
TriviaQA
MIMIC-CXR
CNN/DM
Molecules
0.3
Non-Confornity: sim
# Queries
6.570 + 0.210
20.000 + 0.000
20.000 +: 0.000
19.280 + 0.223
Time
2.710 0.019
113.677 10.891
105.907 13.137
15.853 = 1.441
CLM
Set Size
2.011 0.388
14.434 2.229
6.720 2.244
17.448 1: 3.645
Frac. Reject
0.000 0.000
0.240 + 0.000
0.023 + 0.000
0.097 + 0.000
# Queries
4.187 0.106
10.000 1: 0.000
10.000 1: 0.000
7.109 1: 0.069
Time
0.012
1.615
26.996 1.354
CLM roduced max
Set Size
2.463 + 0.776
16.226 1.790
6.190 = 1.792
Frac. Reject
0,020 0.000
0.817 +: 0.000
0.207 0.000
1.000 0,000
# Queries
2.910 0 0.2
4.214 1.011
3.456 = 0. 0.178
8. 8.606 + 0.591
Time
0.001
SCOPE config,
Set Size
1 2.2 0.164
7,390 + 1.856
3,609 = 0.910
9.409 + 1.099
Frac. Reject
0.000 0.000
0.203 + 0.000
0.057 0.000
0.097 0.000
Queries Time
5.216 + 0.710
4.128 = 0.452
SCOPE-Gen conlig.
0.023
0.017
Set Size
5.839 1 1.144
2.973 1 0.814
Reject
0.090 1
0.017
Queries
3.611 0.166
6.518 1: 0.310
5.525 1 0.297
9.888 0.412
SCOPE-Gen gen. only
Time
0.005 1 0.000
0.004 1 0.000
0.004 0.001
0.005 0.000
Set Size
2.050 0.144
6.003 + 1.040
3.302 + 0.579
10.038 - 0.984
Reject
0.000
1 0.000
0.000
Queries
4.581 + 1.121
3,530 0.531
SCOPE flipped
Time
0.048 1 0.013
0.044 0.005
Set Size
7,848 + 1.976
3.635 4 0.924
Frac. Rejoct
0.033 0.000
Non-Conformity; cownt
Queries
6.581 0.210
20.000 0.000
20.000 0.000
19.263 1 0.217
Time
2.260 0.015
90.593 7.089
84.864 9.882
16.118 - 3.096
CLM
Set Size
3.912 + 1.104
18.221 + 1.616
15.762 + 3.265
23.209 = 3.153
Reject
0.000
1
0.020 0.000
Queries
4.203 0.109
10.000 0.000
10.000 0.000
7.117 1 0.067
Time
0.465 0.007
10.922 0.325
10.011 0.332
max
Set Size
3.660 0.880
17.822 1.462
12.530 + 3.353
Reject
0.000
0.000
0.190
Queries
2.879 + 0.223
4.466 + 1.038
3.514
8.530 0.584
SCOPE-Gen contig.
Time
0,010 + 0.000
0.059 + 0.033
0.011 = 0.016
0.012 + 0.001
Set Size
1.255 0.169
7.865 + 1.909
3.850 + 1.014
9.853 1.288
Frac. Reject
0.000 0.000
0.163 1 0.000
0.027 0.000
0.000 0.000
Queries
5.385
4.162 0.458
Time
0.015 + 0.007
0.010 + 0.003
SCOPE-Gen config.
Set Size
5.899 + 1.044
2.970 : 0.551
Frac. Reject
0.080 1 0.000
0.013 0.000
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Method
Metric
TriviaQA
MIMIC-CXR
CNN/DM
Molecules
Queries
3.611 1: 0.166
6.518 1: 0.310
5.525 1 0.297
9.888 1: 0.412
Time
0.004 0.000
0.004 1 0.000
0.004 1 0.001
0.004 + 0.001
SCOPE-Gen only
Set Size
2.106 0.236
6.693 + 1.083
3.927 0.731
10.049 = 0.969
Frac. Reject
0.000 1 0.0000
0.000 1 0.000
0.000 1: 0.000
0.000 1: 0.000
# Queries Time Set Size Frac. Rejoct
4.760 +: 1.160
3.670 + 0.570
SCOPF:Gen flipped
0.029 1: 0.013
0.025 1: 0.006
7.744 + 2.026
3.945 0.995
0.143 = 0.000
0.023 # 0.000
Mon-Confomityy max
# Queries
6.567 0.196
20.000 0.000
20.000 0.000
19.286 1: 0.230
Time Sot Size
2.782 + 0.024
113.662
13.219
106.804 + 11.600
15.086 = 0.972
CLM
1.787 0.330
1.998
2.751 0.596
2.264 1.258
Frac. Reject
0.000 + 0.000
0.223 + 0.000
0.027 = 0.000
0.080 + 0.000
# Queries
4.209 0.117
10.000 0.000
10.000 + 0.000
7.108 0.070
Time
0.975 0.010
26. 193 1.702
26.740 + 1.540
CLM reduced max
Set Size
2.262
16.756
3.192 0.692
Frac. Reject
0.033 + 0.000
0.823 + 0.000
0.223 = 0.000
1.000 + 0.000
# Queries
3.054 0.117
4.176 1.006
3.478 + 0.474
8.510 + 0.590
Time
0.024 0.000
0,071 + 0.031
0.059 0.013
0.076 0.002
SCOPE-Gen config.
Set Size
1.351 0.143
7.525 1: 1.922
3.892 0.960
9.720 1.283
Frac. Reject
0.000 1 0.000
0.230 1: 0.000
0.043 1: 0.000
0.000 1 0.000
# Queries
5.096 1: 0.744
4.199 1 0.422
Time
0.021 + 0.007
0.017 0.002
SCOPE-Gen coufig.
Set Size
5.761 + 0.980
3.078 = 0.375
Frac. Reject
0.160 1 0.000
0.007 0.000
# Queries
3.611 0.166
6.518 + 0.310
5.525 + 0.297
9.888 + 0.412
Time
0.000
0.004 1:
SCOPE-Gen gen. only
Set Size
3.061 0.112
6.549 + 0.987
3.872 + 0.497
9.829 + 0.964
Frac. Rejoct
0.000 0.000
0.000 + 0.000
0.000 0.000
0.000 0.000
Queries
4.395 + 1.133
3.629 : 0.539
SCOPE-Gea dipppdd
Time
0.041 0.013
0.042 0.005
Set Size
7.460 +: 1.866
3.955 4 0.988
Reject
0.220 +
0.033 0.000
0.35
Non Conformity: sum
# Queries
6.581 + 0.210
20 20,000 0.000
20.000 + 0.000
19.269 = 0.222
Time
2.755 0.028
106.192
14.696
102.641
12.754
15.574 : 1.669
CLM
Set Size
1.674 0.224
11.240 2.075
4.094 1.118
13.573
2.615
Frac. Reject
0.000 + 0.000
0.017 # 0.000
0.000 = 0.000
0.000 - 0.000
# Queries
4.212 0.1114
10.000 0.000
10.000 0.000
7.107 1. 0.064
CLM reduced max
Time
0.977 0.009
23.906
26.360 1.630
0.874
Set Size
1.633 1 0.443
13.774 2.340
4.245 1: 1.165
9.280 1. 0.000
Frac. Reject
0.000 0.000
0.187 + 0.000
0.000 + 0.000
0.997 0.000
# Queries
2.757 0.151
3.881 1 0.213
3.352 1 0.299
7.973 1: 0.536
SCOPE-Gen config,
Time
0.001
+
0.055
0.094
Set Size
1.072 0.069
4.345 + 0.802
2.901 = 0.553
7.468 0.432
Frac. Reject
0.000 0.000
0.000 + 0.000
0.000 0.000
0.000 0.000
# Queries Time
4.929 + 0.136
3,835 + 0.332
SCOPE-Gen conlig.
Sei Size
4.190 1: 0.707
2.083 1 0.354
Frac. Reject
0.003 + 0.000
0.000 0.000
Queries Time
3.633 + 0.036
6.518 + 0.310
5.525 + 0.297
9.641 + 0.462
SCOPE-Gen gen. only
0.00
0.002
0.002
Sei Size
1.685 i 0.010
3.979 1 0.557
2.163 1 0.315
7.050 : 0.436
Reject
0.000
1
0.000
Queries
3.903 1 0.119
2.994 0.102
SCOPF-Gen flipped
Time
0.043 1 0.002
0.041 0.002
Set Size
4.475 + 0.512
2.326 + 040
Frac. Rejoct
0.000 0.000
0.000
Non-Conformity; cownt
# Queries
6.562 + 0.197
20.000 0.000
20.000 + 0.000
19.258 + 0.218
Time
2.300 0.021
16.173
CLM
Set Size
3.855 1 1.104
18.646 1.637
15.203
1: 2.207
20.236
1 3.853
Reject
+
0.000
Queries
||
4.204 0.114
10.000 0.000
10.000 1: 0.000
7.105 0.070
max
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Method
Metric
TriviaQA
MIMIC-CXR
CNN/DM
Molecules
Time
0.469 + 0.007
9.922 + 0.088
10.170 0.426
0.405 0.008
Set Size
3.819 1: 1.029
18.257 1.709
13.249 1: 3.114
17.753 1 0.000
Reject
1:
Queries
2.754 0.204
3.974 1: 0.063
3.172 1 0.186
7.896 0.485
SCOPE-Gen config.
Time
0.011 0.001
0.040 1 0.002
0.033 0.003
0.011 0.001
Set Size
1.055 0.128
4.569 = 0.274
2.538 = 0.451
7.723 + 0.479
Reject
0.000
0.000
Queries
+ 0,011 + 0.003
3.924
Time
0.008 = 0.001
SCOPE-Gen contig.
Set Size
4.288 + 0.7U3
2.226 0.371
Frac. Rejoct
0.000 0.000
0.000 0.000
Queries
0.036
+ 0.1
5.525 0.297
Time
0.005 0.000
0.004 0.000
0.002 0.000
0.005 + 0.000
SCOPE-Gen gen. only
Set Size
1.722 0.191
4.000 + 0.000
2.7U7 0.491
7.074 0 0.486
Frac. Reject
0.000 0.000
0.000 1: 0.000
0.000 0.000
0.000 0.000
0.530
Time
0.028 1 0.004
0.021 1 0.002
SCOPE Gen dipped
2.310
Frac. Rejoct
0.000 + 0.000
0.000
0.000
Non: Non-Confon Confooofoomtty
Queries
6.544 0.203
20.000 0.000
20.000 0.000
19.267 - 0.212
Time
2.785 + 0.021
111.025 13.329
102.087
12.566
15.301 = 1.092
CLM
Size
1.411 0.199
10.699 1.959
2.121 0.301 0.000 0.000
2.004 + 0.144
Frac. Reject
0.000 0.000
0.000 1: 0.000
0.000 0.000
0.105
0.000
10.000
7.107
Time
0.985 1 0.010
24.432 0.677
26.455 1: 1.557
0.872 1. 0.012
CL.M reduced
1.499 0.304
13.781 2.486
2.401 0.426
2.420
Frac. Rejoct
0.000 0.000
0,150 + 0.000
0.003 0.000
0.997 0.000
# Queries
3.056 0.009
3.922 + 0.305
3.379 0.156
7.891 0.532
Time
0.025 1 0.001
0.061 1 0.008
0.055 1 0.005
0.077 1. 0.003
SCOPE Gen config.
0.076
+
2.697
Frac. Reject
0.000 0.000
0.000 = 0.000
0.000
0.000
0.000 0.000
# Queries Time
5.096 +: 0.744
4.199 0.422
0.021 + 0.007
0.017 = 0.002
SCOPE-Gen config.
5.761
Frac. Reject
0.160 1: 0.000
0.007 1 0.000
# Queries
3.633 + 0.036
6.138 + 0.119
5.525 = 0.297
9.637 : 0.462
Time
0.008 0.000
0.005 1: 0.000
0.002 1 0.000
0.008 0.001
SCOPE-Gen only
Size
3.024 0.080
3.609 0.173
2.865 0.307
0.118
Frac. Reject
0.000 0.000
0.000 1 0.000
0.000 : 0.000
0.000 + 0.000
# Queries
4.156 + 0.129
3.381 + 0.123
SCOPE Gen lipped
Time
0.043 + 0.002
0.040 0.002
Set Size Frac. Reject
5.017 1 0.743
3.315 0.368
0.000 + 0.000
0.000 1 0.000
= 0.4
Non-Conlomiity
Queries
6.555 0.196
20.000 0.000
20.000 0.000
19.247 # 0.215
Time
2.724 - 0.018
107. 107.511 15.823
100.752 + 12.215
15.054 + 1.231
CLM
1.397 0.258
8.105 + 1.708
2.810 0.500
9.932 2.174
Frac. Reject
0.000 0.000
0.000 + 0.000
0.000 0.000
0.000 0.000
Queries
4:207 0.100
10.000 : 0.000
10.000
Time
0.977 0.009
23.955 0.596
26.075 + 1.515
0.861 + 0.011
CLM reduced
Frac. Reject
0.000 0.000
0.003 1: 0.000
0.000 1 0.000
0.890 +: 0.000
# Queries
2.674 0.147
3.724 1: 0.343
2.698 0.033
7.600 1: 0.443
Time
0.026 0.001
0.052 1 0.004
0.044 1: 0.002
0.096 1: 0.004
SCOPE-Gen config.
Set Size
0.917 0.053
3.609 + 0.606
1.379 0.058
5.864 0.219
Frac. Reject
0.000 1 0.000
0.000 1 0.000
0.000 1: 0.000
0.000 1 0.000
# Queries Time Set Size Frac. Reject
4.599 + 0.355
3.653 : 0.316
0.017 1 0.001
0.015 1 0.001
SCOPE-Gen config.
3.1 + 0.454
1.578 0.277
0.000 + 0.000
0.000 = 0.000
# Queries Time
3.633 0.036
6.518 + 0.310
5.525 4 0.297
9.646 + 0.464
SCOPE-Gen gen. only
0.006 0.000
0.002 + 0.000
0.002 0.000
0.006 0.000
Set Size
1.484 + 0.021
2.889 + 0.348
1.586 0.158
5.540 0.168
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Method
|| Metric
TriviaQA
MIMIC-CXR
CNN/DM
Molecules
||
Prac. Reject
0.000 0.000
0.000 + 0.000
0.000 0.000
0.000 0.000
Queries
3.785 1: 0.156
2.775 0.113
Time
0.012 + 0.002
0.010 = 0.003
SCOPE-Gen lipped
Size
3.244 1: 0.468
1.486 1 0.255
Frac. Reject
0.000 1: 0.000
0.000 0.000
Non-Conformity:
Queries
6.532 0.193
20 000 0.000
20,000 0.000
19.261 0.223
Time
2.301 + 0.026
87.296 +: 15.006
83.194 + 10.589
15.572 = 1.655
Set Size
4.690 1: 1.879
19.155 1.166
12.349 1.964
16.278
1 4.197
Frac. Reject
0.000 0.000
0.000 0.000
0.000 0.000
0.000 0.000
Queries
10.000 0.000
0.065
Time
0.471 + 0.007
10.006 + 0.127
10.306 + 0.534
0.409 + 0.008
Set Size
4.790 1.840
19.281 1.183
11.934 2.491
14.779 1 3.371
Frac. Reject
0.000 0.000
0.000 + 0.000
0.000 0.000
0.833 0.000
Queries
0.099
2.937
SCOPE-Gen
Time
0.010 0.000
0.032 + 0.003
0.026 + 0.003
0.011 + 0.001
0.938 0.077
3.425 + 0.149
1.708 0.257
6.009 0.450
Frac. Reject
0.000 0.000
0.000 + 0.000
0.000 0.000
0.000 0.000
Queries
3.633 0.036
6.138 0.119
5.525 0.297
9.641 0.462
Time
0.005 0.000
0.004 0.000
0.002 = 0.000
0.005 + 0.001
SCOPE-Gen gen. only
1.553 0.013
2.007 0.081
0.272
Frac. Reject
0.000 0.000
0.000 0.000
0.000 0.000
0.000 0.000
# Queries
3.910 + 0.061
3.091 0.475
Time
0.021 + 0.001
0.019 = 0.003
SCOPE-Gen dlppped
Frac. Reject
0.000 1 0.000
0.000
0.000
Non-Confomn
Qucries
6.574 0.197
000 0.000
20,000
19.255
Time
2.816 + 0.032
105.393 + 12.837
101.326 + 11.619
15.101 - 0.937
CLM
0.155
Frac. Reject
0.000 + 0.000
0,000 + 0.000
0.000 0.000
0.000 0.000
Queries
4:207 0.120
10.000 0.000
10.000 0.000
7.111 0.066
Time
0.987 0.010
21.634 0.634
26.286 + 1.712
0.880 + 0.013
CLM reduced
1:
Frac. Reject
0.000 + 0.000
0.003 1 0.000
0.000 1 0.000
0.837 + 0.000
# Queries
3.024 0.103
3.711 1 0.192
3.032 1 0.089
7.513 0.448
Time
0.024 0.000
0.052 1 0.003
0.046 1 0.002
0.076 + 0.002
SCOPE-Gen config.
Set Size
1.244 0.098
3.622 + 0.421
2.043 0.078
6.942 0.300
Frac. Rejoct
0.000 0.000
0.000 + 0.000
0.000 = 0.000
0.000 = 0.000
# Queries
4.732 + 0.398
3.703 0.293
Time Set Size Frac. Rejoct
0.008 1 0.001
0.006 1: 0.001
SCOPE-Gen config.
3.279 + 0.520
1.708 263
0.000 + 0.000
0.000 = 0.000
# Queries
3.633 0.036
6.138 + 0.1
5.525 # 0.297
9.646 + 0.444
SCOPE-Gen gen. only
Time Set Size
0.005 0.000
0.005 + 0.001
0.002 0.000
0.006 0.002
2.935 0.107
2.652 + 0.158
2.247 : 0.203
5.586 0.229
Frac. Reject
0.000 0.000
0.000 1 0.000
0.000 0.000
0.000 0.000
# Queries
3.921 + 0.375
3.019 : 0.178
SCOPE-Gea flipped
Time
0.040 + 0.002
0.037 0.002
Set Size
4.083 + 0.791
1.855 # 0.145
Frac. Reject
0.000 1 0.000
0.000 0.000
24

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Published as a conference paper at ICLR 2025
G QUALITATIVE RESULTS
We show randomly chosen prediction sets from SCOPE-Gen (config. 1, see App. D.I) in comparison to prediction sets generated by CLM. We demonstrate examples for TriviaQA and MIMIC-CRR.
G.1 TRIVIAQA
We calibrate both methods on single (same) calibration set of size 1200 and a = 0.2. Admissibility of an answer is denoted by the checkmark symbol V. If an answer is inadmissible, we denote it by X.
Prediction Set
Question
CLM
SCOPE-Gen
What former U.S. president is known for his staunch support of Habitat for Humanity?
(Jimmy Carter (V))
(Jimmy Carter (V))
What cat food "tastes so good, cats ask for it by name"?
Friskies (X), Sheba (X),
[Friskies (X), Whiskas (X),
Whiskas (X), Fancy Feast
Fancy Feast (X), Sheba (X),
(X), Felix (X), Purina (X))
Felix (X)
What is the name of the giraffe that Toys-r-us uses as its' mascot?
(Geoffrey (V), Geoffrey the
[Geoffrey (V)
Giraffe (X), George (X)
Where do you find the Bridal
(Niagara Falls (V), Niagara
(Niagara Falls
Niagara Niagra
Veil, American, and Horseshoe Falls?
Falls, Canada (V), Niagra Falls (V), Niagara (X))
Falls, Canada )
Falls (0)
The worlds largest marketer of fruit juices, what is the juice arm of the Coca Cola company?
(Minute Maid (V))
(Minute Maid (V))
Whose backing band is known as The Miami Sound Machine?
(Gloria Estefan (V), Gloria Estefan & Miami Sound
(Gloria Estefan (V), Gloria
Estefan & Miami Sound
Machine (V), Gloria
Machine (V))
Estefan's 's (X), Gloria
Estafan (V))
With a motto of Always Ready, Always There, what US military branch had it's founding on Dec 14, 1636?
[The Salvation Army (X). US Marine Corps (X), The Continental Army (X),
[The National Guard (V).
The Coast Guard (X), US Marine Corps (X))
Marines (X), The US Navy
(X), The National Guard
(V), The Coast Guard (X),
The Marine Corps (X), The
US Coast Guard (X)
Who tried to steal Christmas from the town of Whoville?
(The Grinch (V))
(The Grinch (F))
What is the name of the parson mentioned in the lyrics of the Christmas carol "Winter Wonderland"?
(Rev (X), Father (X), Frosty the Snowman (X), Reverend Johnson (2), Frosty (X))
(Father (X), Rev (X))
In what outdoor sport, sanctioned by the NHPA, do you score 3 points for ringer, 2 for a leaner, and the closet scores point?
[Bocce (X), Bowling (X), Darts (X), Ten-Pin Bowling (X), Horseshoes (V))
|Bowling (x), Darts (X),
Bocce (X)
25

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Published as a conference paper at ICLR 2025
G.2 MIMIC-CXR
We demonstrate predictions sets for a single instance (study_id: 59999516, subject_idt 13541358), where we calibrate SCOPE-Gen and CLM a single (same) calibration set of size 1200 and a 0.35. Admissibility of an answer is denoted by the checkmark symbol V. We remove all newline characters in the generated answers for improved readability. We stress that outputs of both methods are sets and have no internal order. We index answers for the purpose of obtaining identifiers for the different predictions.
Prompt
FINAL REPORT EXAMINATION: CHEST (PORTABLE AP)
INDICATION:
year old woman with AMS of unclear cause, HCAP //
Evaluate
interval change RLL infiltrate Evaluate interval change in RLL infiltrate
IMPRESSION:
Reference Report ("Ground Truth")
Compared prior chest radiographs through
New consolidation in the left lower lobe accompanied by ipsilateral mediastinal shift. Although that indicates component of atelectasis, there could concurrent pneumonia in the left lower lobe particularly patient has aspirated. Right lung is clear. Heart size top-normal. Left pleural effusion is presumed, but not large.
Left PIC line ends placement with the chin down. Esophageal drainage tube ends in nondistended stomach.
mid SVC. ET tube tip is one em below optimal
SCOPE-Gen
Index
Generated
Admissible
Comparison to The endotracheal tube has been slightly advanced. The tip of the device now projects approximately em above the carina. Mild retrocardiac atelectasis persists. Mild fluid overload but no overt pulmonary edema. No larger pleural effusions. Borderline size of the cardiac silhouette. The nasogastrie tube has been removed.
Continued on next page
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Published as a conference paper at ICLR 2025
Index
Generated
Admissible
In comparison with the study of the monitoring and support devices are essentially unchanged. Continued enlargement of the cardiac silhou- 2 ette with pulmonary vascular congestion. Opacification at the left base consistent with volume loss in the left lower lobe and probable small left pleural effusion.
Compared to chest radiographs through Left lower lobe still collapsed, either pneumonia or atelectasis. This could be the result of aspiration on and subsequent development of lung abscess. Pleural effusion is minimal, if any. No pneumothorax. Heart is top-norma size. ET tube standard placement. Nasogastric tube ends in the upper stomach. Left subclavian line ends in the upper right atrium.
3
Tracheostomy is in place. Heart size and mediastinum are stable. Left lower lobe consolidation is present. Substantial left upper lobe atelectasis and more pronounced in the left perihilar region are unchanged. There no pneumothorax.
4
Comparison to atelectasis, restricted the left and right upper lobe continues be minimally improved. Decrease in extent of a retrocardiac atclectasis. Signs of mild fluid overload no overt pulmonary edema.. Stable size of the cardiac silhouette.
The lung volumes have increased, the areas of
5
X
CLM
Index
Report
Admissible
2, 4,5
identical 2, from SCOPE-Gen
above
Compared to chest radiographs through ET tube, left PIC line, and upper enteric drainage tube in standard placements. Left lower lobe atclectasis unchanged. responsible for large leftward mediastinal shift. Mild cardiomegaly unchanged. Pulmonary vaseular engorgement slightly improved since Pleural effusions small if any. No evidence pneumothorax.
6
In comparison with the study of there is little overall change cept for increase in opacification at the left base consistent with some combination of pleural fluid and volume loss in the left lower lobe with underlying consolidations. The upper zone vessels are more prominent, consistent with greater vascular congestion.
7
ET tube tip is 2 em above the carinal. Left PICC line tip is at the level of mid SVC. NG tube tip passes below the diaphragm and most likely is in the stomach. Heart size and mediastinum are unchanged compared to previous study. The left upper lobe collapsed. Small left pleural effusion is most likely present.
8
Previous mild to moderate pulmonary edema improved and left lower lobe atelectasis has decreased. Heart size top-norma unchanged. Plcural effusion small if any. No pneumothorax. ET tube, left PIC line, and esophageal drainage tubes are in standard positions.
Compared to chest radiographs
through
9
ET tube tip is 3.3 em above the carinal. NG tube tip is in the stomach. Left PICC line tip at the level the mid to lower SVC. Hiatal hermia still present. Since the prior study pulmonary vascular congestion has improved. Small amount of bilateral pleural effusion is more pronounced on the left than on the right, consistent with improved pulmonary vascular congestion. No pneumothorax is seen.
10
Continued on next page
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Published as a conference paper at ICLR 2025
Index
Generated
Admissible
In comparison with the study of there is further increase in the opacification at the right base with silhouetting hemidiaphragm, consis- tent with worsening pneumonia or effusion or even pulmonary edema. Endotracheal tube been removed. The left subclavian catheter again extends to about the level of the carina.
11
x
ET tube tip is approximately cm above the carinal pointing toward the right apex. NG tube tip in the stomach. There no pneumothorax. NOTIFICATION: The findings were discussed with M.D. by M.D. on the telephone on ery of the findings.
12
X
10:07 AM, 2 minutes after discov-
Comparison to The lung volumes have increased, the size of the cardiac silhouette is now at the upper range of normal, there has been development of left basilar opacity. These abnormalities are visible with elevation of the left hemidiaphragm and the presence of small left pleural effusion. The right lung is moderately well inflated. No pleural effusions. No pneumonia.
13
ET tube tip is 2.5 em above the carinal. NG tube tip is in the stomach. Heart size is top-normal. Mediastinum is overall unremarkable with slight deviation of the left minor fissure to the left. There is no pneu- mothorax.
14
x
No previous images. Endotracheal tube tip lies approximately 5 cm above the carina. Cardiomediastinal silhouette is within normal limits. Left pleural effusion with compressive basilar atelectasis, left, essentially unchanged.
15
the
16 Comparison to There is minimally improved ventilation in the retrocardiac lung region. Otherwise the radiograph is unchanged. The patient has received endotracheal tube and nasogastric tube.
x
ET tube tip is 3.5 em above the carina. NG tube tip is in the stomach. There is left retrocardiac consolidation that could represent consolida- tion in the left lower lobe or infrahilar consolidation due to pneumonia. Followup radiograph is recommended. RECOMMENDATIONSS) Fol- lowup radiograph is recommended.
17
X
Compared chest radiographs through at 07:47. Large left lower lobe pneumonia unchanged over several days. Pulmonary vascular congestion now appears mild, Heart size normal. No pneumothorax. tube in standard placement. Nasogastric drainage tube would need to be advanced at least em to move all the side ports into the stomach, if any.
18
X
As compared to no relevant change is seen, Improved ventilation of the left lower lobe. Unchanged size of the cardiac silhouette.
19
H POST-EVALUATING ADMISSIBILITY
a human domain expert is used to assess admissibility, we recommend post-evaluating the achieved admissibility in the following way: First, certain amount from the calibration data ) aside, such that we have two data sets
{a and {a.)0m+11
(21)
Second, calibrate SCOPE-Gen on {-;]m, Finally, use the test set to generate prediction sets, using the calibrated parameters. Query the admissibility function assess the fraction of admissible
28

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Published as a conference paper at ICLR 2025
prediction sets:
= Σ [(((Cx-(I))) =
(22)
7 m
2m1++1
This fraction À provides an unbiased estimate of the achieved admissibility, conditionally on the calibration data.
Choosing three different values for m, sum non-conformity and three different levels for a and always such that on the calibration data):
300, we can get the following admissibility estimates (that are conditional
TriviaQA
a 0.3
0.35
0.4
m 300
0.86 + 0.35
0.69 0.46
0.65 + 0.48
m 600
0.77 = 0.42
0.71 0.46
0.67 + 0.47
m
1200
0.69 + 0.46
0.63 0.48
0.58 + 0.49
MIMIC-CXR
0.3
0.35
0.4
300
0.71 + 0.45
0.66 = 0.47
0.61 + 0.49
m 600
0.67 0.47
0.62 0.49
0.61 + 0.49
m
1200
0.71 + 0.45
0.65 0.48
0.57 + 0.50
CNN-DM
0.3
0.35
0.4
300
0.70 + 0.46
0.67 = 0.47
0.55 + 0.50
m
600
0.70 + 0.46
0.65 0.48
0.58 + 0.49
m
1200
0.73 + 0.45
0.68 0.47
0.61 + 0.49
Molecules
a: 0.3
0.35
0.4
300
0.75 + 0.43
0.71 + 0.46
0.67 +: 0.47
600
0.73 + 0.44
0.66 + 0.47
0.63 + 0.48
m
1200
0.70 0.46
0.65 0.48
0.62 + 0.49
In this manner, we can empirically assess the achieved admissibility post calibration.
29

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Published as a conference paper at ICLR 2025
1 DISCUSSION & LIMITATIONS
Data Splitting. SCOPE-Gen partitions calibration data across the prediction steps to control the factors the Markov chain (7). However, this segmentation leads to increased variance and looser conformal prediction sets due to reduced calibration set sizes at each step. A promising alternative could involve controlling the total risk through family-wise error rate control (Benjamini & Braun 2002). This approach could be particularly advantageous when combined with our sequential filtering strategy, which only requires accounting for K distinct tests rather than the y tests required by the method of Quaah al. (2024) (where K is the amount of calibration parameters and is the amount of points on parameter grid required for CLM)).
Conformal Prediction Learn-then-Test In general, the learn- Cearn-then-tee -ettthheeeetttttt framework is more flex- ible than conformal prediction as it does not require assumptions of monotonicity or uni-dimensional calibration parameters. Nonetheless, the present work demonstrates that reformulating the given problem into multiple conformal prediction problems has benefits (as shown experimentally $ In addition, the intuitive admissibility guarantee of conformal prediction ( requires specification of single parameter only, in comparison to the complex two- two-parameter guarantee of learn-then-tes ([2) While the latter guarantee bounds the conformal admissibility guarantee, we note that the optimization strategy employed in our experiments (see $ 5 would in practice have to be conducted on separate data set (due to data contamination), leading to decreased sample efficiency.
Generality vs. Computational Demand. SCOPE-Gen is applicable for wide variety of generative models, because it assumes access to i.i.d. samples, which are available for virtually any type of generative model. During inference, however, SCOPE-Ger presents computational overhead in comparison to i.i.d. sampling. This fact can be traced back to the sequential filters, which remove some of the initial i.i.d. predictions. In settings where computational demand during inference is concern, we note that our method could be combined with architecture ensuring diversity (e.g.. Corso al. (2023); Kirchhof et al. (2024); Vilnis et al. (2023)) and high quality samples (c.g., by sampling at low temperature), in order to reduce the amount of examples that are filtered out. Assuming that the sampling performed consistently during calibration and for the test point (X (X,+1, see ).) such sampling techniques do not affect the admissibility control guarantee
approaches for
30


Reviews:
[{"review_id": "AW5VZrfOX8", "reviewer": "Reviewer_XFHD", "summary": "This fairly well-explicated paper considers the following question of much recent interest: how could we obtain some semblance of guarantees for generative models' outputs i.e. in terms of factuality. This is related to the problem of hallucination control directly, since a method involving calibration for correctness could reduce hallucination if a suitable domain-specific calibration set were available. The approach of the paper is simple yet innovative. In a basic sense it does the following: In the first step, the method samples from the generative model conditioned on a fixed input. There is a calibration parameter that controls, based on a suitable non-conformity measure, that the generations contain at least one correct generation. Then, the generated set is pruned further using separate calibration parameters based on diversity and factuality considerations. Unlike some previous works, the sequential nature of the process permits the overall admissibility to be easily factorizable, permitting a direct application of conformal prediction proper. An interesting connection is also made to the pareto methods since there are multiple calibration parameters to be handled. The experiments report a general improvement datasets and are sufficient to demonstrate the applicability of the proposed method.", "questions": "-- I might have missed it, but do at least a fraction of the experiments report some kind of human evaluation? I think to validate the method, at least some of it might be reasonable. While using another generative model (as a judge or to generate a calibration set) is popular, it still presents an incomplete analysis. \n\n-- The authors might also want to discuss the works on conditional language validity by Cherian https://arxiv.org/abs/2406.09714 and also the earlier work by Mohri and Hashimoto https://arxiv.org/abs/2402.10978. Further, there is also a literature on confidence scoring which is often used for fine-tuning and reducing hallucinations. e.g. Kuhn et al. https://arxiv.org/abs/2302.09664, Lin et al. https://arxiv.org/abs/2305.19187, Wang and Holmes https://web3.arxiv.org/abs/2406.05213. It would be useful to include a brief discussion of these and how conformal methods might be used to calibrate such scores. It would help to bridge the two somewhat separate lines of enquiry together.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "-- The paper is quite well-written and clear. Each of the steps are well-described and easy to follow. \n\n-- The method is novel along multiple axes: Wrappers generally make far more simplifying assumptions due to the intractability of conformal prediction directly in such settings; the admissibility control criteria and the connections to pareto methods are interesting and could provide straightforward avenues for future work.\n\n-- While still compute intensive (since multiple generations are required), it could be tuned based on available data for some domain.", "weaknesses": "-- There are now a bunch of papers on using conformal wrappers for filtering long form generations by dividing them into segments and then scoring. I think it would have been great to evaluate on such tasks as well, as generally QA type tasks are a bit too easy.\n\n-- Sampling multiple times and expecting a correct response can be quite compute-intensive.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RuMXySUOKw", "reviewer": "Reviewer_WrdN", "summary": "The paper presents SCOPE-Gen, a sequential conformal prediction method designed to generate prediction sets that satisfy admissibility guarantees with high probability. The method operates in two main stages: a generation stage and a filtering stage. In the generation stage, i.i.d. samples are drawn from the generative model until a specified non-conformity measure (related to sample count or quality) surpasses a threshold set by calibration with ground-truth samples. In the filtering stage, the prediction set is refined in a greedy manner, optimizing for diversity and quality based on another threshold derived from calibration. To ensure admissibility, the approach leverages a Markov chain factorization for admissibility control, and calibration is conducted on independent, non-overlapping data subsets to enable this factorization. Experimental results demonstrate that SCOPE-Gen reduces both the number of queries to the admission function during calibration and the size of the prediction set needed to meet admissibility requirements, outperforming baseline methods like CLM.", "questions": "* The paper defines admissibility as including at least one (semantically) correct answer in the prediction set and aims to minimize the prediction set size while ensuring this inclusion. This is achieved by a “sub-sampling” technique, sampling answers based on a quality score ranking. Can the proposed method generalize to a broader admissibility definition, such as including multiple correct answers (e.g., 5 out of 10) or maximizing the fraction of correct answers? How would this method perform compared to baselines if the goal were to optimize the fraction of acceptable answers within a fixed prediction set size?\n* How does the sequence of filtering stages (diversity vs. quality) impact performance? Why is diversity filtering prioritized in the proposed method?", "limitations": "", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* This paper presents an efficient approach for generating prediction sets with admissibility guarantees by using a sequential generation and greedy filtering strategy.\n* It reduces the number of admissibility checks during calibration compared to previous baselines, improving computational efficiency.\n* Experimental results support the method’s effectiveness in reducing both query counts and prediction set sizes to meet admissibility criteria.", "weaknesses": "* The paper lacks a theoretical analysis detailing how effectively the proposed method reduces the required admissibility checks and prediction set size.\n* The sequential generation and filtering process may introduce additional computational costs by generating a large number of samples before the filtering stage.\n* The calibration process, which involves sample splitting for generation and each filtering stage, may require extra ground-truth samples to determine accurate threshold (lambda) values.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "yauBGSR1oh", "reviewer": "Reviewer_fuTF", "summary": "The paper proposes a heuristic algorithm to filter predictions of generative model to achieve conformal admissability. It argues that previous techniques need to evaluate the admissability multiple times per instance during the calibration phase, which is impractical when the admissability is evaluated by a human oracle. In their setup, the admissability factorizes into Markov chain and thus es requires fewer queries to the admission function (e.g. human oracle). The paper presents the algorithm for the filtering heuristic as well as the necessary calibration algorithms using two filters based on diversity and quality functions of the generated examples. The experiments over natural language generative tasks and molecular generation reporting favorable metrics in particular in terms of reduction in number of queries and runtime.", "questions": "1. One of the motivations for the method is the possible reliance on human oracle and expenses related to querying it. In the end the experiment use a non-human validation function. Related questions:\n- Would not the human oracle make some of the assumptions invalid (e.g. the need for increasing update function)?\n- As some point you mention that multiple queries over the same example need to be executed - wouldn't the human validation bring even more noise into the whole process and invalidate some of your probabilistic conclusions?\n2. I do not understand equation (6). What level of quantile is this? What is the interpretation of the n-fracion in the right-hand side?\n3. Is there a way to independently post-evaluate that the experimental results are really conformal with the $\\alpha$ level you were trying to achieve. Or would you need to use your own calibration parameters? If it were possible, this would provide additional useful insight.\n4. Please address the concerns mentioned under Weaknesses.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The paper addresses an important problem of current stochastic generative models hallucinating non-factual responses. Formulating this problem within the risk-control framework can provide the mathematical means for addressing it. The experimental evaluation over the natural langauge tasks seems relevant.", "weaknesses": "I find the empirical evaluation very difficult to asses both, on its own as well as in comparison to previous methods. To understand the effects of various parts of the proposed algorithms, it would be beneficial to perform ablation studies that could provide more insights into the effects of its individual components (e.g. the update function, the coverage level $\\alpha$, etc.). \nI am not convinced about the benefits of the molecular example - when there is only one valid/admissable example, it seems to me that simple checking of the validity at the generation time for each generated specimen should be enough. I do not see the benefit of the proposed method in this setup. This also applies to the TriviaQA experiment.\nThe algorithm requires an independent calibration set which seems to be very difficult to obtain in practice. In the presented experiments either boils down to something very trivial (single example being the valid one) or relying on another model which itself may be of uncertain quality. Further, I see similar issue with the update and filter functions which seem difficult to formulate reasonable in realistic scenarios. For me these are major limitations of the method which shall be discussed. \n\nThe main text of the paper (section 9) spills over to page 11. As per the call for papers, there is a strict 10 page limit on the main text and the call suggests a desk reject in case of violations of this limit.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KkOryU1Tzz", "reviewer": "Reviewer_7ufb", "summary": "This manuscript introduces a sequential conformal prediction method called SCOPE-Gen. SCOPE-Gen uses a sequential pruning approach to iteratively refine the prediction set, allowing for separate control over each factor in the Markov chain, and demonstrates a significant reduction in the number of admissibility evaluations required during calibration. The method has been experimentally validated in natural language generation and molecular graph extension tasks.", "questions": "- Can the author clarify the results in Table 2 of the appendix? It appears that the performance gap between SCOPE and CLM is narrowing - can the authors explain why this might be happening?", "limitations": "", "rating": 6, "confidence": 1, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "Generally well-written; it’s clear that the manuscript is largely inspired (and adopted) from the setup in Quach et al 2024. Nevertheless, the authors detailed differences to Quach et al 2024 and highlight the efficiency of their method by leveraging sequential factorization.", "weaknesses": "- (minor) Fig 1 is slightly unclear — the caption should at least include some explanation of \\nu, which is not specified until Sec 3", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)